├── LICENSE ├── README.md ├── esp32-i2s-slm.ino ├── math ├── c_weighting.m ├── ics43432.m ├── ics43434.m ├── im69d130.m ├── inmp441.m └── sph645lm4h-b.m ├── misc ├── esp32-i2s-slm-bp.svg └── ics-43434-afr.svg └── sos-iir-filter.h /LICENSE: -------------------------------------------------------------------------------- 1 | GNU GENERAL PUBLIC LICENSE 2 | Version 3, 29 June 2007 3 | 4 | Copyright (C) 2007 Free Software Foundation, Inc. 5 | Everyone is permitted to copy and distribute verbatim copies 6 | of this license document, but changing it is not allowed. 7 | 8 | Preamble 9 | 10 | The GNU General Public License is a free, copyleft license for 11 | software and other kinds of works. 12 | 13 | The licenses for most software and other practical works are designed 14 | to take away your freedom to share and change the works. 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It is safest 630 | to attach them to the start of each source file to most effectively 631 | state the exclusion of warranty; and each file should have at least 632 | the "copyright" line and a pointer to where the full notice is found. 633 | 634 | 635 | Copyright (C) 636 | 637 | This program is free software: you can redistribute it and/or modify 638 | it under the terms of the GNU General Public License as published by 639 | the Free Software Foundation, either version 3 of the License, or 640 | (at your option) any later version. 641 | 642 | This program is distributed in the hope that it will be useful, 643 | but WITHOUT ANY WARRANTY; without even the implied warranty of 644 | MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 645 | GNU General Public License for more details. 646 | 647 | You should have received a copy of the GNU General Public License 648 | along with this program. If not, see . 649 | 650 | Also add information on how to contact you by electronic and paper mail. 651 | 652 | If the program does terminal interaction, make it output a short 653 | notice like this when it starts in an interactive mode: 654 | 655 | Copyright (C) 656 | This program comes with ABSOLUTELY NO WARRANTY; for details type `show w'. 657 | This is free software, and you are welcome to redistribute it 658 | under certain conditions; type `show c' for details. 659 | 660 | The hypothetical commands `show w' and `show c' should show the appropriate 661 | parts of the General Public License. Of course, your program's commands 662 | might be different; for a GUI interface, you would use an "about box". 663 | 664 | You should also get your employer (if you work as a programmer) or school, 665 | if any, to sign a "copyright disclaimer" for the program, if necessary. 666 | For more information on this, and how to apply and follow the GNU GPL, see 667 | . 668 | 669 | The GNU General Public License does not permit incorporating your program 670 | into proprietary programs. If your program is a subroutine library, you 671 | may consider it more useful to permit linking proprietary applications with 672 | the library. If this is what you want to do, use the GNU Lesser General 673 | Public License instead of this License. But first, please read 674 | . 675 | -------------------------------------------------------------------------------- /README.md: -------------------------------------------------------------------------------- 1 | # Sound Level Meter with Arduino IDE, ESP32 and I2S MEMS microphone 2 | 3 | Arduino/ESP32 Sound Level Meter (SLM) using inexpensive, factory calibrated, digital I2S MEMS microphone and digital IIR filters (vs. FFT) for equalization and A-weighting. 4 | 5 | The basic idea is: 6 | 7 | ![Basic principle](./misc/esp32-i2s-slm-bp.svg) 8 | 9 | And the microphone response after equalization should look like: 10 | 11 | ![Adjusted frequency response](./misc/ics-43434-afr.svg) 12 | 13 | Theoretically, i.e. with factory calibrated ICS-4343x, this should get you ±1dB(A) measurement within 20Hz-20KHz range. 14 | 15 | The code in this repository is mostly intended as example how you can integrate resonable noise measurement (i.e. *L*Aeq, Equivalent Continuous Sound Level) in your projects. 16 | 17 | You can find a bit more information in my [hackday.io](https://hackaday.io/project/166867-esp32-i2s-slm) project. 18 | -------------------------------------------------------------------------------- /esp32-i2s-slm.ino: -------------------------------------------------------------------------------- 1 | /* 2 | * Display A-weighted sound level measured by I2S Microphone 3 | * 4 | * (c)2019 Ivan Kostoski 5 | * 6 | * This program is free software: you can redistribute it and/or modify 7 | * it under the terms of the GNU General Public License as published by 8 | * the Free Software Foundation, either version 3 of the License, or 9 | * (at your option) any later version. 10 | * 11 | * This program is distributed in the hope that it will be useful, 12 | * but WITHOUT ANY WARRANTY; without even the implied warranty of 13 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 14 | * GNU General Public License for more details. 15 | * 16 | * You should have received a copy of the GNU General Public License 17 | * along with this program. If not, see . 18 | */ 19 | 20 | /* 21 | * Sketch samples audio data from I2S microphone, processes the data 22 | * with digital IIR filters and calculates A or C weighted Equivalent 23 | * Continuous Sound Level (Leq) 24 | * 25 | * I2S is setup to sample data at Fs=48000KHz (fixed value due to 26 | * design of digital IIR filters). Data is read from I2S queue 27 | * in 'sample blocks' (default 125ms block, equal to 6000 samples) 28 | * by 'i2s_reader_task', filtered trough two IIR filters (equalizer 29 | * and weighting), summed up and pushed into 'samples_queue' as 30 | * sum of squares of filtered samples. The main task then pulls data 31 | * from the queue and calculates decibel value relative to microphone 32 | * reference amplitude, derived from datasheet sensitivity dBFS 33 | * value, number of bits in I2S data, and the reference value for 34 | * which the sensitivity is specified (typically 94dB, pure sine 35 | * wave at 1KHz). 