espressif/esp-dsp

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# ESP-DSP ESP32-Azure IoT kit 3d graphics demo application The demo is developed for [ESP32-Azure IoT kit](https://github.com/espressif/esp-bsp/tree/master/esp32_azure_iot_kit) development board and is demonstrating the usage of matrices with `ESP-DSP` `Mat` class, Kalman filter and basic 3D graphics. The 3D Graphics demo displays a 2D graphics, converted to 3D as a 3D rotating object, on the development board's display. Button press changes the rotation direction of the 3D object. Run the menuconfig using the following command: idf.py mencuonfig In the menuconfig's menu item `Demo user configuration` select which 3D object to display. It's either a 3D cube, or ESP logo, or a user-defined graphics. Getting the user-defined graphics is described in an [example](../../graphics/img_to_3d_matrix/example/) ## Running the demo To start the demo, run the following command: idf.py build flash monitor The expected output is the following: I (570) 3D image demo: Selected 3D image - ESP Logo I (570) 3D image demo: Showing ESP text I (6730) 3D image demo: Showing 3D image Note, that the first line `Selected 3D image` from the expected output depends on the user's Kconfing menu selection <div align="center"> <img src= "applications/azure_board_apps/apps/3d_graphics/3d_graphics.gif"> </div>

# ESP-DSP ESP32-Azure IoT kit Kalman filter demo application The demo is developed for [ESP32-Azure IoT kit](https://github.com/espressif/esp-bsp/tree/master/esp32_azure_iot_kit) development board and is demonstrating the usage of matrices with `ESP-DSP` `Mat` class, Kalman filter and basic 3D graphics. The Kalman filter demo displays a 2D graphics, converted to 3D as a 3D object, on the development board's display. The 3D object follows the movements of the development board, where the Kalman filter is used for processing the output signals of the IMU sensors accommodated on the development board. The 3D object rotation is calculated by the Kalman filter class methods. All 3 IMU sensors present on the dev board (accelerometer, gyroscope and magnetometer) are used for sensing the development board's position. If the board is inactive (no, or very low rotation is detected) for a set period of time, the demo enters an "Idle" state, in which a 3D rotating object is displayed. Once a certain set level of the board's rotation is detected, the demo enters a normal, "Active", state. For the project settings, run the menuconfig using the following command: idf.py mencuonfig In the menuconfig's menu item `Demo user configuration` select which 3D object to display. It's either 3D cube, or ESP logo, or a user-defined graphics. Getting the user-defined 3D object is described in the [3D Graphics demo](../3d_graphics) ## Kalman filter #### Calibration The filter must be calibrated before the first run, which takes several minutes. But the calibration process before each run can be omitted by calibrating the filter once, saving Kalman's filter state vectors to the NVS, and loading those vectors back into the Kalman filter before the run. In addition, every 5 minutes a current state vectors are saved into the flash memory. ## Running the demo To start the demo, run the following command: idf.py build flash monitor The expected output is the following: I (589) Kalman filter demo: Selected 3D image - 3D cube I (590) Kalman filter demo: Filter state vectors present in the NVS I (592) Kalman filter demo: Loading state vectors into the filter structure I (604) Kalman filter demo: State vectors loaded from the NVS I (606) Barometer: disabled I (619) Board status: board put to active mode I (95780) Board status: board put to idle mode I (300619) Kalman filter demo: State vectors saved to NVS Note, that the first line `Selected 3D image` from the expected output depends on the user's Kconfing menu selection To start the demo and run the initial Kalman filter calibration, one must erase the flash memory, to remove the previously stored Kalman filter's state vectors. To do so, run the following command: idf.py erase_flash build flash monitor The expected output is the following: I (592) Kalman filter demo: Selected 3D image - 3D cube I (595) Kalman filter demo: Filter state vectors not present in the NVS I (595) Kalman filter demo: Starting Kalman filter calibration loop I (100699) Kalman filter demo: Exiting Kalman filter calibration loop I (100894) Kalman filter demo: Estimated gyroscope bias error [deg/sec]: -0.020715 -0.000431 -0.022452 I (100900) Kalman filter demo: State vectors saved to the NVS I (100900) Barometer: disabled I (100911) Board status: board put to active mode I (196072) Board status: board put to idle mode I (400912) Kalman filter demo: State vectors saved to NVS <div align="center"> <img src= "applications/azure_board_apps/apps/kalman_filter/kalman_filter.gif"> </div>

# ESP-DSP LyraT Board audio processing application The demo applications are developed for the ESP32-LyraT development board and demonstrate the usage of IIR filters from the ESP-DSP library. This example showcases how to use IIR filter functionality to process audio stream data. To hear the audio please connect headphones or speakers to the ESP32-LyraT audio output. The example performs the following steps: 1. Read samples from a file * read samples from file * write audio samples to the triple buffer 2. Process audio samples * process volume/bass/treble * apply digital limiter to the audio data * control audio buffer overflow 3. Pass samples to the audio codec To control the volume/bass/treble, please select the value by press 'Set' button and adjust the value by '+/-' buttons. ## The Triple Audio Buffer In audion processing, it's possible to have situation when one task write data to the processing buffer (processing task), and another task read data from the same buffer, and still in reading process. Triple buffering is a technique used in audio processing to minimize latency and ensure smooth playback. It involves using three buffers to store audio data. Here's a description of how it works: * Buffer A: This buffer holds the audio data that is currently being processed by the audio system. It is typically filled with samples from the audio source and processed in real-time. * Buffer B: When Buffer A is full, the audio system begins reading from Buffer A and starts processing the data. At the same time, Buffer B is filled with new audio samples from the source. * Buffer C: Once Buffer B is full, the audio system switches its attention to Buffer B and continues processing data. Buffer C is then filled with the latest audio samples. The cycle continues, with the audio system always processing the data from a buffer while the other two buffers are being filled. This approach helps ensure a continuous and uninterrupted audio playback, as there is always a buffer ready to be processed. It reduces the chances of audio glitches or dropouts caused by delays in reading or processing the audio data. Triple buffering is particularly useful when working with real-time audio processing applications, where low latency and uninterrupted playback are crucial. ## Audio Processing Flow The audio processing flow contains next blocks: 1. Audio processing task * Read data from file and store to the triple buffer * Read from triple buffer and concert data from int16_t to float * Process bass * Process treble * Process volume * Apply digital limiter * Convert data from float to int16_t and store to the triple buffer 2. Audio output task * Write data from triple buffer to audio codec 3. Buttons control task * React on buttons and adjust the control values * Calculates IIR filter coefficients ## How to use the example ### Hardware required This example require LyraT development board. ### Configure the project Under Component Config ---> DSP Library ---> DSP Optimization, it's possible to choose either the optimized or ANSI implementation, to compare them. ### Build and flash Build the project and flash it to the board, then run monitor tool to view serial output (replace PORT with serial port name): ``` idf.py flash monitor ``` (To exit the serial monitor, type ``Ctrl-]``.) See the Getting Started Guide for full steps to configure and use ESP-IDF to build projects.

