tmk_core/tool/mbed/mbed-sdk/libraries/dsp/cmsis_dsp/FilteringFunctions/arm_biquad_cascade_df1_32x64_q31.c

   1 /* ----------------------------------------------------------------------
   2 * Copyright (C) 2010-2013 ARM Limited. All rights reserved.
   3 *
   4 * $Date:        17. January 2013
   5 * $Revision:    V1.4.1
   6 *
   7 * Project:          CMSIS DSP Library
   8 * Title:            arm_biquad_cascade_df1_32x64_q31.c
   9 *
  10 * Description:  High precision Q31 Biquad cascade filter processing function
  11 *
  12 * Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
  13 *
  14 * Redistribution and use in source and binary forms, with or without
  15 * modification, are permitted provided that the following conditions
  16 * are met:
  17 *   - Redistributions of source code must retain the above copyright
  18 *     notice, this list of conditions and the following disclaimer.
  19 *   - Redistributions in binary form must reproduce the above copyright
  20 *     notice, this list of conditions and the following disclaimer in
  21 *     the documentation and/or other materials provided with the
  22 *     distribution.
  23 *   - Neither the name of ARM LIMITED nor the names of its contributors
  24 *     may be used to endorse or promote products derived from this
  25 *     software without specific prior written permission.
  26 *
  27 * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
  28 * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
  29 * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
  30 * FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
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  39 * -------------------------------------------------------------------- */
  40
  41 #include "arm_math.h"
  42
  43 /**
  44  * @ingroup groupFilters
  45  */
  46
  47 /**
  48  * @defgroup BiquadCascadeDF1_32x64 High Precision Q31 Biquad Cascade Filter
  49  *
  50  * This function implements a high precision Biquad cascade filter which operates on
  51  * Q31 data values.  The filter coefficients are in 1.31 format and the state variables
  52  * are in 1.63 format.  The double precision state variables reduce quantization noise
  53  * in the filter and provide a cleaner output.
  54  * These filters are particularly useful when implementing filters in which the
  55  * singularities are close to the unit circle.  This is common for low pass or high
  56  * pass filters with very low cutoff frequencies.
  57  *
  58  * The function operates on blocks of input and output data
  59  * and each call to the function processes <code>blockSize</code> samples through
  60  * the filter. <code>pSrc</code> and <code>pDst</code> points to input and output arrays
  61  * containing <code>blockSize</code> Q31 values.
  62  *
  63  * \par Algorithm
  64  * Each Biquad stage implements a second order filter using the difference equation:
  65  * <pre>
  66  *     y[n] = b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2]
  67  * </pre>
  68  * A Direct Form I algorithm is used with 5 coefficients and 4 state variables per stage.
  69  * \image html Biquad.gif "Single Biquad filter stage"
  70  * Coefficients <code>b0, b1, and b2 </code> multiply the input signal <code>x[n]</code> and are referred to as the feedforward coefficients.
  71  * Coefficients <code>a1</code> and <code>a2</code> multiply the output signal <code>y[n]</code> and are referred to as the feedback coefficients.
  72  * Pay careful attention to the sign of the feedback coefficients.
  73  * Some design tools use the difference equation
  74  * <pre>
  75  *     y[n] = b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] - a1 * y[n-1] - a2 * y[n-2]
  76  * </pre>
  77  * In this case the feedback coefficients <code>a1</code> and <code>a2</code> must be negated when used with the CMSIS DSP Library.
  78  *
  79  * \par
  80  * Higher order filters are realized as a cascade of second order sections.
  81  * <code>numStages</code> refers to the number of second order stages used.
  82  * For example, an 8th order filter would be realized with <code>numStages=4</code> second order stages.
  83  * \image html BiquadCascade.gif "8th order filter using a cascade of Biquad stages"
  84  * A 9th order filter would be realized with <code>numStages=5</code> second order stages with the coefficients for one of the stages configured as a first order filter (<code>b2=0</code> and <code>a2=0</code>).
  85  *
  86  * \par
  87  * The <code>pState</code> points to state variables array .