36 | * 37 | * Displays line on the small OLED screen with 'short' LAeq(125ms) 38 | * response and numeric LAeq(1sec) dB value from the signal RMS. 39 | */ 40 | 41 | #include 42 | #include "sos-iir-filter.h" 43 | 44 | // 45 | // Configuration 46 | // 47 | 48 | #define LEQ_PERIOD 1 // second(s) 49 | #define WEIGHTING C_weighting // Also avaliable: 'C_weighting' or 'None' (Z_weighting) 50 | #define LEQ_UNITS "LAeq" // customize based on above weighting used 51 | #define DB_UNITS "dBA" // customize based on above weighting used 52 | #define USE_DISPLAY 1 53 | 54 | // NOTE: Some microphones require at least DC-Blocker filter 55 | #define MIC_EQUALIZER ICS43434 // See below for defined IIR filters or set to 'None' to disable 56 | #define MIC_OFFSET_DB 3.0103 // Default offset (sine-wave RMS vs. dBFS). Modify this value for linear calibration 57 | 58 | // Customize these values from microphone datasheet 59 | #define MIC_SENSITIVITY -26 // dBFS value expected at MIC_REF_DB (Sensitivity value from datasheet) 60 | #define MIC_REF_DB 94.0 // Value at which point sensitivity is specified in datasheet (dB) 61 | #define MIC_OVERLOAD_DB 116.0 // dB - Acoustic overload point 62 | #define MIC_NOISE_DB 29 // dB - Noise floor 63 | #define MIC_BITS 24 // valid number of bits in I2S data 64 | #define MIC_CONVERT(s) (s >> (SAMPLE_BITS - MIC_BITS)) 65 | #define MIC_TIMING_SHIFT 0 // Set to one to fix MSB timing for some microphones, i.e. SPH0645LM4H-x 66 | 67 | // Calculate reference amplitude value at compile time 68 | constexpr double MIC_REF_AMPL = pow(10, double(MIC_SENSITIVITY)/20) * ((1<<(MIC_BITS-1))-1); 69 | 70 | // 71 | // I2S pins - Can be routed to almost any (unused) ESP32 pin. 72 | // SD can be any pin, inlcuding input only pins (36-39). 73 | // SCK (i.e. BCLK) and WS (i.e. L/R CLK) must be output capable pins 74 | // 75 | // Below ones are just example for my board layout, put here the pins you will use 76 | // 77 | #define I2S_WS 18 78 | #define I2S_SCK 23 79 | #define I2S_SD 19 80 | 81 | // I2S peripheral to use (0 or 1) 82 | #define I2S_PORT I2S_NUM_0 83 | 84 | // 85 | // Setup your display library (and geometry) here 86 | // 87 | #if (USE_DISPLAY > 0) 88 | // ThingPulse/esp8266-oled-ssd1306, you may need the latest source and PR#198 for 64x48 89 | #include 90 | #define OLED_GEOMETRY GEOMETRY_64_48 91 | //#define OLED_GEOMETRY GEOMETRY_128_32 92 | //#define OLED_GEOMETRY GEOMETRY_128_64 93 | #define OLED_FLIP_V 1 94 | SSD1306Wire display(0x3c, SDA, SCL, OLED_GEOMETRY); 95 | #endif 96 | 97 | 98 | // 99 | // IIR Filters 100 | // 101 | 102 | // DC-Blocker filter - removes DC component from I2S data 103 | // See: https://www.dsprelated.com/freebooks/filters/DC_Blocker.html 104 | // a1 = -0.9992 should heavily attenuate frequencies below 10Hz 105 | SOS_IIR_Filter DC_BLOCKER = { 106 | gain: 1.0, 107 | sos: {{-1.0, 0.0, +0.9992, 0}} 108 | }; 109 | 110 | // 111 | // Equalizer IIR filters to flatten microphone frequency response 112 | // See respective .m file for filter design. Fs = 48Khz. 113 | // 114 | // Filters are represented as Second-Order Sections cascade with assumption 115 | // that b0 and a0 are equal to 1.0 and 'gain' is applied at the last step 116 | // B and A coefficients were transformed with GNU Octave: 117 | // [sos, gain] = tf2sos(B, A) 118 | // See: https://www.dsprelated.com/freebooks/filters/Series_Second_Order_Sections.html 119 | // NOTE: SOS matrix 'a1' and 'a2' coefficients are negatives of tf2sos output 120 | // 121 | 122 | // TDK/InvenSense ICS-43434 123 | // Datasheet: https://www.invensense.com/wp-content/uploads/2016/02/DS-000069-ICS-43434-v1.1.pdf 124 | // B = [0.477326418836803, -0.486486982406126, -0.336455844522277, 0.234624646917202, 0.111023257388606]; 125 | // A = [1.0, -1.93073383849136326, 0.86519456089576796, 0.06442838283825100, 0.00111249298800616]; 126 | SOS_IIR_Filter ICS43434 = { 127 | gain: 0.477326418836803, 128 | sos: { // Second-Order Sections {b1, b2, -a1, -a2} 129 | {+0.96986791463971267, 0.23515976355743193, -0.06681948004769928, -0.00111521990688128}, 130 | {-1.98905931743624453, 0.98908924206960169, +1.99755331853906037, -0.99755481510122113} 131 | } 132 | }; 133 | 134 | // TDK/InvenSense ICS-43432 135 | // Datasheet: https://www.invensense.com/wp-content/uploads/2015/02/ICS-43432-data-sheet-v1.3.pdf 136 | // B = [-0.45733702338341309 1.12228667105574775 -0.77818278904413563, 0.00968926337978037, 0.10345668405223755] 137 | // A = [1.0, -3.3420781082912949, 4.4033694320978771, -3.0167072679918010, 1.2265536567647031, -0.2962229189311990, 0.0251085747458112] 138 | SOS_IIR_Filter ICS43432 = { 139 | gain: -0.457337023383413, 140 | sos: { // Second-Order Sections {b1, b2, -a1, -a2} 141 | {-0.544047931916859, -0.248361759321800, +0.403298891662298, -0.207346186351843}, 142 | {-1.909911869441421, +0.910830292683527, +1.790285722826743, -0.804085812369134}, 143 | {+0.000000000000000, +0.000000000000000, +1.148493493802252, -0.150599527756651} 144 | } 145 | }; 146 | 147 | // TDK/InvenSense INMP441 148 | // Datasheet: https://www.invensense.com/wp-content/uploads/2015/02/INMP441.pdf 149 | // B ~= [1.00198, -1.99085, 0.98892] 150 | // A ~= [1.0, -1.99518, 0.99518] 151 | SOS_IIR_Filter INMP441 = { 152 | gain: 1.00197834654696, 153 | sos: { // Second-Order Sections {b1, b2, -a1, -a2} 154 | {-1.986920458344451, +0.986963226946616, +1.995178510504166, -0.995184322194091} 155 | } 156 | }; 157 | 158 | // Infineon IM69D130 Shield2Go 159 | // Datasheet: https://www.infineon.com/dgdl/Infineon-IM69D130-DS-v01_00-EN.pdf?fileId=5546d462602a9dc801607a0e46511a2e 160 | // B ~= [1.001240684967527, -1.996936108836337, 0.995703101823006] 161 | // A ~= [1.0, -1.997675693595542, 0.997677044195563] 162 | // With additional DC blocking component 163 | SOS_IIR_Filter IM69D130 = { 164 | gain: 1.00124068496753, 165 | sos: { 166 | {-1.0, 0.0, +0.9992, 0}, // DC blocker, a1 = -0.9992 167 | {-1.994461610298131, 0.994469278738208, +1.997675693595542, -0.997677044195563} 168 | } 169 | }; 170 | 171 | // Knowles SPH0645LM4H-B, rev. B 172 | // https://cdn-shop.adafruit.com/product-files/3421/i2S+Datasheet.PDF 173 | // B ~= [1.001234, -1.991352, 0.990149] 174 | // A ~= [1.0, -1.993853, 0.993863] 175 | // With additional DC blocking component 176 | SOS_IIR_Filter SPH0645LM4H_B_RB = { 177 | gain: 1.00123377961525, 178 | sos: { // Second-Order Sections {b1, b2, -a1, -a2} 179 | {-1.0, 0.0, +0.9992, 0}, // DC blocker, a1 = -0.9992 180 | {-1.988897663539382, +0.988928479008099, +1.993853376183491, -0.993862821429572} 181 | } 182 | }; 183 | 184 | // 185 | // Weighting filters 186 | // 187 | 188 | // 189 | // A-weighting IIR Filter, Fs = 48KHz 190 | // (By Dr. Matt L., Source: https://dsp.stackexchange.com/a/36122) 191 | // B = [0.169994948147430, 0.280415310498794, -1.120574766348363, 0.131562559965936, 0.974153561246036, -0.282740857326553, -0.152810756202003] 192 | // A = [1.0, -2.12979364760736134, 0.42996125885751674, 1.62132698199721426, -0.96669962900852902, 0.00121015844426781, 0.04400300696788968] 193 | SOS_IIR_Filter A_weighting = { 194 | gain: 0.169994948147430, 195 | sos: { // Second-Order Sections {b1, b2, -a1, -a2} 196 | {-2.00026996133106, +1.00027056142719, -1.060868438509278, -0.163987445885926}, 197 | {+4.35912384203144, +3.09120265783884, +1.208419926363593, -0.273166998428332}, 198 | {-0.70930303489759, -0.29071868393580, +1.982242159753048, -0.982298594928989} 