# ESP-DSP ESP32-S3-BOX-Lite Board demo application The demo applications are developed for the ESP32-S3-BOX-Lite development board and demonstrate the usage of FFT functions from the ESP-DSP library. This example showcases how to use FFT functionality to process audio stream data. The application record sound from two microphones and show the spectrum from them at display as 2D plot. ## Audio Processing Flow The audio processing flow contains next blocks: 1. Audio processing task * Read left and right channel data from the microphone * Apply window multiplication to both channels * Process FFT and apply bit reverse * Split complex spectrum from two channels to two spectrums of two real channels * Calculate absolute spectrum and convert it to dB * Calculate moving average of the spectrum 2. Image Display Task * Read data from the * Write data from triple buffer to audio codec ## How to use the example Just flash the application to the ESP32-S3-BOX-Lite development board, and play some music around or start to speak to the board microphones. The display will show the real-time spectrum. The microphone sensitivity could be adjusted in the code. ### Hardware required This example does not require any special hardware, and can be run on any common development board. ### Configure the project Under Component Config ---> DSP Library ---> DSP Optimization, it's possible to choose either the optimized or ANSI implementation, to compare them. ### Build and flash Build the project and flash it to the board, then run monitor tool to view serial output (replace PORT with serial port name): ``` idf.py flash monitor ``` (To exit the serial monitor, type ``Ctrl-]``.) See the Getting Started Guide for full steps to configure and use ESP-IDF to build projects.

# ESP-DSP ESP32-Azure IoT kit 3d graphics demo application The demo is developed for [ESP32-Azure IoT kit](https://github.com/espressif/esp-bsp/tree/master/esp32_azure_iot_kit) development board and is demonstrating the usage of matrices with `ESP-DSP` `Mat` class, Kalman filter and basic 3D graphics. The 3D Graphics demo displays a 2D graphics, converted to 3D as a 3D rotating object, on the development board's display. Button press changes the rotation direction of the 3D object. Run the menuconfig using the following command: idf.py mencuonfig In the menuconfig's menu item `Demo user configuration` select which 3D object to display. It's either a 3D cube, or ESP logo, or a user-defined graphics. Getting the user-defined graphics is described in an [example](../../graphics/img_to_3d_matrix/example/) ## Running the demo To start the demo, run the following command: idf.py build flash monitor The expected output is the following: I (570) 3D image demo: Selected 3D image - ESP Logo I (570) 3D image demo: Showing ESP text I (6730) 3D image demo: Showing 3D image Note, that the first line `Selected 3D image` from the expected output depends on the user's Kconfing menu selection <div align="center"> <img src= "applications/azure_board_apps/apps/3d_graphics/3d_graphics.gif"> </div>

# ESP-DSP ESP32-Azure IoT kit Kalman filter demo application The demo is developed for [ESP32-Azure IoT kit](https://github.com/espressif/esp-bsp/tree/master/esp32_azure_iot_kit) development board and is demonstrating the usage of matrices with `ESP-DSP` `Mat` class, Kalman filter and basic 3D graphics. The Kalman filter demo displays a 2D graphics, converted to 3D as a 3D object, on the development board's display. The 3D object follows the movements of the development board, where the Kalman filter is used for processing the output signals of the IMU sensors accommodated on the development board. The 3D object rotation is calculated by the Kalman filter class methods. All 3 IMU sensors present on the dev board (accelerometer, gyroscope and magnetometer) are used for sensing the development board's position. If the board is inactive (no, or very low rotation is detected) for a set period of time, the demo enters an "Idle" state, in which a 3D rotating object is displayed. Once a certain set level of the board's rotation is detected, the demo enters a normal, "Active", state. For the project settings, run the menuconfig using the following command: idf.py mencuonfig In the menuconfig's menu item `Demo user configuration` select which 3D object to display. It's either 3D cube, or ESP logo, or a user-defined graphics. Getting the user-defined 3D object is described in the [3D Graphics demo](../3d_graphics) ## Kalman filter #### Calibration The filter must be calibrated before the first run, which takes several minutes. But the calibration process before each run can be omitted by calibrating the filter once, saving Kalman's filter state vectors to the NVS, and loading those vectors back into the Kalman filter before the run. In addition, every 5 minutes a current state vectors are saved into the flash memory. ## Running the demo To start the demo, run the following command: idf.py build flash monitor The expected output is the following: I (589) Kalman filter demo: Selected 3D image - 3D cube I (590) Kalman filter demo: Filter state vectors present in the NVS I (592) Kalman filter demo: Loading state vectors into the filter structure I (604) Kalman filter demo: State vectors loaded from the NVS I (606) Barometer: disabled I (619) Board status: board put to active mode I (95780) Board status: board put to idle mode I (300619) Kalman filter demo: State vectors saved to NVS Note, that the first line `Selected 3D image` from the expected output depends on the user's Kconfing menu selection To start the demo and run the initial Kalman filter calibration, one must erase the flash memory, to remove the previously stored Kalman filter's state vectors. To do so, run the following command: idf.py erase_flash build flash monitor The expected output is the following: I (592) Kalman filter demo: Selected 3D image - 3D cube I (595) Kalman filter demo: Filter state vectors not present in the NVS I (595) Kalman filter demo: Starting Kalman filter calibration loop I (100699) Kalman filter demo: Exiting Kalman filter calibration loop I (100894) Kalman filter demo: Estimated gyroscope bias error [deg/sec]: -0.020715 -0.000431 -0.022452 I (100900) Kalman filter demo: State vectors saved to the NVS I (100900) Barometer: disabled I (100911) Board status: board put to active mode I (196072) Board status: board put to idle mode I (400912) Kalman filter demo: State vectors saved to NVS <div align="center"> <img src= "applications/azure_board_apps/apps/kalman_filter/kalman_filter.gif"> </div>

# ESP-DSP ESP32-Azure IoT kit 3d graphics demo application The demo is developed for [ESP32-Azure IoT kit](https://github.com/espressif/esp-bsp/tree/master/esp32_azure_iot_kit) development board and is demonstrating the usage of matrices with `ESP-DSP` `Mat` class, Kalman filter and basic 3D graphics. The 3D Graphics demo displays a 2D graphics, converted to 3D as a 3D rotating object, on the development board's display. Button press changes the rotation direction of the 3D object. Run the menuconfig using the following command: idf.py mencuonfig In the menuconfig's menu item `Demo user configuration` select which 3D object to display. It's either a 3D cube, or ESP logo, or a user-defined graphics. Getting the user-defined graphics is described in an [example](../../graphics/img_to_3d_matrix/example/) ## Running the demo To start the demo, run the following command: idf.py build flash monitor The expected output is the following: I (570) 3D image demo: Selected 3D image - ESP Logo I (570) 3D image demo: Showing ESP text I (6730) 3D image demo: Showing 3D image Note, that the first line `Selected 3D image` from the expected output depends on the user's Kconfing menu selection <div align="center"> <img src= "applications/azure_board_apps/apps/3d_graphics/3d_graphics.gif"> </div>