  88  * Each Biquad stage has 4 state variables <code>x[n-1], x[n-2], y[n-1],</code> and <code>y[n-2]</code> and each state variable in 1.63 format to improve precision.
  89  * The state variables are arranged in the array as:
  90  * <pre>
  91  *     {x[n-1], x[n-2], y[n-1], y[n-2]}
  92  * </pre>
  93  *
  94  * \par
  95  * The 4 state variables for stage 1 are first, then the 4 state variables for stage 2, and so on.
  96  * The state array has a total length of <code>4*numStages</code> values of data in 1.63 format.
  97  * The state variables are updated after each block of data is processed; the coefficients are untouched.
  98  *
  99  * \par Instance Structure
 100  * The coefficients and state variables for a filter are stored together in an instance data structure.
 101  * A separate instance structure must be defined for each filter.
 102  * Coefficient arrays may be shared among several instances while state variable arrays cannot be shared.
 103  *
 104  * \par Init Function
 105  * There is also an associated initialization function which performs the following operations:
 106  * - Sets the values of the internal structure fields.
 107  * - Zeros out the values in the state buffer.
 108  * To do this manually without calling the init function, assign the follow subfields of the instance structure:
 109  * numStages, pCoeffs, postShift, pState. Also set all of the values in pState to zero.
 110  *
 111  * \par
 112  * Use of the initialization function is optional.
 113  * However, if the initialization function is used, then the instance structure cannot be placed into a const data section.
 114  * To place an instance structure into a const data section, the instance structure must be manually initialized.
 115  * Set the values in the state buffer to zeros before static initialization.
 116  * For example, to statically initialize the filter instance structure use
 117  * <pre>
 118  *     arm_biquad_cas_df1_32x64_ins_q31 S1 = {numStages, pState, pCoeffs, postShift};
 119  * </pre>
 120  * where <code>numStages</code> is the number of Biquad stages in the filter; <code>pState</code> is the address of the state buffer;
 121  * <code>pCoeffs</code> is the address of the coefficient buffer; <code>postShift</code> shift to be applied which is described in detail below.
 122  * \par Fixed-Point Behavior
 123  * Care must be taken while using Biquad Cascade 32x64 filter function.
 124  * Following issues must be considered:
 125  * - Scaling of coefficients
 126  * - Filter gain
 127  * - Overflow and saturation
 128  *
 129  * \par
 130  * Filter coefficients are represented as fractional values and
 131  * restricted to lie in the range <code>[-1 +1)</code>.
 132  * The processing function has an additional scaling parameter <code>postShift</code>
 133  * which allows the filter coefficients to exceed the range <code>[+1 -1)</code>.
 134  * At the output of the filter's accumulator is a shift register which shifts the result by <code>postShift</code> bits.
 135  * \image html BiquadPostshift.gif "Fixed-point Biquad with shift by postShift bits after accumulator"
 136  * This essentially scales the filter coefficients by <code>2^postShift</code>.
 137  * For example, to realize the coefficients
 138  * <pre>
 139  *    {1.5, -0.8, 1.2, 1.6, -0.9}
 140  * </pre>
 141  * set the Coefficient array to:
 142  * <pre>
 143  *    {0.75, -0.4, 0.6, 0.8, -0.45}
 144  * </pre>
 145  * and set <code>postShift=1</code>
 146  *
 147  * \par
 148  * The second thing to keep in mind is the gain through the filter.
 149  * The frequency response of a Biquad filter is a function of its coefficients.
 150  * It is possible for the gain through the filter to exceed 1.0 meaning that the filter increases the amplitude of certain frequencies.
 151  * This means that an input signal with amplitude < 1.0 may result in an output > 1.0 and these are saturated or overflowed based on the implementation of the filter.
 152  * To avoid this behavior the filter needs to be scaled down such that its peak gain < 1.0 or the input signal must be scaled down so that the combination of input and filter are never overflowed.
 153  *
 154  * \par
 155  * The third item to consider is the overflow and saturation behavior of the fixed-point Q31 version.