199 | } 200 | }; 201 | 202 | // 203 | // C-weighting IIR Filter, Fs = 48KHz 204 | // Designed by invfreqz curve-fitting, see respective .m file 205 | // B = [-0.49164716933714026, 0.14844753846498662, 0.74117815661529129, -0.03281878334039314, -0.29709276192593875, -0.06442545322197900, -0.00364152725482682] 206 | // A = [1.0, -1.0325358998928318, -0.9524000181023488, 0.8936404694728326 0.2256286147169398 -0.1499917107550188, 0.0156718181681081] 207 | SOS_IIR_Filter C_weighting = { 208 | gain: -0.491647169337140, 209 | sos: { 210 | {+1.4604385758204708, +0.5275070373815286, +1.9946144559930252, -0.9946217070140883}, 211 | {+0.2376222404939509, +0.0140411206016894, -1.3396585608422749, -0.4421457807694559}, 212 | {-2.0000000000000000, +1.0000000000000000, +0.3775800047420818, -0.0356365756680430} 213 | } 214 | }; 215 | 216 | 217 | // 218 | // Sampling 219 | // 220 | #define SAMPLE_RATE 48000 // Hz, fixed to design of IIR filters 221 | #define SAMPLE_BITS 32 // bits 222 | #define SAMPLE_T int32_t 223 | #define SAMPLES_SHORT (SAMPLE_RATE / 8) // ~125ms 224 | #define SAMPLES_LEQ (SAMPLE_RATE * LEQ_PERIOD) 225 | #define DMA_BANK_SIZE (SAMPLES_SHORT / 16) 226 | #define DMA_BANKS 32 227 | 228 | // Data we push to 'samples_queue' 229 | struct sum_queue_t { 230 | // Sum of squares of mic samples, after Equalizer filter 231 | float sum_sqr_SPL; 232 | // Sum of squares of weighted mic samples 233 | float sum_sqr_weighted; 234 | // Debug only, FreeRTOS ticks we spent processing the I2S data 235 | uint32_t proc_ticks; 236 | }; 237 | QueueHandle_t samples_queue; 238 | 239 | // Static buffer for block of samples 240 | float samples[SAMPLES_SHORT] __attribute__((aligned(4))); 241 | 242 | // 243 | // I2S Microphone sampling setup 244 | // 245 | void mic_i2s_init() { 246 | // Setup I2S to sample mono channel for SAMPLE_RATE * SAMPLE_BITS 247 | // NOTE: Recent update to Arduino_esp32 (1.0.2 -> 1.0.3) 248 | // seems to have swapped ONLY_LEFT and ONLY_RIGHT channels 249 | const i2s_config_t i2s_config = { 250 | mode: i2s_mode_t(I2S_MODE_MASTER | I2S_MODE_RX), 251 | sample_rate: SAMPLE_RATE, 252 | bits_per_sample: i2s_bits_per_sample_t(SAMPLE_BITS), 253 | channel_format: I2S_CHANNEL_FMT_ONLY_LEFT, 254 | communication_format: i2s_comm_format_t(I2S_COMM_FORMAT_I2S | I2S_COMM_FORMAT_I2S_MSB), 255 | intr_alloc_flags: ESP_INTR_FLAG_LEVEL1, 256 | dma_buf_count: DMA_BANKS, 257 | dma_buf_len: DMA_BANK_SIZE, 258 | use_apll: true, 259 | tx_desc_auto_clear: false, 260 | fixed_mclk: 0 261 | }; 262 | // I2S pin mapping 263 | const i2s_pin_config_t pin_config = { 264 | bck_io_num: I2S_SCK, 265 | ws_io_num: I2S_WS, 266 | data_out_num: -1, // not used 267 | data_in_num: I2S_SD 268 | }; 269 | 270 | i2s_driver_install(I2S_PORT, &i2s_config, 0, NULL); 271 | 272 | #if (MIC_TIMING_SHIFT > 0) 273 | // Undocumented (?!) manipulation of I2S peripheral registers 274 | // to fix MSB timing issues with some I2S microphones 275 | REG_SET_BIT(I2S_TIMING_REG(I2S_PORT), BIT(9)); 276 | REG_SET_BIT(I2S_CONF_REG(I2S_PORT), I2S_RX_MSB_SHIFT); 277 | #endif 278 | 279 | i2s_set_pin(I2S_PORT, &pin_config); 280 | 281 | //FIXME: There is a known issue with esp-idf and sampling rates, see: 282 | // https://github.com/espressif/esp-idf/issues/2634 283 | // In the meantime, the below line seems to set sampling rate at ~47999.992Hz 284 | // fifs_req=24576000, sdm0=149, sdm1=212, sdm2=5, odir=2 -> fifs_reached=24575996 285 | //NOTE: This seems to be fixed in ESP32 Arduino 1.0.4, esp-idf 3.2 286 | // Should be safe to remove... 287 | //#include 288 | //rtc_clk_apll_enable(1, 149, 212, 5, 2); 289 | } 290 | 291 | // 292 | // I2S Reader Task 293 | // 294 | // Rationale for separate task reading I2S is that IIR filter 295 | // processing cam be scheduled to different core on the ESP32 296 | // while main task can do something else, like update the 297 | // display in the example 298 | // 299 | // As this is intended to run as separate hihg-priority task, 300 | // we only do the minimum required work with the I2S data 301 | // until it is 'compressed' into sum of squares 302 | // 303 | // FreeRTOS priority and stack size (in 32-bit words) 304 | #define I2S_TASK_PRI 4 305 | #define I2S_TASK_STACK 2048 306 | // 307 | void mic_i2s_reader_task(void* parameter) { 308 | mic_i2s_init(); 309 | 310 | // Discard first block, microphone may have startup time (i.e. INMP441 up to 83ms) 311 | size_t bytes_read = 0; 312 | i2s_read(I2S_PORT, &samples, SAMPLES_SHORT * sizeof(int32_t), &bytes_read, portMAX_DELAY); 313 | 314 | while (true) { 315 | // Block and wait for microphone values from I2S 316 | // 317 | // Data is moved from DMA buffers to our 'samples' buffer by the driver ISR 318 | // and when there is requested ammount of data, task is unblocked 319 | // 320 | // Note: i2s_read does not care it is writing in float[] buffer, it will write 321 | // integer values to the given address, as received from the hardware peripheral. 322 | i2s_read(I2S_PORT, &samples, SAMPLES_SHORT * sizeof(SAMPLE_T), &bytes_read, portMAX_DELAY); 323 | 324 | TickType_t start_tick = xTaskGetTickCount(); 325 | 326 | // Convert (including shifting) integer microphone values to floats, 327 | // using the same buffer (assumed sample size is same as size of float), 328 | // to save a bit of memory 329 | SAMPLE_T* int_samples = (SAMPLE_T*)&samples; 330 | for(int i=0; i 0) 365 | display.init(); 366 | #if (OLED_FLIP_V > 0) 367 | display.flipScreenVertically(); 368 | #endif 369 | display.setFont(ArialMT_Plain_16); 370 | #endif 371 | 372 | // Create FreeRTOS queue 373 | samples_queue = xQueueCreate(8, sizeof(sum_queue_t)); 374 | 375 | // Create the I2S reader FreeRTOS task 376 | // NOTE: Current version of ESP-IDF will pin the task 377 | // automatically to the first core it happens to run on 378 | // (due to using the hardware FPU instructions). 379 | // For manual control see: xTaskCreatePinnedToCore 380 | xTaskCreate(mic_i2s_reader_task, "Mic I2S Reader", I2S_TASK_STACK, NULL, I2S_TASK_PRI, NULL); 381 | 382 | sum_queue_t q; 383 | uint32_t Leq_samples = 0; 384 | double Leq_sum_sqr = 0; 385 | double Leq_dB = 0; 386 | 387 | // Read sum of samaples, calculated by 'i2s_reader_task' 388 | while (xQueueReceive(samples_queue, &q, portMAX_DELAY)) { 389 | 390 | // Calculate dB values relative to MIC_REF_AMPL and adjust for microphone reference 391 | double short_RMS = sqrt(double(q.sum_sqr_SPL) / SAMPLES_SHORT); 392 | double short_SPL_dB = MIC_OFFSET_DB + MIC_REF_DB + 20 * log10(short_RMS / MIC_REF_AMPL); 393 | 394 | // In case of acoustic overload or below noise floor measurement, report infinty Leq value 395 | if (short_SPL_dB > MIC_OVERLOAD_DB) { 396 | Leq_sum_sqr = INFINITY; 397 | } else if (isnan(short_SPL_dB) || (short_SPL_dB < MIC_NOISE_DB)) { 398 | Leq_sum_sqr = -INFINITY; 399 | } 400 | 401 | // Accumulate Leq sum 402 | Leq_sum_sqr += q.sum_sqr_weighted; 403 | Leq_samples += SAMPLES_SHORT; 404 | 405 | // When we gather enough samples, calculate new Leq value 406 | if (Leq_samples >= SAMPLE_RATE * LEQ_PERIOD) { 407 | double Leq_RMS = sqrt(Leq_sum_sqr / Leq_samples); 408 | Leq_dB = MIC_OFFSET_DB + MIC_REF_DB + 20 * log10(Leq_RMS / MIC_REF_AMPL); 409 | Leq_sum_sqr = 0; 410 | Leq_samples = 0; 411 | 412 | // Serial output, customize (or remove) as needed 413 | Serial.printf("%.1f\n", Leq_dB); 414 | 415 | // Debug only 416 | //Serial.printf("%u processing ticks\n", q.proc_ticks); 417 | } 418 | 419 | #if (USE_DISPLAY > 0) 420 | 421 | // 422 | // Example code that displays the measured value. 