# ESP-DSP ESP32-Azure IoT kit Kalman filter demo application The demo is developed for [ESP32-Azure IoT kit](https://github.com/espressif/esp-bsp/tree/master/esp32_azure_iot_kit) development board and is demonstrating the usage of matrices with `ESP-DSP` `Mat` class, Kalman filter and basic 3D graphics. The Kalman filter demo displays a 2D graphics, converted to 3D as a 3D object, on the development board's display. The 3D object follows the movements of the development board, where the Kalman filter is used for processing the output signals of the IMU sensors accommodated on the development board. The 3D object rotation is calculated by the Kalman filter class methods. All 3 IMU sensors present on the dev board (accelerometer, gyroscope and magnetometer) are used for sensing the development board's position. If the board is inactive (no, or very low rotation is detected) for a set period of time, the demo enters an "Idle" state, in which a 3D rotating object is displayed. Once a certain set level of the board's rotation is detected, the demo enters a normal, "Active", state. For the project settings, run the menuconfig using the following command: idf.py mencuonfig In the menuconfig's menu item `Demo user configuration` select which 3D object to display. It's either 3D cube, or ESP logo, or a user-defined graphics. Getting the user-defined 3D object is described in the [3D Graphics demo](../3d_graphics) ## Kalman filter #### Calibration The filter must be calibrated before the first run, which takes several minutes. But the calibration process before each run can be omitted by calibrating the filter once, saving Kalman's filter state vectors to the NVS, and loading those vectors back into the Kalman filter before the run. In addition, every 5 minutes a current state vectors are saved into the flash memory. ## Running the demo To start the demo, run the following command: idf.py build flash monitor The expected output is the following: I (589) Kalman filter demo: Selected 3D image - 3D cube I (590) Kalman filter demo: Filter state vectors present in the NVS I (592) Kalman filter demo: Loading state vectors into the filter structure I (604) Kalman filter demo: State vectors loaded from the NVS I (606) Barometer: disabled I (619) Board status: board put to active mode I (95780) Board status: board put to idle mode I (300619) Kalman filter demo: State vectors saved to NVS Note, that the first line `Selected 3D image` from the expected output depends on the user's Kconfing menu selection To start the demo and run the initial Kalman filter calibration, one must erase the flash memory, to remove the previously stored Kalman filter's state vectors. To do so, run the following command: idf.py erase_flash build flash monitor The expected output is the following: I (592) Kalman filter demo: Selected 3D image - 3D cube I (595) Kalman filter demo: Filter state vectors not present in the NVS I (595) Kalman filter demo: Starting Kalman filter calibration loop I (100699) Kalman filter demo: Exiting Kalman filter calibration loop I (100894) Kalman filter demo: Estimated gyroscope bias error [deg/sec]: -0.020715 -0.000431 -0.022452 I (100900) Kalman filter demo: State vectors saved to the NVS I (100900) Barometer: disabled I (100911) Board status: board put to active mode I (196072) Board status: board put to idle mode I (400912) Kalman filter demo: State vectors saved to NVS <div align="center"> <img src= "applications/azure_board_apps/apps/kalman_filter/kalman_filter.gif"> </div>

# Basic Math Example (See the README.md file in the upper level 'examples' directory for more information about examples.) This example demonstrates how to use basic math functions from esp-dsp library. Example does the following steps: 1. Initialize the library 2. Initialize input signals with 1024 samples 3. Apply window to input signal by standard C loop. 4. Calculate FFT for 1024 complex samples and show the result 5. Show results on the plots 6. Apply window to input signal by basic math functions dsps_mul_f32 and dsps_mulc_f32. 7. Calculate FFT for 1024 complex samples 8. Show results on the plots ## How to use example ### Hardware required This example does not require any special hardware, and can be run on any common development board. ### Configure the project Under Component Config ---> DSP Library ---> DSP Optimization, it's possible to choose either the optimized or ANSI implementation, to compare them. ### Build and flash Build the project and flash it to the board, then run monitor tool to view serial output (replace PORT with serial port name): ``` idf.py -p PORT flash monitor ``` (To exit the serial monitor, type ``Ctrl-]``.) See the Getting Started Guide for full steps to configure and use ESP-IDF to build projects. ## Example output Here is an typical example console output. ```bash I (132) main: *** Start Example. *** I (132) main: *** Multiply tone signal with Hann window by standard C loop. *** I (152) view: Data min[432] = -173.749878, Data max[205] = 23.849705 ________________________________________________________________ 0 | | 1 | | 2 | | 3 || | 4 | | | 5 || | | 6 ||| || | 7 ||||| |||| | 8||||||||||||||| |||||| | 9 ||||||||||||||||||||||||| 0123456789012345678901234567890123456789012345678901234567890123 I (162) view: Plot: Length=512, min=-120.000000, max=40.000000 I (162) main: *** Multiply tone signal with Hann window by esp-dsp basic math functions. *** I (162) view: Data min[432] = -173.749878, Data max[205] = 23.849705 ________________________________________________________________ 0 | | 1 | | 2 | | 3 || | 4 | | | 5 || | | 6 ||| || | 7 ||||| |||| | 8||||||||||||||| |||||| | 9 ||||||||||||||||||||||||| 0123456789012345678901234567890123456789012345678901234567890123 I (172) view: Plot: Length=512, min=-120.000000, max=40.000000 I (172) main: *** End Example. *** ```

# Dot Product Calculation Example (See the README.md file in the upper level 'examples' directory for more information about examples.) This example demonstrates how to use dotprod dsps_dotprod_f32 from esp-dsp library. Example does the following steps: 1. Initialize the input arrays 2. Calculate dot product of two arrays 3. Compare results and calculate execution time in cycles. ## How to use example ### Hardware required This example does not require any special hardware, and can be run on any common development board. ### Configure the project Under Component Config ---> DSP Library ---> DSP Optimization, it's possible to choose either the optimized or ANSI implementation, to compare them. ### Build and flash Build the project and flash it to the board, then run monitor tool to view serial output (replace PORT with serial port name): ``` idf.py -p PORT flash monitor ``` (To exit the serial monitor, type ``Ctrl-]``.) See the Getting Started Guide for full steps to configure and use ESP-IDF to build projects. ## Example output Here is an typical example console output. ``` I (55) main: Start Example. I (55) main: The sum of 101 elements from 0..100 = 5050.000000 I (55) main: Operation for 101 samples took 1381 cycles I (65) main: End Example. ```

# FFT Example (See the README.md file in the upper level 'examples' directory for more information about examples.) This example demonstrates how to use FFT functionality from esp-dsp library. Example does the following steps: 1. Initialize the library 2. Initialize input signals with 1024 samples: one 0 dB, second with -20 dB 3. Combine two signals as one complex input signal and apply window to input signals paar. 4. Calculate FFT for 1024 complex samples 5. Apply bit reverse operation for output complex vector 6. Split one complex FFT output spectrum to two real signal spectrums 7. Show results on the plots 8. Show execution time of FFT ## How to use example ### Hardware required This example does not require any special hardware, and can be run on any common development board. ### Configure the project Under Component Config ---> DSP Library ---> DSP Optimization, it's possible to choose either the optimized or ANSI implementation, to compare them. ### Build and flash Build the project and flash it to the board, then run monitor tool to view serial output (replace PORT with serial port name): ``` idf.py -p PORT flash monitor ``` (To exit the serial monitor, type ``Ctrl-]``.) See the Getting Started Guide for full steps to configure and use ESP-IDF to build projects. ## Example output Here is an typical example console output. ``` I (59) main: Start Example. W (89) main: Signal x1 I (89) view: Data min[495] = -162.760925, Data max[164] = 23.938747 ________________________________________________________________ 0 | 1 | | 2 | | 3 | | 4 | | 5 | | 6 | | | 7 | | | 8 || || | 9|||||||||||||||||| |||||||||||||||||||||||||||||||||||||||||| 0123456789012345678901234567890123456789012345678901234567890123 I (159) view: Plot: Length=512, min=-60.000000, max=40.000000 W (169) main: Signal x2 I (169) view: Data min[502] = -164.545135, Data max[205] = 3.857752 ________________________________________________________________ 0 | 1 | 2 | 3 | | 4 | | 5 | | 6 | | 7 || | 8 | | | 9|||||||||||||||||||||||| |||||||||||||||||||||||||||||||||||||| 0123456789012345678901234567890123456789012345678901234567890123 I (249) view: Plot: Length=512, min=-60.000000, max=40.000000 W (249) main: Signals x1 and x2 on one plot I (259) view: Data min[505] = -159.215271, Data max[164] = 23.938747 ________________________________________________________________ 0 | 1 | | 2 | | 3 | | | 4 | | | 5 | | | 6 | | | | 7 | | || | 8 || || | | | 9|||||||||||||||||| | |||||||||||||||||||||||||||||||||||||| 0123456789012345678901234567890123456789012345678901234567890123 I (339) view: Plot: Length=512, min=-60.000000, max=40.000000 I (339) main: FFT for 1024 complex points take 140472 cycles I (349) main: End Example. ```