 156  * This is described in the function specific documentation below.
 157  */
 158
 159 /**
 160  * @addtogroup BiquadCascadeDF1_32x64
 161  * @{
 162  */
 163
 164 /**
 165  * @details
 166
 167  * @param[in]  *S points to an instance of the high precision Q31 Biquad cascade filter.
 168  * @param[in]  *pSrc points to the block of input data.
 169  * @param[out] *pDst points to the block of output data.
 170  * @param[in]  blockSize number of samples to process.
 171  * @return none.
 172  *
 173  * \par
 174  * The function is implemented using an internal 64-bit accumulator.
 175  * The accumulator has a 2.62 format and maintains full precision of the intermediate multiplication results but provides only a single guard bit.
 176  * Thus, if the accumulator result overflows it wraps around rather than clip.
 177  * In order to avoid overflows completely the input signal must be scaled down by 2 bits and lie in the range [-0.25 +0.25).
 178  * After all 5 multiply-accumulates are performed, the 2.62 accumulator is shifted by <code>postShift</code> bits and the result truncated to
 179  * 1.31 format by discarding the low 32 bits.
 180  *
 181  * \par
 182  * Two related functions are provided in the CMSIS DSP library.
 183  * <code>arm_biquad_cascade_df1_q31()</code> implements a Biquad cascade with 32-bit coefficients and state variables with a Q63 accumulator.
 184  * <code>arm_biquad_cascade_df1_fast_q31()</code> implements a Biquad cascade with 32-bit coefficients and state variables with a Q31 accumulator.
 185  */
 186
 187 void arm_biquad_cas_df1_32x64_q31(
 188   const arm_biquad_cas_df1_32x64_ins_q31 * S,
 189   q31_t * pSrc,
 190   q31_t * pDst,
 191   uint32_t blockSize)
 192 {
 193   q31_t *pIn = pSrc;                             /*  input pointer initialization  */
 194   q31_t *pOut = pDst;                            /*  output pointer initialization */
 195   q63_t *pState = S->pState;                     /*  state pointer initialization  */
 196   q31_t *pCoeffs = S->pCoeffs;                   /*  coeff pointer initialization  */
 197   q63_t acc;                                     /*  accumulator                   */
 198   q31_t Xn1, Xn2;                                /*  Input Filter state variables        */
 199   q63_t Yn1, Yn2;                                /*  Output Filter state variables        */
 200   q31_t b0, b1, b2, a1, a2;                      /*  Filter coefficients           */
 201   q31_t Xn;                                      /*  temporary input               */
 202   int32_t shift = (int32_t) S->postShift + 1;    /*  Shift to be applied to the output */
 203   uint32_t sample, stage = S->numStages;         /*  loop counters                     */
 204   q31_t acc_l, acc_h;                            /*  temporary output               */
 205   uint32_t uShift = ((uint32_t) S->postShift + 1u);
 206   uint32_t lShift = 32u - uShift;                /*  Shift to be applied to the output */
 207
 208
 209 #ifndef ARM_MATH_CM0_FAMILY
 210
 211   /* Run the below code for Cortex-M4 and Cortex-M3 */
 212
 213   do
 214   {
 215     /* Reading the coefficients */
 216     b0 = *pCoeffs++;
 217     b1 = *pCoeffs++;
 218     b2 = *pCoeffs++;
 219     a1 = *pCoeffs++;
 220     a2 = *pCoeffs++;
 221
 222     /* Reading the state values */
 223     Xn1 = (q31_t) (pState[0]);
 224     Xn2 = (q31_t) (pState[1]);
 225     Yn1 = pState[2];
 226     Yn2 = pState[3];
 227
 228     /* Apply loop unrolling and compute 4 output values simultaneously. */
 229     /* The variable acc hold output value that is being computed and
 230      * stored in the destination buffer
 231      * acc =  b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2]
 232      */
 233
 234     sample = blockSize >> 2u;
 235
 236     /* First part of the processing with loop unrolling. Compute 4 outputs at a time.