423 | // You should customize the below code for your display 424 | // and display library used. 425 | // 426 | 427 | display.clear(); 428 | 429 | // It is important to somehow notify when the deivce is out of its range 430 | // as the calculated values are very likely with big error 431 | if (Leq_dB > MIC_OVERLOAD_DB) { 432 | // Display 'Overload' if dB value is over the AOP 433 | display.drawString(0, 24, "Overload"); 434 | } else if (isnan(Leq_dB) || (Leq_dB < MIC_NOISE_DB)) { 435 | // Display 'Low' if dB value is below noise floor 436 | display.drawString(0, 24, "Low"); 437 | } 438 | 439 | // The 'short' Leq line 440 | double short_Leq_dB = MIC_OFFSET_DB + MIC_REF_DB + 20 * log10(sqrt(double(q.sum_sqr_weighted) / SAMPLES_SHORT) / MIC_REF_AMPL); 441 | uint16_t len = min(max(0, int(((short_Leq_dB - MIC_NOISE_DB) / MIC_OVERLOAD_DB) * (display.getWidth()-1))), display.getWidth()-1); 442 | display.drawHorizontalLine(0, 0, len); 443 | display.drawHorizontalLine(0, 1, len); 444 | display.drawHorizontalLine(0, 2, len); 445 | 446 | // The Leq numeric decibels 447 | display.drawString(0, 4, String(Leq_dB, 1) + " " + DB_UNITS); 448 | 449 | display.display(); 450 | 451 | #endif // USE_DISPLAY 452 | } 453 | } 454 | 455 | void loop() { 456 | // Nothing here.. 457 | } 458 | -------------------------------------------------------------------------------- /math/c_weighting.m: -------------------------------------------------------------------------------- 1 | % 2 | % C-weighting IIR filter design 3 | % 4 | % (c)2019 Ivan Kostoski 5 | % 6 | 7 | clear; 8 | format long; 9 | pi = 3.14159265358979; 10 | 11 | % Sampling Rate 12 | Fs = 48000; 13 | 14 | % IEC specified frequencies 15 | IEC_f = [10, 12.5, 16, 20, 25, 31.5, 40, 50, 63, 80, ... 16 | 100, 125, 160, 200, 250, 315, 400, 500, 630, 800, ... 17 | 1000, 1250, 1600, 2000, 2500, 3150, 4000, 5000, 6300, 8000, ... 18 | 10000, 12500, 16000, 20000]; 19 | 20 | % Logarithmic frequencies for graphs 21 | f = logspace(0, 5, 2048); 22 | 23 | % IEC specified attenuation for C-weighting 24 | IEC_f_cw = [-14.3, -11.2, -8.5, -6.2, -4.4, -3.0, -2.0, -1.3, -.8, -.5, ... 25 | -.3, -.2, -.1, 0, 0, 0, 0, 0, 0, 0, ... 26 | 0, 0, -.1, -.2, -.3, -.5, -.8, -1.3, -2.0, -3.0, ... 27 | -4.4, -6.2, -8.5, -11.2]; 28 | 29 | % Analog C-weighting filter according to IEC/CD 1672. 30 | f1 = 20.598997; %Hz 31 | f2 = 107.65265; %Hz 32 | f3 = 737.86223; %Hz 33 | f4 = 12194.217; %Hz 34 | C1000 = 0.0619; 35 | NUM = [(2*pi*f4)^2*(10^(C1000/20)), 0, 0]; 36 | DEN = conv([1, +4*pi*f4, (2*pi*f4)^2], [1, +4*pi*f1, (2*pi*f1)^2]); 37 | % Analog transfer function 38 | H_a = freqs(NUM, DEN, f.*(2*pi)); 39 | 40 | % Bilinear transformation of analog design to get the digital 41 | [B_bt, A_bt] = bilinear(NUM, DEN, 1/Fs); 42 | H_bt = freqz(B_bt, A_bt, f, Fs); 43 | 44 | % We will take the only the low frequency part of bilinear transformation 45 | % Which was calculated to be approximately (the first SOS): 46 | B_lo = [1, -2, 1]; 47 | A_lo = [1, -1.9946144559930206, 0.9946217070140836]; 48 | [sos_lo, gain_lo] = tf2sos(B_lo, A_lo); 49 | 50 | % 51 | % Curve fitting of the 'high' frequency part with invfreqz 52 | % 53 | f_hi = [1000, 1250, 10000, 16000, 20000, 24000]; 54 | dB_hi = [ 0, 0, -4.4, -8.6, -11.3, -15.0]; 55 | w_hi = f_hi.*((2*pi)/Fs); 56 | mag_hi = arrayfun(@db2mag, dB_hi); 57 | [B_hi, A_hi] = invfreqz(mag_hi, w_hi, 4, 4); 58 | [sos_hi, gain_hi] = tf2sos(B_hi, A_hi); 59 | 60 | % Merge SOS sections 61 | sos = [sos_lo; sos_hi] 62 | % Multiply the gain and reduce it a bit 63 | gain = gain_lo * gain_hi * 0.996 64 | 65 | % Convert to transfer function and try to stabilize 66 | [B_tf, A_tf] = sos2tf(sos, gain); 67 | B_tf_s = polystab(B_tf) * norm(B_tf) / norm(polystab(B_tf)); 68 | A_tf_s = polystab(A_tf) * norm(A_tf) / norm(polystab(A_tf)); 69 | A_tf_s0 = A_tf_s(1); 70 | % Caluclate and display stable coefficients 71 | B = B_tf_s./A_tf_s0 72 | A = A_tf_s./A_tf_s0 73 | % Display the roots 74 | roots(B) 75 | roots(A) 76 | H = freqz(B, A, f, Fs); 77 | 78 | % Frequency response graph 79 | clf; 80 | hold on; 81 | grid on; 82 | xlim([10, Fs/2]); 83 | ylim([-15, 5]); 84 | xlabel('Frequency (Hz)'); 85 | ylabel('Magnitude (dB)'); 86 | semilogx(f, 20*log10(abs(H_a)), 'g;IEC specified transfer function for C-weighting;'); 87 | semilogx(f, 20*log10(abs(H_bt)), 'r;Bilinear trasformation;'); 88 | semilogx(f, 20*log10(abs(H)), 'b;High frequency part curve fitting with invfreqz;'); 89 | hold off 90 | 91 | % Filter error graph 92 | clf; 93 | hold on; 94 | grid on; 95 | grid minor; 96 | xlim([10, 20000]); 97 | ylim([-1, +1]); 98 | xlabel('Frequency (Hz)'); 99 | ylabel('Filter error (dB)'); 100 | semilogx(f, 20*log10(abs(H_bt)) - 20*log10(abs(H_a)), 'r;Error with just bilinear trasformation filter;'); 101 | semilogx(f, 20*log10(abs(H)) - 20*log10(abs(H_a)), 'b;Error with additional curve fitting via invfreqz;'); 102 | hold off; 103 | 104 | % Display the sections 105 | [sos1, gain1] = tf2sos(B, A) 106 | -------------------------------------------------------------------------------- /math/ics43432.m: -------------------------------------------------------------------------------- 1 | % 2 | % ICS-43432 Equalizer filter design 3 | % 4 | % (c)2019 Ivan Kostoski 5 | % 6 | 7 | clear; 8 | Fs = 48000; 9 | format long G; 10 | 11 | % IEC specified frequencies 12 | iec_f = [10, 12.5, 16, 20, 25, 31.5, 40, 50, 63, 80, ... 13 | 100, 125, 160, 200, 250, 315, 400, 500, 630, 800, ... 14 | 1000, 1250, 1600, 2000, 2500, 3150, 4000, 5000, 6300, 8000, ... 15 | 10000, 12500, 16000, 20000]; 16 | 17 | % Values visually estimated from ICS-43432 datasheet for IEC frequencies 18 | % https://www.invensense.com/wp-content/uploads/2015/02/ICS-43432-data-sheet-v1.3.pdf 19 | % Figure 5 on page 9 20 | % 10, 12.5, 16, 20, 25, 31.5, 40, 50, 63, 80, 21 | ds_e_dB = [ -22, -19, -15, -12, -8, -6, -4.5, -3.5, -2.1, -1.1, ... 22 | -0.4, +0.1, +0.6, +0.9, +1.0, 0.9, +0.8, +0.6, +0.4, +0.3, ... 23 | 0, +0.3, +0.4, +0.5, +0.7, +1.0, +1.2, +1.4, +1.8, +2.3, ... 