# FFT 4 Real Input Example (See the README.md file in the upper level 'examples' directory for more information about examples.) This example demonstrates how to use FFT functionality from esp-dsp library. Example does the following steps: 1. Initialize the library 2. Initialize input signals with 1024 samples: one 0 dB, second with -20 dB 3. Calculate FFT Radix-2 for 1024 complex samples 4. Calculate FFT Radix-4 for 1024 complex samples 5. Apply bit reverse operation for output complex vectors 6. Show results on the plots 7. Show execution time of FFTs ## How to use example ### Hardware required This example does not require any special hardware, and can be run on any common development board. ### Configure the project Under Component Config ---> DSP Library ---> DSP Optimization, it's possible to choose either the optimized or ANSI implementation, to compare them. ### Build and flash Build the project and flash it to the board, then run monitor tool to view serial output (replace PORT with serial port name): ``` idf.py -p PORT flash monitor ``` (To exit the serial monitor, type ``Ctrl-]``.) See the Getting Started Guide for full steps to configure and use ESP-IDF to build projects. ## Example output Here is an typical example console output. ``` I (344) main: Start Example. W (424) main: Signal x1 I (424) view: Data min[673] = -103.113297, Data max[328] = 20.490950 ________________________________________________________________ 0 | 1 | | 2 | | 3 | | 4 | | 5 | | 6 | | 7 | | | 8 | | | 9||||||||||||||||||| ||||||||||||||||||||||||||||||||||||||||||| 0123456789012345678901234567890123456789012345678901234567890123 I (494) view: Plot: Length=1024, min=-60.000000, max=40.000000 W (504) main: Signal x2 I (504) view: Data min[582] = -103.113297, Data max[328] = 20.490950 ________________________________________________________________ 0 | 1 | | 2 | | 3 | | 4 | | 5 | | 6 | | 7 | | | 8 | | | 9||||||||||||||||||| ||||||||||||||||||||||||||||||||||||||||||| 0123456789012345678901234567890123456789012345678901234567890123 I (584) view: Plot: Length=1024, min=-60.000000, max=40.000000 W (593) main: Difference between signals x1 and x2 on one plot I (594) view: Data min[0] = 0.000000, Data max[392] = 0.313019 ________________________________________________________________ 0 | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8----------------------------------------------------------------| 9 | 0123456789012345678901234567890123456789012345678901234567890123 I (674) view: Plot: Length=1024, min=0.000000, max=40.000000 I (674) main: FFT Radix 2 for 1024 complex points take 168652 cycles I (684) main: FFT Radix 4 for 1024 complex points take 104665 cycles I (694) main: End Example. ```

# FFT Window Example (See the README.md file in the upper level 'examples' directory for more information about examples.) This example demonstrates how to use Window and FFT functionality from esp-dsp library. Example does the following steps: 1. Initialize the library 2. Initialize input signals with 1024 samples 3. Apply window to input signal. 4. Calculate FFT for 1024 complex samples 5. Apply bit reverse operation for output complex vector 6. Split one complex FFT output spectrum to two real signal spectrums 7. Show results on the plots ## How to use example ### Hardware required This example does not require any special hardware, and can be run on any common development board. ### Configure the project Under Component Config ---> DSP Library ---> DSP Optimization, it's possible to choose either the optimized or ANSI implementation, to compare them. ### Build and flash Build the project and flash it to the board, then run monitor tool to view serial output (replace PORT with serial port name): ``` idf.py -p PORT flash monitor ``` (To exit the serial monitor, type ``Ctrl-]``.) See the Getting Started Guide for full steps to configure and use ESP-IDF to build projects. ## Example output Here is an typical example console output. ``` I (128) main: Start Example. W (128) main: Hann Window I (128) view: Data min[256] = -inf, Data max[1] = 24.086628 ________________________________________________________________ 0| | 1| | 2| | 3| | 4| | 5 | | 6 | | 7 ||||| | 8 ||||||||||||||| | 9 |||||||||||||||||||||||||||||||||||||||||| 0123456789012345678901234567890123456789012345678901234567890123 I (138) view: Plot: Length=512, min=-120.000000, max=40.000000 W (138) main: Blackman Window I (148) view: Data min[355] = -165.295654, Data max[1] = 24.083012 ________________________________________________________________ 0| | 1| | 2| | 3| | 4| | 5| | 6 | | 7 ||| | 8 ||||||||| | 9 ||||||||||||||||||||||||||||||||||||||||||||||||||| 0123456789012345678901234567890123456789012345678901234567890123 I (158) view: Plot: Length=512, min=-120.000000, max=40.000000 W (158) main: Blackman-Harris Window I (168) view: Data min[128] = -inf, Data max[1] = 23.874702 ________________________________________________________________ 0| | 1| | 2| | 3| | 4| | 5| | 6| | 7|| | 8| |||| | 9 ||||||||||||||||||||||||||||||||||||||||||||||||||||||||||| 0123456789012345678901234567890123456789012345678901234567890123 I (178) view: Plot: Length=512, min=-120.000000, max=40.000000 W (178) main: Blackman-Nuttall Window I (188) view: Data min[128] = -inf, Data max[1] = 23.890663 ________________________________________________________________ 0| | 1| | 2| | 3| | 4| | 5| | 6| | 7 || | 8 |||| | | 9 | |||||||||||||||||||||||||||||||||||||||||||||||||||||||| 0123456789012345678901234567890123456789012345678901234567890123 I (198) view: Plot: Length=512, min=-120.000000, max=40.000000 W (198) main: Nuttall Window I (208) view: Data min[203] = -175.147400, Data max[1] = 23.858671 ________________________________________________________________ 0| | 1| | 2| | 3| | 4| | 5| | 6| | 7|| | 8 ||| | 9 |||||||||||||||||||||||||||||||||||||||||||||||||||||||||||| 0123456789012345678901234567890123456789012345678901234567890123 I (218) view: Plot: Length=512, min=-120.000000, max=40.000000 W (218) main: Flat-Top Window I (228) view: Data min[256] = -inf, Data max[1] = 22.490753 ________________________________________________________________ 0| | 1| | 2| | 3| | 4| | 5| | 6| | 7 || | 8 ||||| | 9 ||||||||||||||||||||||||||||||||||||||||||||||||||||||||| 0123456789012345678901234567890123456789012345678901234567890123 I (238) view: Plot: Length=512, min=-120.000000, max=40.000000 I (238) main: End Example. ```