 237      ** a second loop below computes the remaining 1 to 3 samples. */
 238     while(sample > 0u)
 239     {
 240       /* Read the input */
 241       Xn = *pIn++;
 242
 243       /* acc =  b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] */
 244
 245       /* acc =  b0 * x[n] */
 246       acc = (q63_t) Xn *b0;
 247
 248       /* acc +=  b1 * x[n-1] */
 249       acc += (q63_t) Xn1 *b1;
 250
 251       /* acc +=  b[2] * x[n-2] */
 252       acc += (q63_t) Xn2 *b2;
 253
 254       /* acc +=  a1 * y[n-1] */
 255       acc += mult32x64(Yn1, a1);
 256
 257       /* acc +=  a2 * y[n-2] */
 258       acc += mult32x64(Yn2, a2);
 259
 260       /* The result is converted to 1.63 , Yn2 variable is reused */
 261       Yn2 = acc << shift;
 262
 263       /* Calc lower part of acc */
 264       acc_l = acc & 0xffffffff;
 265
 266       /* Calc upper part of acc */
 267       acc_h = (acc >> 32) & 0xffffffff;
 268
 269       /* Apply shift for lower part of acc and upper part of acc */
 270       acc_h = (uint32_t) acc_l >> lShift | acc_h << uShift;
 271
 272       /* Store the output in the destination buffer in 1.31 format. */
 273       *pOut = acc_h;
 274
 275       /* Read the second input into Xn2, to reuse the value */
 276       Xn2 = *pIn++;
 277
 278       /* acc =  b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] */
 279
 280       /* acc +=  b1 * x[n-1] */
 281       acc = (q63_t) Xn *b1;
 282
 283       /* acc =  b0 * x[n] */
 284       acc += (q63_t) Xn2 *b0;
 285
 286       /* acc +=  b[2] * x[n-2] */
 287       acc += (q63_t) Xn1 *b2;
 288
 289       /* acc +=  a1 * y[n-1] */
 290       acc += mult32x64(Yn2, a1);
 291
 292       /* acc +=  a2 * y[n-2] */
 293       acc += mult32x64(Yn1, a2);
 294
 295       /* The result is converted to 1.63, Yn1 variable is reused */
 296       Yn1 = acc << shift;
 297
 298       /* Calc lower part of acc */
 299       acc_l = acc & 0xffffffff;
 300
 301       /* Calc upper part of acc */
 302       acc_h = (acc >> 32) & 0xffffffff;
 303
 304       /* Apply shift for lower part of acc and upper part of acc */
 305       acc_h = (uint32_t) acc_l >> lShift | acc_h << uShift;
 306
 307       /* Read the third input into Xn1, to reuse the value */
 308       Xn1 = *pIn++;
 309
 310       /* The result is converted to 1.31 */
 311       /* Store the output in the destination buffer. */
 312       *(pOut + 1u) = acc_h;
 313
 314       /* acc =  b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] */
 315
 316       /* acc =  b0 * x[n] */
 317       acc = (q63_t) Xn1 *b0;
 318
 319       /* acc +=  b1 * x[n-1] */
 320       acc += (q63_t) Xn2 *b1;
 321
 322       /* acc +=  b[2] * x[n-2] */
 323       acc += (q63_t) Xn *b2;
 324
 325       /* acc +=  a1 * y[n-1] */
 326       acc += mult32x64(Yn1, a1);
 327
 328       /* acc +=  a2 * y[n-2] */
 329       acc += mult32x64(Yn2, a2);
 330
 331       /* The result is converted to 1.63, Yn2 variable is reused  */
 332       Yn2 = acc << shift;
 333
 334       /* Calc lower part of acc */
 335       acc_l = acc & 0xffffffff;
 336
 337       /* Calc upper part of acc */
 338       acc_h = (acc >> 32) & 0xffffffff;
 339
 340       /* Apply shift for lower part of acc and upper part of acc */
 341       acc_h = (uint32_t) acc_l >> lShift | acc_h << uShift;
 342
 343       /* Store the output in the destination buffer in 1.31 format. */