24 | +3.5, +6.0, +9.0, +14.0]; 25 | 26 | % Manually chosen and adjusted values for fitting the transfer function 27 | ds_f = [ 20, 100, 630, 1150, 2000, 10000, 20000]; 28 | ds_dB = [-16, -0.5, +0.7, 0, +0.5, +3.5, +14]; 29 | [ds_B, ds_A] = invfreqz(arrayfun(@db2mag, ds_dB), (ds_f.*((2*pi)/Fs)), 6, 4); 30 | % Stabilize polynoms 31 | ds_Bs = polystab(ds_B) * norm(ds_B) / norm(polystab(ds_B)); 32 | ds_As = polystab(ds_A) * norm(ds_A) / norm(polystab(ds_A)); 33 | ds_H = freqz(ds_Bs, ds_As, iec_f, Fs); 34 | 35 | % Equalizer filter, i.e. inverse from estimated transfer filter 36 | % Swap A and B coefficients, and normalize to ds_B(1) 37 | eq_B = ds_As./ds_Bs(1) 38 | eq_A = ds_Bs./ds_Bs(1) 39 | eq_H = freqz(eq_B, eq_A, iec_f, Fs); 40 | % Check for poles ouside unit circle 41 | roots(eq_B) 42 | roots(eq_A) 43 | 44 | clf; 45 | hold on; 46 | semilogx(iec_f, ds_e_dB, 'g;ICS-43432 Datasheet plot (estimated);'); 47 | semilogx(iec_f, 20 * log10 (abs (ds_H)), 'r;IIR filter frequency response;'); 48 | semilogx(iec_f, (ds_e_dB + 20*log10(abs(eq_H))), 'b;Adjusted frequency response;', 'linewidth', 3); 49 | title("ICS-43432 Adjusted frequency response"); 50 | grid minor; 51 | xlabel('Frequency (Hz)'); 52 | xlim([10, 20000]); 53 | ylabel('Amplitude (dB)'); 54 | ylim([-20, 20]); 55 | legend ('boxoff'); 56 | legend ('location', 'northwest'); 57 | ylim ([-20, 20]); 58 | grid on; 59 | hold off; 60 | 61 | [sos, gain] = tf2sos(eq_B, eq_A) 62 | -------------------------------------------------------------------------------- /math/ics43434.m: -------------------------------------------------------------------------------- 1 | % 2 | % ICS-43434 Equalizer filter design 3 | % 4 | % (c)2019 Ivan Kostoski 5 | % 6 | 7 | clear; 8 | % Sampling frequency 9 | Fs = 48000; 10 | 11 | % IEC specified frequencies 12 | iec_f = [10, 12.5, 16, 20, 25, 31.5, 40, 50, 63, 80, ... 13 | 100, 125, 160, 200, 250, 315, 400, 500, 630, 800, ... 14 | 1000, 1250, 1600, 2000, 2500, 3150, 4000, 5000, 6300, 8000, ... 15 | 10000, 12500, 16000, 20000]; 16 | 17 | % IEC Class 1 tolerances (top/bottom) 18 | iec_c1_t_dB = [+3.5, +3.0, +2.5, +2.5, +2.5, +2.0, +1.5, +1.5, +1.5, +1.5, ... 19 | +1.5, +1.5, +1.5, +1.5, +1.4, +1.4, +1.4, +1.4, +1.4, +1.4, ... 20 | +1.1, +1.4, +1.4, +1.6, +1.6, +1.6, +1.6, +2.1, +2.1, +2.1, ... 21 | +2.6, +3.0, +3.5, +4.0]; 22 | iec_c1_b_dB = [-inf, -inf, -4.5, -2.5, -2.5, -2.0, -1.5, -1.5, -1.5, -1.5, ... 23 | -1.5, -1.5, -1.5, -1.5, -1.4, -1.4, -1.4, -1.4, -1.4, -1.4, ... 24 | -1.1, -1.4, -1.4, -1.6, -1.6, -1.6, -1.6, -2.1, -2.6, -3.1, ... 25 | -3.6, -6.0, -17, -inf]; 26 | 27 | % IEC Class 2 tolerances (top/bottom) 28 | iec_c2_t_dB = [+5.5, +5.5, +5.5, +3.5, +3.5, +3.5, +2.5, +2.5, +2.5, +2.5, ... 29 | +2.0, +2.0, +2.0, +2.0, +1.9, +1.9, +1.9, +1.9, +1.9, +1.9, ... 30 | +1.4, +1.9, +2.6, +2.6, +3.1, +3.1, +3.6, +4.1, +5.1, +5.6, ... 31 | +6.0, +6.0, +6.0, +6.0]; 32 | iec_c2_b_dB = [-inf, -inf, -inf, -3.5, -3.5, -3.5, -2.5, -2.5, -2.5, -2.5, ... 33 | -2.0, -2.0, -2.0, -2.0, -1.9, -1.9, -1.9, -1.9, -1.9, -1.9, ... 34 | -1.4, -1.9, -2.6, -2.6, -3.1, -3.1, -3.6, -4.1, -5.1, -5.6, ... 35 | -inf, -inf, -inf, -inf]; 36 | 37 | % Values visually estimated from ICS-43434 datasheet 'Typical Frequency Response' plot 38 | ds_dB = [ -26, -22, -17, -13, -10, -8, -6, -4, -2.8, -2.1, ... 39 | -1.8, -1.4, -1.0, -0.5, -0.5, 0, 0, 0, 0, 0, ... 40 | 0, 0, 0, 0, 0, +0.5, +0.6, +1.1, +1.8, +2.5, ... 41 | +3.1, +4.5, +8.0, +14.0]; 42 | 43 | % These value are selected and adjusted for better curve fit 44 | ds_l_f = [ 10, 20, 50, 100, 1000]; 45 | ds_l_dB = [-26, -12, -3.5, -1.5, 0]; 46 | ds_h_f = [ 1000, 5000, 10000, 20000]; 47 | ds_h_dB = [ 0, +1.1, +3.1, +14.0]; 48 | 49 | % Low frequency filter design 50 | % Convert Hz in rad/s and normalize for Fs 51 | ds_l_w = ds_l_f.*((2*pi)/Fs); 52 | % Convert plot decibels to magnitude 53 | ds_l_mag = arrayfun(@db2mag, ds_l_dB); 54 | % Estimate coefficients 55 | [ds_l_B, ds_l_A] = invfreqz(ds_l_mag, ds_l_w, 2, 2); 56 | % Stabilize and normalize the filter 57 | ds_l_As = polystab(ds_l_A) * norm(ds_l_A) / norm(polystab(ds_l_A)); 58 | ds_l_Bs = polystab(ds_l_B) * norm(ds_l_B) / norm(polystab(ds_l_B)); 59 | 60 | % High frequency filter design 61 | [ds_h_B, ds_h_A] = invfreqz(arrayfun(@db2mag, ds_h_dB), (ds_h_f.*((2*pi)/Fs)) , 2, 2); 62 | ds_h_As = polystab(ds_h_A) * norm(ds_h_A) / norm(polystab(ds_h_A)); 63 | ds_h_Bs = polystab(ds_h_B) * norm(ds_h_B) / norm(polystab(ds_h_B)); 64 | 65 | % Convolve into single 4th order filter 66 | ds_A = conv(ds_l_As, ds_h_As); 67 | ds_B = conv(ds_l_Bs, ds_h_Bs); 68 | ds_H = freqz(ds_B, ds_A, iec_f, Fs); 69 | 70 | % Equalizer filter, i.e. inverse from estimated transfer filter 71 | % Swap A and B coefficients, and normalize to ds_B(1) 72 | eq_B = ds_A./ds_B(1) 73 | eq_A = ds_B./ds_B(1) 74 | eq_H = freqz(eq_B, eq_A, iec_f, Fs); 75 | % Check for poles ouside unit circle 76 | roots(eq_B) 77 | roots(eq_A) 78 | 79 | clf; 80 | semilogx(iec_f, ds_dB, 'g;ICS-43434 Datasheet plot (approx.);'); 81 | hold on; 82 | title("ICS-43434 Frequency response"); 83 | grid minor; 84 | xlabel('Frequency (Hz)'); 85 | xlim([10, 20000]); 86 | ylabel('Amplitude (dB)'); 87 | ylim([-20, 20]); 88 | legend ('boxoff'); 89 | legend ('location', 'northwest'); 90 | semilogx(iec_f, iec_c1_t_dB, '--r;IEC 61672-1:2013 Class 1 tolerance;'); 91 | semilogx(iec_f, iec_c1_b_dB, '--r'); 92 | semilogx(iec_f, iec_c2_t_dB, 'r;IEC 61672-1:2013 Class 2 tolerance;'); 93 | semilogx(iec_f, iec_c2_b_dB, 'r'); 94 | semilogx(iec_f, 20*log10(abs(ds_H)), '--c;IIR filter frequency response;'); 95 | semilogx(iec_f, (ds_dB + 20*log10(abs(eq_H))), 'b;Adjusted frequency response;', 'linewidth', 3); 96 | hold off; 97 | -------------------------------------------------------------------------------- /math/im69d130.m: -------------------------------------------------------------------------------- 1 | % 2 | % IM69D130 Equalizer filter design 3 | % 4 | % (c)2019 Ivan Kostoski 5 | % 6 | 7 | clear; 8 | clf; 9 | format long; 10 | pi = 3.14159265358979; 11 | 12 | % Sampling Rate 13 | Fs = 48000; 14 | 15 | % IEC specified frequencies 16 | iec_f = [10, 12.5, 16, 20, 25, 31.5, 40, 50, 63, 80, ... 17 | 100, 125, 160, 200, 250, 315, 400, 500, 630, 800, ... 18 | 1000, 1250, 1600, 2000, 2500, 3150, 4000, 5000, 6300, 8000, ... 19 | 10000, 12500, 16000, 20000]; 20 | 21 | % IEC Class 1 tolerances (top/bottom) 22 | iec_c1_t_dB = [+3.5, +3.0, +2.5, +2.5, +2.5, +2.0, +1.5, +1.5, +1.5, +1.5, ... 23 | +1.5, +1.5, +1.5, +1.5, +1.4, +1.4, +1.4, +1.4, +1.4, +1.4, ... 24 | +1.1, +1.4, +1.4, +1.6, +1.6, +1.6, +1.6, +2.1, +2.1, +2.1, ... 25 | +2.6, +3.0, +3.5, +4.0]; 26 | iec_c1_b_dB = [-inf, -inf, -4.5, -2.5, -2.5, -2.0, -1.5, -1.5, -1.5, -1.5, ... 27 | -1.5, -1.5, -1.5, -1.5, -1.4, -1.4, -1.4, -1.4, -1.4, -1.4, ... 28 | -1.1, -1.4, -1.4, -1.6, -1.6, -1.6, -1.6, -2.1, -2.6, -3.1, ... 