# FIR Filter Example (See the README.md file in the upper level 'examples' directory for more information about examples.) This example demonstrates how to use FIR filter functionality from esp-dsp library. Example does the following steps: 1. Initialize the FFT library 2. Initialize input signal * 1st Sine wave (f = 0.2Fs) * 2nd Sine wave (f = 0.4Fs) * Combine the waves 3. Show input signal * Calculate windows coefficients * Apply the windowing to the input signal * Do the FFT * Show the frequency response on a plot * Calculate execution performance 4. Show filtered signal * Initialize the FIR filter library * Calculate Windowed-Sinc coefficients of FIR filter * Apply the FIR filter to the input signal * Do the FFT * Show the frequency response on a plot * Calculate execution performance ## How to use the example ### Hardware required This example does not require any special hardware, and can be run on any common development board. ### Configure the project Under Component Config ---> DSP Library ---> DSP Optimization, it's possible to choose either the optimized or ANSI implementation, to compare them. ### Build and flash Build the project and flash it to the board, then run monitor tool to view serial output (replace PORT with serial port name): ``` idf.py -p PORT flash monitor ``` (To exit the serial monitor, type ``Ctrl-]``.) See the Getting Started Guide for full steps to configure and use ESP-IDF to build projects. ## Example output Here is a typical example of console output. ``` I (340) main: Start Example. I (400) view: Data min[388] = -108.419342, Data max[205] = 30.267143 ________________________________________________________________ 0 | | | 1 | || | 2 || || | 3 || || | 4 || || | 5 || ||| | 6 || || | | | 7|||||||||||||||||||||||| |||||||||||||||||||||| |||||||||||| 8 | 9 | 0123456789012345678901234567890123456789012345678901234567890123 I (470) view: Plot: Length=512, min=-120.000000, max=40.000000 I (490) view: Data min[254] = -114.853371, Data max[205] = 27.247583 ________________________________________________________________ 0 | | 1 | | 2 | | 3 | | | 4 | | | 5 | | | 6 | ||| ||| | 7||||||||||||||||||||||||||||||||||||||||||||||| | ||||| | 8 ||||| 9 | 0123456789012345678901234567890123456789012345678901234567890123 I (560) view: Plot: Length=256, min=-120.000000, max=40.000000 I (560) main: FIR for 1024 samples and decimation 2 takes 763647 cycles I (570) main: End Example. ```

# IIR Filter Example (See the README.md file in the upper level 'examples' directory for more information about examples.) This example demonstrates how to use IIR filters functionality from esp-dsp library. Example does the following steps: 1. Initialize the library 2. Initialize input signal 3. Show LPF filter with Q factor 1 * Calculate iir filter coefficients * Filter the input test signal (delta function) * Shows impulse response on the plot * Shows frequency response on the plot * Calculate execution performance 4. The same for LPF filter with Q factor 10 ## How to use example ### Hardware required This example does not require any special hardware, and can be run on any common development board. ### Configure the project Under Component Config ---> DSP Library ---> DSP Optimization, it's possible to choose either the optimized or ANSI implementation, to compare them. ### Build and flash Build the project and flash it to the board, then run monitor tool to view serial output (replace PORT with serial port name): ``` idf.py -p PORT flash monitor ``` (To exit the serial monitor, type ``Ctrl-]``.) See the Getting Started Guide for full steps to configure and use ESP-IDF to build projects. ## Example output Here is an typical example console output. ``` I (58) main: Start Example. I (58) main: Impulse response of IIR filter with F=0.100000, qFactor=1.000000 I (68) view: Data min[8] = -0.060052, Data max[2] = 0.333517 ________________________________________________________________ 0 | 1 | 2 - | 3- - | 4 -------------------------------------------------------------| 5 | 6 | 7 | 8 | 9 | 0123456789012345678901234567890123456789012345678901234567890123 I (138) view: Plot: Length=128, min=-1.000000, max=1.000000 I (148) view: Data min[511] = -149.983795, Data max[0] = 0.000000 ________________________________________________________________ 0 | 1 | 2----------------- | 3 ---------- | 4 ------------- | 5 ---------- | 6 ------- | 7 --- | 8 -- | 9 --| 0123456789012345678901234567890123456789012345678901234567890123 I (228) view: Plot: Length=512, min=-100.000000, max=0.000000 I (228) main: IIR for 1024 samples take 20276 cycles I (238) main: Impulse response of IIR filter with F=0.100000, qFactor=10.000000 I (248) view: Data min[7] = -0.453739, Data max[2] = 0.526114 ________________________________________________________________ 0 | 1 | 2 - - | 3- - - - --- --- - - | 4- - - - - ---- -------------------------------------| 5 -- -- -- -- | 6 | 7 | 8 | 9 | 0123456789012345678901234567890123456789012345678901234567890123 I (318) view: Plot: Length=128, min=-1.000000, max=1.000000 I (328) view: Data min[511] = -149.480377, Data max[0] = 0.000000 ________________________________________________________________ 0 -- | 1 -- - | 2---------- ----- | 3 -------- | 4 ------------ | 5 ---------- | 6 ------- | 7 --- | 8 -- | 9 --| 0123456789012345678901234567890123456789012345678901234567890123 I (408) view: Plot: Length=512, min=-100.000000, max=0.000000 I (408) main: IIR for 1024 samples take 17456 cycles I (418) main: End Example. ```