 344       *(pOut + 2u) = acc_h;
 345
 346       /* Read the fourth input into Xn, to reuse the value */
 347       Xn = *pIn++;
 348
 349       /* acc =  b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] */
 350       /* acc =  b0 * x[n] */
 351       acc = (q63_t) Xn *b0;
 352
 353       /* acc +=  b1 * x[n-1] */
 354       acc += (q63_t) Xn1 *b1;
 355
 356       /* acc +=  b[2] * x[n-2] */
 357       acc += (q63_t) Xn2 *b2;
 358
 359       /* acc +=  a1 * y[n-1] */
 360       acc += mult32x64(Yn2, a1);
 361
 362       /* acc +=  a2 * y[n-2] */
 363       acc += mult32x64(Yn1, a2);
 364
 365       /* The result is converted to 1.63, Yn1 variable is reused  */
 366       Yn1 = acc << shift;
 367
 368       /* Calc lower part of acc */
 369       acc_l = acc & 0xffffffff;
 370
 371       /* Calc upper part of acc */
 372       acc_h = (acc >> 32) & 0xffffffff;
 373
 374       /* Apply shift for lower part of acc and upper part of acc */
 375       acc_h = (uint32_t) acc_l >> lShift | acc_h << uShift;
 376
 377       /* Store the output in the destination buffer in 1.31 format. */
 378       *(pOut + 3u) = acc_h;
 379
 380       /* Every time after the output is computed state should be updated. */
 381       /* The states should be updated as:  */
 382       /* Xn2 = Xn1    */
 383       /* Xn1 = Xn     */
 384       /* Yn2 = Yn1    */
 385       /* Yn1 = acc    */
 386       Xn2 = Xn1;
 387       Xn1 = Xn;
 388
 389       /* update output pointer */
 390       pOut += 4u;
 391
 392       /* decrement the loop counter */
 393       sample--;
 394     }
 395
 396     /* If the blockSize is not a multiple of 4, compute any remaining output samples here.
 397      ** No loop unrolling is used. */
 398     sample = (blockSize & 0x3u);
 399
 400     while(sample > 0u)
 401     {
 402       /* Read the input */
 403       Xn = *pIn++;
 404
 405       /* acc =  b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] */
 406
 407       /* acc =  b0 * x[n] */
 408       acc = (q63_t) Xn *b0;
 409       /* acc +=  b1 * x[n-1] */
 410       acc += (q63_t) Xn1 *b1;
 411       /* acc +=  b[2] * x[n-2] */
 412       acc += (q63_t) Xn2 *b2;
 413       /* acc +=  a1 * y[n-1] */
 414       acc += mult32x64(Yn1, a1);
 415       /* acc +=  a2 * y[n-2] */
 416       acc += mult32x64(Yn2, a2);
 417
 418       /* Every time after the output is computed state should be updated. */
 419       /* The states should be updated as:  */
 420       /* Xn2 = Xn1    */
 421       /* Xn1 = Xn     */
 422       /* Yn2 = Yn1    */
 423       /* Yn1 = acc    */
 424       Xn2 = Xn1;
 425       Xn1 = Xn;
 426       Yn2 = Yn1;
 427       /* The result is converted to 1.63, Yn1 variable is reused  */
 428       Yn1 = acc << shift;
 429
 430       /* Calc lower part of acc */
 431       acc_l = acc & 0xffffffff;
 432
 433       /* Calc upper part of acc */
 434       acc_h = (acc >> 32) & 0xffffffff;
 435
 436       /* Apply shift for lower part of acc and upper part of acc */
 437       acc_h = (uint32_t) acc_l >> lShift | acc_h << uShift;
 438
 439       /* Store the output in the destination buffer in 1.31 format. */
 440       *pOut++ = acc_h;
 441       //Yn1 = acc << shift;
 442
 443       /* Store the output in the destination buffer in 1.31 format. */
 444 //      *pOut++ = (q31_t) (acc >> (32 - shift));
 445
 446       /* decrement the loop counter */
 447       sample--;