29 | -3.6, -6.0, -17, -inf]; 30 | 31 | % IEC Class 2 tolerances (top/bottom) 32 | iec_c2_t_dB = [+5.5, +5.5, +5.5, +3.5, +3.5, +3.5, +2.5, +2.5, +2.5, +2.5, ... 33 | +2.0, +2.0, +2.0, +2.0, +1.9, +1.9, +1.9, +1.9, +1.9, +1.9, ... 34 | +1.4, +1.9, +2.6, +2.6, +3.1, +3.1, +3.6, +4.1, +5.1, +5.6, ... 35 | +6.0, +6.0, +6.0, +6.0]; 36 | iec_c2_b_dB = [-inf, -inf, -inf, -3.5, -3.5, -3.5, -2.5, -2.5, -2.5, -2.5, ... 37 | -2.0, -2.0, -2.0, -2.0, -1.9, -1.9, -1.9, -1.9, -1.9, -1.9, ... 38 | -1.4, -1.9, -2.6, -2.6, -3.1, -3.1, -3.6, -4.1, -5.1, -5.6, ... 39 | -inf, -inf, -inf, -inf]; 40 | 41 | % Values visually estimated from datasheet 42 | ds_dB = [ -inf, -inf, -inf, -5, -3.2, -2.5, -1.8, -1.1, -0.8, -0.6, ... 43 | -0.4, -0.2, -0.1, 0, 0, 0, 0, 0, 0, 0, ... 44 | 0, 0, 0, 0, 0, 0, 0, 0, -0.1, -0.2, ... 45 | -0.3, -0.4, +0.8, +2.5]; 46 | 47 | % These value are selected and adjusted for better curve fit 48 | ds_l_w = [ 20, 31.5, 50, 1000]; 49 | ds_l_dB = [ -4, -3.2, -1.1, 0]; 50 | 51 | % Low frequency filter design 52 | % Convert Hz in rad/s and normalize for Fs 53 | ds_l_wn = ds_l_w.*((2*pi)/Fs); 54 | % Convert plot decibels to magnitude 55 | ds_l_mag = arrayfun(@db2mag, ds_l_dB); 56 | % Estimate coefficients 57 | [ds_l_B, ds_l_A] = invfreqz(ds_l_mag, ds_l_wn, 2, 2); 58 | % Stabilize and normalize the filter 59 | ds_B = polystab(ds_l_B) * norm(ds_l_B) / norm(polystab(ds_l_B)); 60 | ds_A = polystab(ds_l_A) * norm(ds_l_A) / norm(polystab(ds_l_A)); 61 | ds_H = freqz(ds_B, ds_A, iec_f, Fs); 62 | 63 | % Equalizer filter, i.e. inverse from estimated transfer filter 64 | % Swap A and B coefficients, and normalize to ds_B(1) 65 | eq_B = ds_A./ds_B(1) 66 | eq_A = ds_B./ds_B(1) 67 | % eq_B = 1.001240684967618 -1.996936108836719 0.995703101823296 68 | % eq_A = 1.000000000000000 -1.997675693595923 0.997677044195944 69 | eq_H = freqz(eq_B, eq_A, iec_f, Fs); 70 | % Check for poles ouside unit circle 71 | roots(eq_B) 72 | roots(eq_A) 73 | 74 | 75 | clf; 76 | semilogx(iec_f, ds_dB, 'g;IM69D130 Datasheet plot (approx.);'); 77 | hold on; 78 | title("IM69D130 Adjusted Frequency Response"); 79 | grid minor; 80 | xlabel('Frequency (Hz)'); 81 | xlim([10, 24000]); 82 | ylabel('Amplitude (dB)'); 83 | ylim([-20, 20]); 84 | legend ('boxoff'); 85 | legend ('location', 'northwest'); 86 | semilogx(iec_f, iec_c1_t_dB, '--r;IEC 61672-1:2013 Class 1 tolerance;'); 87 | semilogx(iec_f, iec_c1_b_dB, '--r'); 88 | semilogx(iec_f, iec_c2_t_dB, 'r;IEC 61672-1:2013 Class 2 tolerance;'); 89 | semilogx(iec_f, iec_c2_b_dB, 'r'); 90 | semilogx(iec_f, 20*log10(abs(ds_H)), '--c;IIR filter frequency response;'); 91 | semilogx(iec_f, (ds_dB + 20*log10(abs(eq_H))), 'b;Adjusted frequency response;', 'linewidth', 1); 92 | hold off; 93 | 94 | [sos, gain] = tf2sos(eq_B, eq_A) 95 | -------------------------------------------------------------------------------- /math/inmp441.m: -------------------------------------------------------------------------------- 1 | % 2 | % INMP441 Equalizer filter design 3 | % 4 | % (c)2019 Ivan Kostoski 5 | % 6 | 7 | clear; 8 | % Sampling frequency 9 | Fs = 48000; 10 | 11 | % IEC specified frequencies 12 | iec_f = [10, 12.5, 16, 20, 25, 31.5, 40, 50, 63, 80, ... 13 | 100, 125, 160, 200, 250, 315, 400, 500, 630, 800, ... 14 | 1000, 1250, 1600, 2000, 2500, 3150, 4000, 5000, 6300, 8000, ... 15 | 10000, 12500, 16000, 20000]; 16 | 17 | % Values visually estimated from INMP441 datasheet 'Typical Frequency Response' plot 18 | % 10, 12.5, 16, 20, 25, 31.5, 40, 50, 63, 80, ... 19 | ds_dB = [ -inf, -inf, -inf, -12, -10, -8, -6, -4.4, -3.4, -2.5, ... 20 | -1.9, -1.4, -0.9, -0.5, -0.2, 0, 0, 0, 0, 0, ... 21 | 0, 0, 0, 0, 0, 0, -0.4, -0.7, -1.1, -1.8, ... 22 | -2.4, -3.0, -5.0, -inf]; 23 | 24 | % These value are selected and adjusted for better curve fit 25 | ds_l_f = [ 20, 50, 100, 1000]; 26 | ds_l_dB = [ -13, -4.1, -1.8, 0]; 27 | 28 | % Low frequency filter design 29 | % Convert Hz in rad/s and normalize for Fs 30 | ds_l_w = ds_l_f.*((2*pi)/Fs); 31 | % Convert plot decibels to magnitude 32 | ds_l_mag = arrayfun(@db2mag, ds_l_dB); 33 | % Estimate coefficients 34 | [ds_l_B, ds_l_A] = invfreqz(ds_l_mag, ds_l_w, 2, 2); 35 | % Stabilize and normalize the filter 36 | ds_A = polystab(ds_l_A) * norm(ds_l_A) / norm(polystab(ds_l_A)); 37 | ds_B = polystab(ds_l_B) * norm(ds_l_B) / norm(polystab(ds_l_B)); 38 | ds_H = freqz(ds_B, ds_A, iec_f, Fs); 39 | 40 | % Equalizer filter, i.e. inverse from estimated transfer filter 41 | % Swap A and B coefficients, and normalize to ds_B(1) 42 | eq_B = ds_A./ds_B(1) 43 | eq_A = ds_B./ds_B(1) 44 | eq_H = freqz(eq_B, eq_A, iec_f, Fs); 45 | 46 | clf; 47 | figure(1, 'position', [0,0,800,500]); 48 | title("INMP441 Frequency response"); 49 | grid minor; 50 | xlabel('Frequency (Hz)'); 51 | xlim([10, 20000]); 52 | ylabel('Magnitude (dB)'); 53 | ylim([-20, 20]); 54 | hold on; 55 | semilogx(iec_f, ds_dB, 'g;INMP441 Datasheet plot (approx.);'); 56 | semilogx(iec_f, 20*log10(abs(ds_H)), '--c;IIR filter frequency response;'); 57 | semilogx(iec_f, (ds_dB + 20*log10(abs(eq_H))), 'b;Adjusted frequency response;', 'linewidth', 3); 58 | legend ('boxoff'); 59 | legend ('location', 'northwest'); 60 | hold off; 61 | 62 | [sos, gain] = tf2sos(eq_B, eq_A) -------------------------------------------------------------------------------- /math/sph645lm4h-b.m: -------------------------------------------------------------------------------- 1 | % 2 | % SPH0645LM4H-B Equalizer filter design 3 | % 4 | % (c)2019 Ivan Kostoski 5 | % 6 | 7 | clear; 8 | format long; 9 | 10 | % Sampling frequency 11 | Fs = 48000; 12 | 13 | % IEC specified frequencies 14 | iec_f = [10, 12.5, 16, 20, 25, 31.5, 40, 50, 63, 80, ... 15 | 100, 125, 160, 200, 250, 315, 400, 500, 630, 800, ... 16 | 1000, 1250, 1600, 2000, 2500, 3150, 4000, 5000, 6300, 8000, ... 17 | 10000, 12500, 16000, 20000]; 18 | 19 | % IEC Class 1 tolerances (top/bottom) 20 | iec_c1_t_dB = [+3.5, +3.0, +2.5, +2.5, +2.5, +2.0, +1.5, +1.5, +1.5, +1.5, ... 21 | +1.5, +1.5, +1.5, +1.5, +1.4, +1.4, +1.4, +1.4, +1.4, +1.4, ... 22 | +1.1, +1.4, +1.4, +1.6, +1.6, +1.6, +1.6, +2.1, +2.1, +2.1, ... 23 | +2.6, +3.0, +3.5, +4.0]; 24 | iec_c1_b_dB = [-inf, -inf, -4.5, -2.5, -2.5, -2.0, -1.5, -1.5, -1.5, -1.5, ... 25 | -1.5, -1.5, -1.5, -1.5, -1.4, -1.4, -1.4, -1.4, -1.4, -1.4, ... 26 | -1.1, -1.4, -1.4, -1.6, -1.6, -1.6, -1.6, -2.1, -2.6, -3.1, ... 27 | -3.6, -6.0, -17, -inf]; 28 | 29 | % IEC Class 2 tolerances (top/bottom) 30 | iec_c2_t_dB = [+5.5, +5.5, +5.5, +3.5, +3.5, +3.5, +2.5, +2.5, +2.5, +2.5, ... 31 | +2.0, +2.0, +2.0, +2.0, +1.9, +1.9, +1.9, +1.9, +1.9, +1.9, ... 32 | +1.4, +1.9, +2.6, +2.6, +3.1, +3.1, +3.6, +4.1, +5.1, +5.6, ... 33 | +6.0, +6.0, +6.0, +6.0]; 34 | iec_c2_b_dB = [-inf, -inf, -inf, -3.5, -3.5, -3.5, -2.5, -2.5, -2.5, -2.5, ... 