# Extended Kalman Filter This example emulate system with IMU sensors and show how to use Extended Kalman Filter (EKF), with 13 values states vector, to estimate gyroscope errors and calculate system attitude. Also, this example show how to use esp-dsp library to operate with matrices and vectors. In real system, the emulated sensors values should be replace by the real sensors values. Then, in real system, a calibration phase should be implemented and after the calibration phase the state vector X and covariance matrix P should be saved and restored next time, when filter called. It will save time for initial phase. ## How to use example ### Hardware required This example does not require any special hardware, and can be run on any common development board. ### Configure the project Under Component Config ---> DSP Library ---> DSP Optimization, it's possible to choose either the optimized or ANSI implementation, to compare them. ### Build and flash Build the project and flash it to the board, then run monitor tool to view serial output (replace PORT with serial port name): ``` idf.py -p PORT flash monitor ``` (To exit the serial monitor, type ``Ctrl-]``.) See the Getting Started Guide for full steps to configure and use ESP-IDF to build projects. ## Example Output ``` I (380) spi_flash: detected chip: gd I (383) spi_flash: flash io: dio W (387) spi_flash: Detected size(4096k) larger than the size in the binary image header(2048k). Using the size in the binary image header. I (404) cpu_start: Starting scheduler on PRO CPU. I (0) cpu_start: Starting scheduler on APP CPU. I (413) main: Start Example. Gyro error: 0.1 0.2 0.3 Calibration phase started: Loop 1000 from 48000, State data : 0.998361 0.0152476 0.0211183 0.0509682 0.00463435 0.00919946 0.01352 0.998156 0.00619182 -0.000683098 -0.00117112 0.0063196 -0.000952147 Loop 2000 from 48000, State data : 0.941757 0.0877462 0.170681 0.276156 0.016951 0.0334337 0.0498731 0.998804 0.0162317 -0.00225174 0.00389746 0.0110905 -0.000489083 Loop 3000 from 48000, State data : 0.372216 0.24247 0.488788 0.750832 0.0323164 0.0642265 0.0962768 0.997295 0.0269348 -0.00481966 0.00605674 0.00779719 0.00494921 Loop 4000 from 48000, State data : 0.944725 0.0951798 0.165878 0.266308 0.0470155 0.0946294 0.141251 0.998213 0.0337875 -0.00704064 0.00422252 0.0124181 0.00485692 Loop 5000 from 48000, State data : 0.944287 0.102183 0.168344 0.263706 0.0597481 0.12037 0.179946 0.997498 0.0378795 -0.00841348 0.0053515 0.0104612 0.00666854 Loop 6000 from 48000, State data : 0.379137 0.258284 0.476853 0.74977 0.0697741 0.140876 0.210702 0.995523 0.0410914 -0.00911293 0.00510267 0.00764586 0.00913832 Loop 7000 from 48000, State data : 0.947048 0.112494 0.165382 0.251187 0.0773002 0.156661 0.233985 0.996358 0.0425222 -0.00994576 0.00353348 0.00969652 0.00849919 Loop 8000 from 48000, State data : 0.945556 0.120624 0.169212 0.250481 0.082995 0.16838 0.251493 0.995914 0.0433827 -0.0102827 0.0039165 0.00846988 0.00913964 Loop 9000 from 48000, State data : 0.381034 0.276875 0.4647 0.749805 0.0871785 0.177046 0.264439 0.995073 0.0441243 -0.0103565 0.00391002 0.0071649 0.00997719 Loop 10000 from 48000, State data : 0.946592 0.132375 0.168307 0.241068 0.0902326 0.183443 0.273873 0.995445 0.0443655 -0.0106197 0.00326065 0.00799655 0.00960479 Loop 11000 from 48000, State data : 0.944297 0.140946 0.172816 0.242015 0.0924658 0.188118 0.280807 0.995187 0.0445766 -0.0106806 0.00346742 0.00749049 0.00979064 Loop 12000 from 48000, State data : 0.378334 0.295555 0.452859 0.751285 0.0941005 0.191525 0.285886 0.994796 0.0447763 -0.0106511 0.0034986 0.00695604 0.0100697 Loop 13000 from 48000, State data : 0.944329 0.1532 0.172826 0.234315 0.0953075 0.194011 0.289567 0.994899 0.0448155 -0.0107384 0.00323858 0.00728781 0.00989103 Loop 14000 from 48000, State data : 0.941572 0.16194 0.177533 0.236008 0.0961574 0.195842 0.292257 0.994735 0.0448801 -0.0107422 0.00334282 0.0070798 0.00993131 Loop 15000 from 48000, State data : 0.373427 0.314041 0.441061 0.753256 0.0967899 0.197167 0.294234 0.994523 0.0449438 -0.0107112 0.00335898 0.00685221 0.0100213 Loop 16000 from 48000, State data : 0.941028 0.174338 0.177916 0.228952 0.0972752 0.198121 0.295664 0.994518 0.0449512 -0.0107403 0.0032445 0.00697761 0.00993463 Loop 17000 from 48000, State data : 0.937959 0.183145 0.18262 0.230959 0.0975883 0.198844 0.296697 0.994396 0.0449757 -0.0107339 0.0032963 0.00688409 0.00992845 Loop 18000 from 48000, State data : 0.3675 0.33233 0.429142 0.755207 0.0978324 0.199358 0.297465 0.994256 0.0450002 -0.0107104 0.00330113 0.00677742 0.00995297 Loop 19000 from 48000, State data : 0.937014 0.195546 0.183166 0.224089 0.0980371 0.199716 0.298023 0.994211 0.0450036 -0.0107164 0.00324275 0.00681997 0.00990755 Loop 20000 from 48000, State data : 0.933698 0.204372 0.187784 0.226223 0.0981422 0.200008 0.29842 0.994114 0.0450155 -0.0107065 0.00327025 0.00677405 0.00988484 Loop 21000 from 48000, State data : 0.361055 0.350426 0.417036 0.756916 0.0982358 0.200208 0.29872 0.99401 0.0450272 -0.0106858 0.00326787 0.00671759 0.0098834 Loop 22000 from 48000, State data : 0.932425 0.216717 0.188413 0.219358 0.0983318 0.200334 0.298938 0.993947 0.0450303 -0.0106798 0.00323017 0.00672916 0.00985372 Loop 23000 from 48000, State data : 0.928888 0.225543 0.19291 0.221546 0.0983561 0.200458 0.299082 0.993866 0.0450371 -0.0106664 0.00324701 0.00670354 0.00982584 Loop 24000 from 48000, State data : 0.354297 0.36833 0.404722 0.758292 0.0983915 0.200535 0.299203 0.993773 0.045044 -0.0106443 0.00324109 0.00666712 0.00981608 Loop 25000 from 48000, State data : 0.927316 0.237803 0.19359 0.214612 0.0984453 0.200572 0.299291 0.993709 0.0450468 -0.0106303 0.00321085 0.00666748 0.00979369 Loop 26000 from 48000, State data : 0.92357 0.246618 0.197954 0.216824 0.0984385 0.200632 0.299342 0.993629 0.0450514 -0.0106123 0.00322403 0.00665109 0.00976504 Loop 27000 from 48000, State data : 0.347305 0.386034 0.392194 0.759303 0.0984521 0.200663 0.299393 0.993546 0.0450564 -0.0105864 0.00321847 0.00662376 0.00975319 Loop 28000 from 48000, State data : 0.92171 0.258777 0.198672 0.209796 0.0984898 0.200666 0.299433 0.993475 0.045059 -0.0105663 0.00319366 0.00662077 0.00973562 Loop 29000 from 48000, State data : 0.917761 0.267574 0.202895 0.212019 0.0984714 0.2007 0.299446 0.9934 0.0450631 -0.0105437 0.00320563 0.0066091 0.00970881 Loop 30000 from 48000, State data : 0.340113 0.403531 0.379459 0.759933 0.0984762 0.200711 0.299466 0.993322 0.0450673 -0.0105132 0.00320031 0.00658594 0.00969804 Loop 31000 from 48000, State data : 0.915619 0.279623 0.203648 0.204891 0.0985076 0.2007 0.299484 0.993253 0.0450696 -0.0104878 0.00317637 0.00658294 0.00968329 Loop 32000 from 48000, State data : 0.91147 0.288396 0.207727 0.207121 0.0984838 0.200725 0.299481 0.99318 0.0450732 -0.0104599 0.00318786 0.00657435 0.00965871 Loop 33000 from 48000, State data : 0.332734 0.420812 0.366519 0.760177 0.0984844 0.20073 0.299492 0.993105 0.045077 -0.0104242 0.00318322 0.00655352 0.00964965 Loop 34000 from 48000, State data : 0.909049 0.300327 0.208511 0.199891 0.0985129 0.200714 0.299506 0.993034 0.0450794 -0.0103941 0.0031609 0.00655179 0.00963774 Loop 35000 from 48000, State data : 0.904704 0.309072 0.212442 0.202124 0.0984875 0.200736 0.299498 0.992959 0.0450829 -0.0103612 0.0031732 0.00654506 0.00961709 Loop 36000 from 48000, State data : 0.325179 0.437867 0.353384 0.760034 0.098487 0.200738 0.299504 0.992885 0.0450865 -0.0103208 0.00317079 0.00652607 0.00961171 Loop 37000 from 48000, State data : 0.325177 0.437848 0.353377 0.760049 0.0989011 0.200534 0.299617 0.992838 0.0450912 -0.0103039 0.00319877 0.00652725 0.00959415 Loop 38000 from 48000, State data : 0.325194 0.437821 0.353363 0.760064 0.099202 0.200388 0.299726 0.992838 0.0450926 -0.0102998 0.00320422 0.00652895 0.00959084 Loop 39000 from 48000, State data : 0.325211 0.437798 0.353354 0.760074 0.0994169 0.200278 0.299826 0.992816 0.045093 -0.0102979 0.00320263 0.0065278 0.00959847 Loop 40000 from 48000, State data : 0.325222 0.437784 0.353346 0.760081 0.0995754 0.200199 0.299886 0.992816 0.0450925 -0.0102967 0.00320118 0.00652683 0.00960376 Loop 41000 from 48000, State data : 0.325231 0.437773 0.353342 0.760085 0.0996929 0.200142 0.299945 0.992816 0.0450925 -0.0102966 0.00320043 0.00652627 0.00960631 Loop 42000 from 48000, State data : 0.325238 0.437769 0.353336 0.760087 0.0997802 0.200119 0.299978 0.992816 0.0450913 -0.0102965 0.00320007 0.0065261 0.00960773 Loop 43000 from 48000, State data : 0.32524 0.437762 0.353331 0.760093 0.099842 0.200089 0.299979 0.992816 0.0450913 -0.0102961 0.00320001 0.00652608 0.00960857 Loop 44000 from 48000, State data : 