 448     }
 449
 450     /*  The first stage output is given as input to the second stage. */
 451     pIn = pDst;
 452
 453     /* Reset to destination buffer working pointer */
 454     pOut = pDst;
 455
 456     /*  Store the updated state variables back into the pState array */
 457     /*  Store the updated state variables back into the pState array */
 458     *pState++ = (q63_t) Xn1;
 459     *pState++ = (q63_t) Xn2;
 460     *pState++ = Yn1;
 461     *pState++ = Yn2;
 462
 463   } while(--stage);
 464
 465 #else
 466
 467   /* Run the below code for Cortex-M0 */
 468
 469   do
 470   {
 471     /* Reading the coefficients */
 472     b0 = *pCoeffs++;
 473     b1 = *pCoeffs++;
 474     b2 = *pCoeffs++;
 475     a1 = *pCoeffs++;
 476     a2 = *pCoeffs++;
 477
 478     /* Reading the state values */
 479     Xn1 = pState[0];
 480     Xn2 = pState[1];
 481     Yn1 = pState[2];
 482     Yn2 = pState[3];
 483
 484     /* The variable acc hold output value that is being computed and
 485      * stored in the destination buffer
 486      * acc =  b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2]
 487      */
 488
 489     sample = blockSize;
 490
 491     while(sample > 0u)
 492     {
 493       /* Read the input */
 494       Xn = *pIn++;
 495
 496       /* acc =  b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] */
 497       /* acc =  b0 * x[n] */
 498       acc = (q63_t) Xn *b0;
 499       /* acc +=  b1 * x[n-1] */
 500       acc += (q63_t) Xn1 *b1;
 501       /* acc +=  b[2] * x[n-2] */
 502       acc += (q63_t) Xn2 *b2;
 503       /* acc +=  a1 * y[n-1] */
 504       acc += mult32x64(Yn1, a1);
 505       /* acc +=  a2 * y[n-2] */
 506       acc += mult32x64(Yn2, a2);
 507
 508       /* Every time after the output is computed state should be updated. */
 509       /* The states should be updated as:  */
 510       /* Xn2 = Xn1    */
 511       /* Xn1 = Xn     */
 512       /* Yn2 = Yn1    */
 513       /* Yn1 = acc    */
 514       Xn2 = Xn1;
 515       Xn1 = Xn;
 516       Yn2 = Yn1;
 517
 518       /* The result is converted to 1.63, Yn1 variable is reused  */
 519       Yn1 = acc << shift;
 520
 521       /* Calc lower part of acc */
 522       acc_l = acc & 0xffffffff;
 523
 524       /* Calc upper part of acc */
 525       acc_h = (acc >> 32) & 0xffffffff;
 526
 527       /* Apply shift for lower part of acc and upper part of acc */
 528       acc_h = (uint32_t) acc_l >> lShift | acc_h << uShift;
 529
 530       /* Store the output in the destination buffer in 1.31 format. */
 531       *pOut++ = acc_h;
 532
 533       //Yn1 = acc << shift;
 534
 535       /* Store the output in the destination buffer in 1.31 format. */
 536       //*pOut++ = (q31_t) (acc >> (32 - shift));
 537
 538       /* decrement the loop counter */
 539       sample--;
 540     }
 541
 542     /*  The first stage output is given as input to the second stage. */
 543     pIn = pDst;
 544
 545     /* Reset to destination buffer working pointer */
 546     pOut = pDst;
 547
 548     /*  Store the updated state variables back into the pState array */
 549     *pState++ = (q63_t) Xn1;
 550     *pState++ = (q63_t) Xn2;
 551     *pState++ = Yn1;
 552     *pState++ = Yn2;
 553
 554   } while(--stage);
 555
 556 #endif /*    #ifndef ARM_MATH_CM0_FAMILY     */
 557 }
 558
 559   /**
 560    * @} end of BiquadCascadeDF1_32x64 group
 561    */