35 | -2.0, -2.0, -2.0, -2.0, -1.9, -1.9, -1.9, -1.9, -1.9, -1.9, ... 36 | -1.4, -1.9, -2.6, -2.6, -3.1, -3.1, -3.6, -4.1, -5.1, -5.6, ... 37 | -inf, -inf, -inf, -inf]; 38 | 39 | % Values visually estimated from ICS-43434 datasheet 'Typical Frequency Response' plot 40 | % 10, 12.5, 16, 20, 25, 31.5, 40, 50, 63, 80, ... 41 | ds_dB = [ -inf, -inf, -inf, -7.5, -6.5, -5, -3.6, -2.8, -2, -1.3, ... 42 | -1, -0.7, -0.4, -0.3, -0.1, -0.1, 0, 0, 0, 0, ... 43 | 0, 0, 0, 0, +0.1, +0.1, +0.3, +0.5, +0.8, +0.9, ... 44 | +1, +0.8, +0, -5.5]; 45 | 46 | % These value are selected and adjusted for better curve fit 47 | ds_l_f = [ 20, 50, 100, 1000]; 48 | ds_l_dB = [-7.5, -2.8, -1, 0]; 49 | 50 | % Low frequency filter design 51 | % Convert Hz in rad/s and normalize for Fs 52 | ds_l_wn = ds_l_f.*((2*pi)/Fs); 53 | % Convert plot decibels to magnitude 54 | ds_l_mag = arrayfun(@db2mag, ds_l_dB); 55 | % Estimate coefficients 56 | [ds_l_B, ds_l_A] = invfreqz(ds_l_mag, ds_l_wn, 2, 2); 57 | % Stabilize and normalize the filter 58 | ds_l_Bs = polystab(ds_l_B) * norm(ds_l_B) / norm(polystab(ds_l_B)); 59 | ds_l_As = polystab(ds_l_A) * norm(ds_l_A) / norm(polystab(ds_l_A)); 60 | 61 | % High frequency filter design 62 | %ds_h_f = [ 1000, 2000, 4000, 8000, 10000, 16000, 20000]; 63 | %ds_h_dB = [ 0, 0, +0.3, +0.9, +1, 0, -5.5]; 64 | %[ds_h_B, ds_h_A] = invfreqz(arrayfun(@db2mag, ds_h_dB), (ds_h_f.*((2*pi)/Fs)), 4, 3); 65 | %ds_h_Bs = polystab(ds_h_B) * norm(ds_h_B) / norm(polystab(ds_h_B)); 66 | %ds_h_As = polystab(ds_h_A) * norm(ds_h_A) / norm(polystab(ds_h_A)); 67 | 68 | % Convolve into single 4th order filter 69 | ds_B = ds_l_Bs % conv(ds_l_Bs, ds_h_Bs); 70 | ds_A = ds_l_As % conv(ds_l_As, ds_h_As); 71 | ds_H = freqz(ds_B, ds_A, iec_f, Fs); 72 | 73 | % Equalizer filter, i.e. inverse from estimated transfer filter 74 | % Swap A and B coefficients, and normalize to ds_B(1) 75 | eq_B = ds_A./ds_B(1) 76 | eq_A = ds_B./ds_B(1) 77 | % Check for poles ouside unit circle 78 | roots(eq_B) 79 | roots(eq_A) 80 | 81 | % Add DC blocking filter 82 | [sos, gain] = tf2sos(eq_B, eq_A) 83 | sos = [sos; [1.0, -1.0, 0.0, 1.0, -0.9992, 0]]; 84 | [eq_B, eq_A] = sos2tf(sos, gain) 85 | eq_H = freqz(eq_B, eq_A, iec_f, Fs); 86 | 87 | clf; 88 | semilogx(iec_f, ds_dB, 'g;SPH0645LM4H-B Datasheet plot (approx.);'); 89 | hold on; 90 | title("SPH0645LM4H-B Frequency response"); 91 | grid minor; 92 | xlabel('Frequency (Hz)'); 93 | xlim([10, 24000]); 94 | ylabel('Amplitude (dB)'); 95 | ylim([-30, 20]); 96 | legend ('boxoff'); 97 | legend ('location', 'northwest'); 98 | semilogx(iec_f, iec_c1_t_dB, '--r;IEC 61672-1:2013 Class 1 tolerance;'); 99 | semilogx(iec_f, iec_c1_b_dB, '--r'); 100 | semilogx(iec_f, iec_c2_t_dB, 'r;IEC 61672-1:2013 Class 2 tolerance;'); 101 | semilogx(iec_f, iec_c2_b_dB, 'r'); 102 | semilogx(iec_f, 20*log10(abs(ds_H)), '--c;IIR filter frequency response;'); 103 | semilogx(iec_f, (ds_dB + 20*log10(abs(eq_H))), 'b;Adjusted frequency response;', 'linewidth', 3); 104 | hold off; 105 | 106 | % Convert to Second-Order Sections 107 | [sos, gain] = tf2sos(eq_B, eq_A) -------------------------------------------------------------------------------- /misc/ics-43434-afr.svg: -------------------------------------------------------------------------------- 1 | 2 | 8 | 9 | Gnuplot 10 | Produced by GNUPLOT 5.0 patchlevel 7 11 | 12 | 13 | 14 | 15 | 16 | 17 | 18 | 19 | 20 | 21 | 22 | 23 | 24 | 25 | 26 | 27 | 28 | 29 | 30 | 31 | 32 | 33 | 34 | 35 | 36 | 37 | 38 | 39 | 40 | 41 | 42 | 43 | 44 | 45 | 46 | 47 | 48 | 49 | 50 | 51 | -20 52 | 53 | 54 | 55 | 56 | 57 | 58 | 59 | 60 | 61 | 62 | 63 | 64 | 65 | 66 | 67 | 68 | 69 | 70 | 71 | 72 | 73 | 74 | 75 | 76 | 77 | 78 | 79 | 80 | 81 | 82 | 83 | 84 | 85 | 86 | 87 | 88 | -15 89 | 90 | 91 | 92 | 93 | 94 | 95 | 96 | 97 | 98 | 99 | 100 | 101 | 102 | 103 | 104 | 105 | 106 | 107 | 108 | 109 | 110 | 111 | 112 | 113 | 114 | 115 | 116 | 117 | 118 | 119 | 120 | 121 | 122 | 123 | 124 | 125 | -10 126 | 127 | 128 | 129 | 130 | 131 | 132 | 133 | 134 | 135 | 136 | 137 | 138 | 139 | 140 | 141 | 142 | 143 | 144 | 145 | 146 | 147 | 148 | 149 | 150 | 151 | 152 | 153 | 154 | 155 | 156 | 157 | 158 | 159 | 160 | 161 | 162 | -5 163 | 164 | 165 | 166 | 167 | 168 | 169 | 170 | 171 | 172 | 173 | 174 | 175 | 176 | 177 | 178 | 179 | 180 | 181 | 182 | 183 | 184 | 185 | 186 | 187 | 188 | 189 | 190 | 191 | 192 | 193 | 194 | 195 | 196 | 197 | 198 | 199 | 0 200 | 201 | 202 | 203 | 204 | 205 | 206 | 207 | 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372 | 373 | 374 | 375 | 376 | 377 | 378 | 379 | 380 | 381 | 382 | 383 | 384 | 385 | 386 | 387 | 388 | 389 | 390 | 391 | 392 | 393 | 394 | 395 | 396 | 397 | 398 | 399 | 400 | 401 | 402 | 403 | 404 | 405 | 406 | 407 | 408 | 409 | 410 | 411 | 412 | 413 | 414 | 415 | 416 | 417 | 418 | 419 | 420 | 421 | 102 422 | 423 | 424 | 425 | 426 | 427 | 428 | 429 | 430 | 431 | 432 | 433 | 434 | 435 | 436 | 437 | 438 | 439 | 440 | 441 | 442 | 443 | 444 | 445 | 446 | 447 | 448 | 449 | 450 | 451 | 452 | 453 | 454 | 455 | 456 | 457 | 458 | 459 | 460 | 461 | 462 | 463 | 464 | 465 | 466 | 467 | 468 | 469 | 470 | 471 | 472 | 473 | 474 | 475 | 476 | 477 | 478 | 479 | 480 | 481 | 482 | 483 | 484 | 485 | 486 | 487 | 488 | 489 | 490 | 103 491 | 492 | 493 | 494 | 495 | 496 | 497 | 498 | 499 | 500 | 501 | 502 | 503 | 504 | 505 | 506 | 507 | 508 | 509 | 510 | 511 | 512 | 513 | 514 | 515 | 516 | 517 | 518 | 519 | 520 | 521 | 522 | 523 | 524 | 525 | 526 | 527 | 528 | 529 | 530 | 531 | 532 | 533 | 534 | 535 | 536 | 537 | 538 | 539 | 540 | 541 | 542 | 543 | 544 | 545 | 546 | 547 | 548 | 549 | 550 | 551 | 552 | 553 | 554 | 555 | 556 | 557 | 558 | 559 | 104 560 | 561 | 562 | 563 | 564 | 565 | 566 | 567 | 568 | 569 | 570 | 571 | 572 | 573 | 574 | Amplitude (dB) 575 | 576 | 577 | 578 | 579 | Frequency (Hz) 580 | 581 | 582 | 583 | 584 | ICS-43434 Frequency response 585 | 586 | 587 | 588 | 589 | ICS-43434 Datasheet plot (approx.) 590 | 591 | 592 | 593 | 594 | ICS-43434 Datasheet plot (approx.) 595 | 596 | 597 | 598 | 603 | 604 | 605 | 606 | IEC 61672-1:2013 Class 1 tolerance 607 | 608 | 609 | IEC 61672-1:2013 Class 1 tolerance 610 | 611 | 612 | 613 | 618 | 619 | 620 | 621 | gnuplot_plot_3a 622 | 623 | 627 | 628 | IEC 61672-1:2013 Class 2 tolerance 629 | 630 | 631 | IEC 61672-1:2013 Class 2 tolerance 632 | 633 | 634 | 635 | 640 | 641 | 642 | 643 | gnuplot_plot_5a 644 | 645 | 649 | 650 | IIR filter frequency response 651 | 652 | 653 | IIR filter frequency response 654 | 655 | 656 | 657 | 662 | 663 | 664 | 665 | Adjusted frequency response 666 | 667 | 668 | 669 | 670 | Adjusted frequency response 671 | 672 | 673 | 674 | 679 | 680 | 681 | 682 | 683 | 684 | 685 | 686 | 687 | 688 | 689 | 690 | 691 | 692 | 693 | 694 | 695 | 696 | 697 | 698 | 699 | -------------------------------------------------------------------------------- /sos-iir-filter.h: -------------------------------------------------------------------------------- 1 | /* 2 | * ESP32 Second-Order Sections IIR Filter implementation 3 | * 4 | * (c)2019 Ivan Kostoski 5 | * 6 | * This program is free software: you can redistribute it and/or modify 7 | * it under the terms of the GNU General Public License as published by 8 | * the Free Software Foundation, either version 3 of the License, or 9 | * (at your option) any later version. 