0.325241 0.43776 0.353327 0.760095 0.099883 0.200059 0.299979 0.992816 0.045089 -0.0102953 0.00319975 0.00652622 0.00960868 Loop 45000 from 48000, State data : 0.325243 0.437759 0.353325 0.760096 0.0999138 0.200045 0.299979 0.992816 0.0450878 -0.0102956 0.0031996 0.00652593 0.00960985 Loop 46000 from 48000, State data : 0.325245 0.437756 0.353324 0.760097 0.0999355 0.200042 0.299979 0.992816 0.0450878 -0.0102959 0.00319972 0.0065261 0.00960944 Loop 47000 from 48000, State data : 0.325246 0.437757 0.353322 0.760098 0.0999504 0.200039 0.299979 0.992816 0.0450878 -0.0102959 0.00319952 0.00652634 0.00960984 Calibration phase finished. Regular calculation started: Loop 1000 from 48000, State data : 0.9996 6.68374e-06 -7.71055e-05 0.028269 0.0999599 0.199742 0.298758 0.992397 0.0506049 -0.00981295 0.00516875 0.00517689 0.0102406 Loop 2000 from 48000, State data : 0.95186 0.0747648 0.154942 0.253704 0.0997667 0.199899 0.298983 0.992397 0.0504132 -0.0098162 0.00510809 0.00522702 0.0102249 Loop 3000 from 48000, State data : 0.395338 0.237819 0.486861 0.741698 0.0994409 0.200091 0.299095 0.992397 0.0502891 -0.00981838 0.00506923 0.00525921 0.0102147 Loop 4000 from 48000, State data : 0.952465 0.0877289 0.155254 0.247002 0.0992076 0.200299 0.299271 0.992397 0.0502054 -0.00981973 0.00504271 0.00528111 0.0102076 Loop 5000 from 48000, State data : 0.950016 0.096521 0.160702 0.249654 0.0990023 0.200426 0.299306 0.992397 0.05013 -0.00982108 0.00501929 0.00530046 0.0102013 Loop 6000 from 48000, State data : 0.389808 0.256786 0.476033 0.745321 0.0988748 0.200476 0.299331 0.992397 0.050078 -0.00982208 0.0050032 0.00531378 0.0101971 Loop 7000 from 48000, State data : 0.950306 0.109383 0.161046 0.242937 0.0987883 0.200581 0.299444 0.992397 0.0500379 -0.00982289 0.0049906 0.00532416 0.0101938 Loop 8000 from 48000, State data : 0.947646 0.118155 0.166392 0.2456 0.0986931 0.200633 0.299434 0.992397 0.0499987 -0.00982366 0.00497852 0.00533416 0.0101903 Loop 9000 from 48000, State data : 0.383995 0.275557 0.464951 0.748623 0.0986473 0.200627 0.299425 0.992397 0.0499702 -0.00982415 0.00496994 0.00534126 0.0101879 Loop 10000 from 48000, State data : 0.94764 0.130939 0.166769 0.238794 0.0986203 0.200694 0.299509 0.992397 0.0499475 -0.00982454 0.004963 0.00534698 0.0101861 Loop 11000 from 48000, State data : 0.944771 0.139703 0.171999 0.241471 0.0985699 0.200714 0.299481 0.992397 0.0499252 -0.00982467 0.00495605 0.00535274 0.0101844 Loop 12000 from 48000, State data : 0.377949 0.294161 0.453622 0.751566 0.0985571 0.200685 0.299459 0.992397 0.0499092 -0.00982467 0.00495124 0.0053567 0.0101832 Loop 13000 from 48000, State data : 0.944475 0.152413 0.172408 0.234549 0.0985539 0.200736 0.299532 0.992397 0.0498962 -0.00982467 0.00494735 0.0053599 0.0101823 Loop 14000 from 48000, State data : 0.941398 0.16117 0.177516 0.237239 0.0985215 0.200743 0.299498 0.992397 0.0498826 -0.00982467 0.0049434 0.00536316 0.0101813 Loop 15000 from 48000, State data : 0.371694 0.312599 0.442052 0.754132 0.0985222 0.200704 0.299474 0.992397 0.049874 -0.00982467 0.00494084 0.0053653 0.0101808 Loop 16000 from 48000, State data : 0.940819 0.173801 0.177954 0.230187 0.0985277 0.20075 0.299544 0.992397 0.0498671 -0.00982467 0.00493887 0.00536698 0.0101804 Loop 17000 from 48000, State data : 0.937532 0.182552 0.182939 0.232897 0.0985023 0.200752 0.299507 0.992397 0.0498602 -0.00982467 0.0049367 0.0053688 0.0101799 Loop 18000 from 48000, State data : 0.365235 0.33087 0.43025 0.756316 0.0985084 0.200708 0.299482 0.992397 0.0498562 -0.00982467 0.00493555 0.0053698 0.0101796 Loop 19000 from 48000, State data : 0.936669 0.195102 0.183407 0.225717 0.0985175 0.200754 0.299549 0.992397 0.0498532 -0.00982467 0.00493474 0.00537051 0.0101794 Loop 20000 from 48000, State data : 0.933178 0.203841 0.188264 0.22844 0.0984953 0.200754 0.299511 0.992397 0.0498502 -0.00982467 0.00493366 0.00537141 0.010179 Loop 21000 from 48000, State data : 0.35858 0.348967 0.41822 0.758113 0.0985034 0.200709 0.299484 0.992397 0.0498495 -0.00982467 0.00493334 0.00537172 0.0101788 Loop 22000 from 48000, State data : 0.93203 0.216304 0.188763 0.221136 0.0985129 0.200755 0.299549 0.992397 0.0498497 -0.00982467 0.00493327 0.00537182 0.0101787 Loop 23000 from 48000, State data : 0.928336 0.225027 0.193488 0.22387 0.0984918 0.200754 0.29951 0.992397 0.0498497 -0.00982467 0.00493298 0.00537209 0.0101787 Loop 24000 from 48000, State data : 0.351735 0.366882 0.405969 0.759519 0.0985006 0.200707 0.299482 0.992397 0.0498508 -0.00982467 0.00493324 0.00537189 0.0101787 Loop 25000 from 48000, State data : 0.926905 0.237397 0.194017 0.216443 0.0985107 0.200755 0.299545 0.992397 0.0498526 -0.00982467 0.00493366 0.00537159 0.0101787 Loop 26000 from 48000, State data : 0.92301 0.246099 0.198608 0.219185 0.0984902 0.200753 0.299511 0.992397 0.0498537 -0.00982467 0.00493391 0.00537146 0.0101787 Loop 27000 from 48000, State data : 0.344708 0.384605 0.393502 0.760534 0.0984992 0.200706 0.299488 0.992397 0.0498556 -0.00982467 0.00493459 0.00537092 0.0101787 Loop 28000 from 48000, State data : 0.921297 0.258369 0.199166 0.211636 0.0985091 0.200757 0.299555 0.992397 0.0498579 -0.00982467 0.00493535 0.00537033 0.0101787 Loop 29000 from 48000, State data : 0.917204 0.267048 0.203621 0.214385 0.0984891 0.200754 0.29952 0.992397 0.0498601 -0.00982467 0.00493597 0.0053698 0.0101787 Loop 30000 from 48000, State data : 0.337501 0.402129 0.380825 0.761156 0.0984981 0.200706 0.299491 0.992397 0.0498626 -0.00982467 0.00493691 0.00536903 0.0101787 Loop 31000 from 48000, State data : 0.915208 0.279212 0.204208 0.206723 0.0985072 0.200758 0.299553 0.992397 0.0498654 -0.00982467 0.00493789 0.00536824 0.0101787 Loop 32000 from 48000, State data : 0.910918 0.287861 0.208526 0.209479 0.0984873 0.200754 0.299515 0.992397 0.0498676 -0.00982467 0.00493879 0.00536752 0.0101787 Loop 33000 from 48000, State data : 0.330116 0.419445 0.367945 0.761385 0.0984966 0.200704 0.299489 0.992397 0.0498701 -0.00982467 0.00493986 0.00536667 0.0101787 Loop 34000 from 48000, State data : 0.908641 0.299912 0.209141 0.201703 0.0985056 0.200757 0.299551 0.992397 0.0498728 -0.00982467 0.00494093 0.00536582 0.0101787 Loop 35000 from 48000, State data : 0.904158 0.308528 0.213318 0.204462 0.0984862 0.200752 0.299518 0.992397 0.0498751 -0.00982467 0.00494188 0.00536507 0.0101787 Loop 36000 from 48000, State data : 0.322561 0.436541 0.354869 0.761219 0.0984953 0.200702 0.299495 0.992397 0.0498778 -0.00982467 0.00494296 0.00536423 0.0101787 Loop 37000 from 48000, State data : 0.322549 0.436508 0.354868 0.761243 0.0989076 0.200506 0.299634 0.992397 0.0498778 -0.00982467 0.00494296 0.00536423 0.0101787 Loop 38000 from 48000, State data : 0.322568 0.436485 0.354851 0.761257 0.099208 0.200371 0.299726 0.992397 0.0498778 -0.00982467 0.00494296 0.00536423 0.0101787 Loop 39000 from 48000, State data : 0.322581 0.436466 0.354841 0.761267 0.0994207 0.200267 0.299799 0.992397 0.0498778 -0.00982467 0.00494296 0.00536423 0.0101787 Loop 40000 from 48000, State data : 0.322592 0.436454 0.354831 0.761274 0.099581 0.200208 0.299849 0.992397 0.0498778 -0.00982467 0.00494296 0.00536423 0.0101787 Loop 41000 from 48000, State data : 0.322601 0.436443 0.354826 0.761278 0.099701 0.20015 0.299901 0.992397 0.0498778 -0.00982467 0.00494296 0.00536423 0.0101787 Loop 42000 from 48000, State data : 0.322606 0.436435 0.35482 0.761283 0.0997844 0.200101 0.299931 0.992397 0.0498778 -0.00982467 0.00494296 0.00536423 0.0101787 Loop 43000 from 48000, State data : 0.322611 0.436429 0.35482 0.761285 0.0998457 0.200072 0.299961 0.992397 0.0498778 -0.00982467 0.00494296 0.00536423 0.0101787 Loop 44000 from 48000, State data : 0.322615 0.436425 0.354818 0.761286 0.0998883 0.200057 0.29999 0.992397 0.0498778 -0.00982467 0.00494296 0.00536423 0.0101787 Loop 45000 from 48000, State data : 0.322617 0.436423 0.354816 0.761287 0.099912 0.200042 0.300002 0.992397 0.0498778 -0.00982467 0.00494296 0.00536423 0.0101787 Loop 46000 from 48000, State data : 0.322617 0.436421 0.354815 0.761289 0.0999343 0.20003 0.300002 0.992397 0.0498778 -0.00982467 0.00494296 0.00536423 0.0101787 Loop 47000 from 48000, State data : 0.322618 0.436421 0.354814 0.761289 0.0999444 0.20003 0.300002 0.992397 0.0498778 -0.00982467 0.00494296 0.00536423 0.0101787 Final State data : 0.322618 0.436421 0.354814 0.761289 0.0999518 0.20003 0.300002 0.992397 0.0498778 -0.00982467 0.00494296 0.00536423 0.0101787 Estimated error : 0.0999518 0.20003 0.300002 Difference between real and estimated errors : 4.81904e-05 -2.99811e-05 -2.17557e-06 Expected Euler angels (degree) : -29.8215 64.9692 150.241 Calculated Euler angels (degree) : -35.1525 63.3067 156.167 ```

# ESP-DSP LyraT Board audio processing application The demo applications are developed for the ESP32-LyraT development board and demonstrate the usage of IIR filters from the ESP-DSP library. This example showcases how to use IIR filter functionality to process audio stream data. To hear the audio please connect headphones or speakers to the ESP32-LyraT audio output. The example performs the following steps: 1. Read samples from a file * read samples from file * write audio samples to the triple buffer 2. Process audio samples * process volume/bass/treble * apply digital limiter to the audio data * control audio buffer overflow 3. Pass samples to the audio codec To control the volume/bass/treble, please select the value by press 'Set' button and adjust the value by '+/-' buttons. ## The Triple Audio Buffer In audion processing, it's possible to have situation when one task write data to the processing buffer (processing task), and another task read data from the same buffer, and still in reading process. Triple buffering is a technique used in audio processing to minimize latency and ensure smooth playback. It involves using three buffers to store audio data. Here's a description of how it works: * Buffer A: This buffer holds the audio data that is currently being processed by the audio system. It is typically filled with samples from the audio source and processed in real-time. * Buffer B: When Buffer A is full, the audio system begins reading from Buffer A and starts processing the data. At the same time, Buffer B is filled with new audio samples from the source. * Buffer C: Once Buffer B is full, the audio system switches its attention to Buffer B and continues processing data. Buffer C is then filled with the latest audio samples. The cycle continues, with the audio system always processing the data from a buffer while the other two buffers are being filled. This approach helps ensure a continuous and uninterrupted audio playback, as there is always a buffer ready to be processed. It reduces the chances of audio glitches or dropouts caused by delays in reading or processing the audio data. Triple buffering is particularly useful when working with real-time audio processing applications, where low latency and uninterrupted playback are crucial. ## Audio Processing Flow The audio processing flow contains next blocks: 1. Audio processing task * Read data from file and store to the triple buffer * Read from triple buffer and concert data from int16_t to float * Process bass * Process treble * Process volume * Apply digital limiter * Convert data from float to int16_t and store to the triple buffer 2. Audio output task * Write data from triple buffer to audio codec 3. Buttons control task * React on buttons and adjust the control values * Calculates IIR filter coefficients ## How to use the example ### Hardware required This example require LyraT development board. ### Configure the project Under Component Config ---> DSP Library ---> DSP Optimization, it's possible to choose either the optimized or ANSI implementation, to compare them. ### Build and flash Build the project and flash it to the board, then run monitor tool to view serial output (replace PORT with serial port name): ``` idf.py flash monitor ``` (To exit the serial monitor, type ``Ctrl-]``.) See the Getting Started Guide for full steps to configure and use ESP-IDF to build projects.

# Matrix Operations Example (See the README.md file in the upper level 'examples' directory for more information about examples.) This example demonstrates how to use Mat class functionality from esp-dsp library. Example does the following steps: 1. Initialize a matrix A and matirx x 2. Calculate matrix b: b = A*x 3. Find roots x1_: A*x1_ = b, with different methods 4. Print result ## How to use example ### Hardware required This example does not require any special hardware, and can be run on any common development board. ### Configure the project Under Component Config ---> DSP Library ---> DSP Optimization, it's possible to choose either the optimized or ANSI implementation, to compare them. ### Build and flash Build the project and flash it to the board, then run monitor tool to view serial output (replace PORT with serial port name): ``` idf.py -p PORT flash monitor ``` (To exit the serial monitor, type ``Ctrl-]``.) See the Getting Started Guide for full steps to configure and use ESP-IDF to build projects. ## Example output Here is an typical example console output. ``` I (215) main: Start Example. I (215) main: Original vector x: 0 1 2 I (215) main: Solve result: 0 1 2 I (215) main: Roots result: 0 1 2 I (215) main: End Example. ```