10 | * 11 | * This program is distributed in the hope that it will be useful, 12 | * but WITHOUT ANY WARRANTY; without even the implied warranty of 13 | * MERCHANTABILITY or FITNESS FOR A PARTICULAR PURPOSE. See the 14 | * GNU General Public License for more details. 15 | * 16 | * You should have received a copy of the GNU General Public License 17 | * along with this program. If not, see . 18 | */ 19 | 20 | #ifndef SOS_IIR_FILTER_H 21 | #define SOS_IIR_FILTER_H 22 | 23 | #include 24 | 25 | struct SOS_Coefficients { 26 | float b1; 27 | float b2; 28 | float a1; 29 | float a2; 30 | }; 31 | 32 | struct SOS_Delay_State { 33 | float w0 = 0; 34 | float w1 = 0; 35 | }; 36 | 37 | extern "C" { 38 | int sos_filter_f32(float *input, float *output, int len, const SOS_Coefficients &coeffs, SOS_Delay_State &w); 39 | } 40 | __asm__ ( 41 | // 42 | // ESP32 implementation of IIR Second-Order Section filter 43 | // Assumes a0 and b0 coefficients are one (1.0) 44 | // 45 | // float* a2 = input; 46 | // float* a3 = output; 47 | // int a4 = len; 48 | // float* a5 = coeffs; 49 | // float* a6 = w; 50 | // float a7 = gain; 51 | // 52 | ".text \n" 53 | ".align 4 \n" 54 | ".global sos_filter_f32 \n" 55 | ".type sos_filter_f32,@function\n" 56 | "sos_filter_f32: \n" 57 | " entry a1, 16 \n" 58 | " lsi f0, a5, 0 \n" // float f0 = coeffs.b1; 59 | " lsi f1, a5, 4 \n" // float f1 = coeffs.b2; 60 | " lsi f2, a5, 8 \n" // float f2 = coeffs.a1; 61 | " lsi f3, a5, 12 \n" // float f3 = coeffs.a2; 62 | " lsi f4, a6, 0 \n" // float f4 = w[0]; 63 | " lsi f5, a6, 4 \n" // float f5 = w[1]; 64 | " loopnez a4, 1f \n" // for (; len>0; len--) { 65 | " lsip f6, a2, 4 \n" // float f6 = *input++; 66 | " madd.s f6, f2, f4 \n" // f6 += f2 * f4; // coeffs.a1 * w0 67 | " madd.s f6, f3, f5 \n" // f6 += f3 * f5; // coeffs.a2 * w1 68 | " mov.s f7, f6 \n" // f7 = f6; // b0 assumed 1.0 69 | " madd.s f7, f0, f4 \n" // f7 += f0 * f4; // coeffs.b1 * w0 70 | " madd.s f7, f1, f5 \n" // f7 += f1 * f5; // coeffs.b2 * w1 -> result 71 | " ssip f7, a3, 4 \n" // *output++ = f7; 72 | " mov.s f5, f4 \n" // f5 = f4; // w1 = w0 73 | " mov.s f4, f6 \n" // f4 = f6; // w0 = f6 74 | " 1: \n" // } 75 | " ssi f4, a6, 0 \n" // w[0] = f4; 76 | " ssi f5, a6, 4 \n" // w[1] = f5; 77 | " movi.n a2, 0 \n" // return 0; 78 | " retw.n \n" 79 | ); 80 | 81 | extern "C" { 82 | float sos_filter_sum_sqr_f32(float *input, float *output, int len, const SOS_Coefficients &coeffs, SOS_Delay_State &w, float gain); 83 | } 84 | __asm__ ( 85 | // 86 | // ESP32 implementation of IIR Second-Order section filter with applied gain. 87 | // Assumes a0 and b0 coefficients are one (1.0) 88 | // Returns sum of squares of filtered samples 89 | // 90 | // float* a2 = input; 91 | // float* a3 = output; 92 | // int a4 = len; 93 | // float* a5 = coeffs; 94 | // float* a6 = w; 95 | // float a7 = gain; 96 | // 97 | ".text \n" 98 | ".align 4 \n" 99 | ".global sos_filter_sum_sqr_f32 \n" 100 | ".type sos_filter_sum_sqr_f32,@function \n" 101 | "sos_filter_sum_sqr_f32: \n" 102 | " entry a1, 16 \n" 103 | " lsi f0, a5, 0 \n" // float f0 = coeffs.b1; 104 | " lsi f1, a5, 4 \n" // float f1 = coeffs.b2; 105 | " lsi f2, a5, 8 \n" // float f2 = coeffs.a1; 106 | " lsi f3, a5, 12 \n" // float f3 = coeffs.a2; 107 | " lsi f4, a6, 0 \n" // float f4 = w[0]; 108 | " lsi f5, a6, 4 \n" // float f5 = w[1]; 109 | " wfr f6, a7 \n" // float f6 = gain; 110 | " const.s f10, 0 \n" // float sum_sqr = 0; 111 | " loopnez a4, 1f \n" // for (; len>0; len--) { 112 | " lsip f7, a2, 4 \n" // float f7 = *input++; 113 | " madd.s f7, f2, f4 \n" // f7 += f2 * f4; // coeffs.a1 * w0 114 | " madd.s f7, f3, f5 \n" // f7 += f3 * f5; // coeffs.a2 * w1; 115 | " mov.s f8, f7 \n" // f8 = f7; // b0 assumed 1.0 116 | " madd.s f8, f0, f4 \n" // f8 += f0 * f4; // coeffs.b1 * w0; 117 | " madd.s f8, f1, f5 \n" // f8 += f1 * f5; // coeffs.b2 * w1; 118 | " mul.s f9, f8, f6 \n" // f9 = f8 * f6; // f8 * gain -> result 119 | " ssip f9, a3, 4 \n" // *output++ = f9; 120 | " mov.s f5, f4 \n" // f5 = f4; // w1 = w0 121 | " mov.s f4, f7 \n" // f4 = f7; // w0 = f7; 122 | " madd.s f10, f9, f9 \n" // f10 += f9 * f9; // sum_sqr += f9 * f9; 123 | " 1: \n" // } 124 | " ssi f4, a6, 0 \n" // w[0] = f4; 125 | " ssi f5, a6, 4 \n" // w[1] = f5; 126 | " rfr a2, f10 \n" // return sum_sqr; 127 | " retw.n \n" // 128 | ); 129 | 130 | 131 | /** 132 | * Envelops above asm functions into C++ class 133 | */ 134 | struct SOS_IIR_Filter { 135 | 136 | const int num_sos; 137 | const float gain; 138 | SOS_Coefficients* sos = NULL; 139 | SOS_Delay_State* w = NULL; 140 | 141 | // Dynamic constructor 142 | SOS_IIR_Filter(size_t num_sos, const float gain, const SOS_Coefficients _sos[] = NULL): num_sos(num_sos), gain(gain) { 143 | if (num_sos > 0) { 144 | sos = new SOS_Coefficients[num_sos]; 145 | if ((sos != NULL) && (_sos != NULL)) memcpy(sos, _sos, num_sos * sizeof(SOS_Coefficients)); 146 | w = new SOS_Delay_State[num_sos](); 147 | } 148 | }; 149 | 150 | // Template constructor for const filter declaration 151 | template 152 | SOS_IIR_Filter(const float gain, const SOS_Coefficients (&sos)[Array_Size]): SOS_IIR_Filter(Array_Size, gain, sos) {}; 153 | 154 | /** 155 | * Apply defined IIR Filter to input array of floats, write filtered values to output, 156 | * and return sum of squares of all filtered values 157 | */ 158 | inline float filter(float* input, float* output, size_t len) { 159 | if ((num_sos < 1) || (sos == NULL) || (w == NULL)) return 0; 160 | float* source = input; 161 | // Apply all but last Second-Order-Section 162 | for(int i=0; i<(num_sos-1); i++) { 163 | sos_filter_f32(source, output, len, sos[i], w[i]); 164 | source = output; 165 | } 166 | // Apply last SOS with gain and return the sum of squares of all samples 167 | return sos_filter_sum_sqr_f32(source, output, len, sos[num_sos-1], w[num_sos-1], gain); 168 | } 169 | 170 | ~SOS_IIR_Filter() { 171 | if (w != NULL) delete[] w; 172 | if (sos != NULL) delete[] sos; 173 | } 174 | 175 | }; 176 | 177 | // 178 | // For testing only 179 | // 180 | struct No_IIR_Filter { 181 | const int num_sos = 0; 182 | const float gain = 1.0; 183 | 184 | No_IIR_Filter() {}; 185 | 186 | inline float filter(float* input, float* output, size_t len) { 187 | float sum_sqr = 0; 188 | float s; 189 | for(int i=0; i