tmk_core/tool/mbed/mbed-sdk/libraries/dsp/cmsis_dsp/FilteringFunctions/arm_biquad_cascade_df1_f32.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_f32.c
   9 *
  10 * Description:  Processing function for the
  11 *               floating-point Biquad cascade DirectFormI(DF1) filter.
  12 *
  13 * Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
  14 *
  15 * Redistribution and use in source and binary forms, with or without
  16 * modification, are permitted provided that the following conditions
  17 * are met:
  18 *   - Redistributions of source code must retain the above copyright
  19 *     notice, this list of conditions and the following disclaimer.
  20 *   - Redistributions in binary form must reproduce the above copyright
  21 *     notice, this list of conditions and the following disclaimer in
  22 *     the documentation and/or other materials provided with the
  23 *     distribution.
  24 *   - Neither the name of ARM LIMITED nor the names of its contributors
  25 *     may be used to endorse or promote products derived from this
  26 *     software without specific prior written permission.
  27 *
  28 * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
  29 * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
  30 * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
  31 * FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
  32 * COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
  33 * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
  34 * BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
  35 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
  36 * CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
  37 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
  38 * ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
  39 * POSSIBILITY OF SUCH DAMAGE.
  40 * -------------------------------------------------------------------- */
  41
  42 #include "arm_math.h"
  43
  44 /**
  45  * @ingroup groupFilters
  46  */
  47
  48 /**
  49  * @defgroup BiquadCascadeDF1 Biquad Cascade IIR Filters Using Direct Form I Structure
  50  *
  51  * This set of functions implements arbitrary order recursive (IIR) filters.
  52  * The filters are implemented as a cascade of second order Biquad sections.
  53  * The functions support Q15, Q31 and floating-point data types.
  54  * Fast version of Q15 and Q31 also supported on CortexM4 and Cortex-M3.
  55  *
  56  * The functions operate on blocks of input and output data and each call to the function
  57  * processes <code>blockSize</code> samples through the filter.
  58  * <code>pSrc</code> points to the array of input data and
  59  * <code>pDst</code> points to the array of output data.
  60  * Both arrays contain <code>blockSize</code> values.
  61  *
  62  * \par Algorithm
  63  * Each Biquad stage implements a second order filter using the difference equation:
  64  * <pre>
  65  *     y[n] = b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2]
  66  * </pre>
  67  * A Direct Form I algorithm is used with 5 coefficients and 4 state variables per stage.
  68  * \image html Biquad.gif "Single Biquad filter stage"
  69  * Coefficients <code>b0, b1 and b2 </code> multiply the input signal <code>x[n]</code> and are referred to as the feedforward coefficients.
  70  * Coefficients <code>a1</code> and <code>a2</code> multiply the output signal <code>y[n]</code> and are referred to as the feedback coefficients.
  71  * Pay careful attention to the sign of the feedback coefficients.
  72  * Some design tools use the difference equation
  73  * <pre>
  74  *     y[n] = b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] - a1 * y[n-1] - a2 * y[n-2]
  75  * </pre>
  76  * In this case the feedback coefficients <code>a1</code> and <code>a2</code> must be negated when used with the CMSIS DSP Library.
  77  *
  78  * \par
  79  * Higher order filters are realized as a cascade of second order sections.
  80  * <code>numStages</code> refers to the number of second order stages used.
  81  * For example, an 8th order filter would be realized with <code>numStages=4</code> second order stages.
  82  * \image html BiquadCascade.gif "8th order filter using a cascade of Biquad stages"
  83  * 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>).
  84  *
  85  * \par
  86  * The <code>pState</code> points to state variables array.
  87  * Each Biquad stage has 4 state variables <code>x[n-1], x[n-2], y[n-1],</code> and <code>y[n-2]</code>.
  88  * The state variables are arranged in the <code>pState</code> array as:
  89  * <pre>
  90  *     {x[n-1], x[n-2], y[n-1], y[n-2]}
  91  * </pre>
  92  *
  93  * \par
  94  * The 4 state variables for stage 1 are first, then the 4 state variables for stage 2, and so on.
  95  * The state array has a total length of <code>4*numStages</code> values.
  96  * The state variables are updated after each block of data is processed, the coefficients are untouched.
  97  *
  98  * \par Instance Structure
  99  * The coefficients and state variables for a filter are stored together in an instance data structure.
 100  * A separate instance structure must be defined for each filter.
 101  * Coefficient arrays may be shared among several instances while state variable arrays cannot be shared.
 102  * There are separate instance structure declarations for each of the 3 supported data types.
 103  *
 104  * \par Init Functions
 105  * There is also an associated initialization function for each data type.
 106  * The initialization function performs following operations:
 107  * - Sets the values of the internal structure fields.
 108  * - Zeros out the values in the state buffer.
 109  * To do this manually without calling the init function, assign the follow subfields of the instance structure:
 110  * numStages, pCoeffs, pState. Also set all of the values in pState to zero.
 111  *
 112  * \par
 113  * Use of the initialization function is optional.
 114  * However, if the initialization function is used, then the instance structure cannot be placed into a const data section.
 115  * To place an instance structure into a const data section, the instance structure must be manually initialized.
 116  * Set the values in the state buffer to zeros before static initialization.
 117  * The code below statically initializes each of the 3 different data type filter instance structures
 118  * <pre>
 119  *     arm_biquad_casd_df1_inst_f32 S1 = {numStages, pState, pCoeffs};
 120  *     arm_biquad_casd_df1_inst_q15 S2 = {numStages, pState, pCoeffs, postShift};
 121  *     arm_biquad_casd_df1_inst_q31 S3 = {numStages, pState, pCoeffs, postShift};
 122  * </pre>
 123  * where <code>numStages</code> is the number of Biquad stages in the filter; <code>pState</code> is the address of the state buffer;
 124  * <code>pCoeffs</code> is the address of the coefficient buffer; <code>postShift</code> shift to be applied.
 125  *
 126  * \par Fixed-Point Behavior
 127  * Care must be taken when using the Q15 and Q31 versions of the Biquad Cascade filter functions.
 128  * Following issues must be considered:
 129  * - Scaling of coefficients
 130  * - Filter gain
 131  * - Overflow and saturation
 132  *
 133  * \par
 134  * <b>Scaling of coefficients: </b>
 135  * Filter coefficients are represented as fractional values and
 136  * coefficients are restricted to lie in the range <code>[-1 +1)</code>.
 137  * The fixed-point functions have an additional scaling parameter <code>postShift</code>
 138  * which allow the filter coefficients to exceed the range <code>[+1 -1)</code>.
 139  * At the output of the filter's accumulator is a shift register which shifts the result by <code>postShift</code> bits.
 140  * \image html BiquadPostshift.gif "Fixed-point Biquad with shift by postShift bits after accumulator"
 141  * This essentially scales the filter coefficients by <code>2^postShift</code>.
 142  * For example, to realize the coefficients
 143  * <pre>
 144  *    {1.5, -0.8, 1.2, 1.6, -0.9}
 145  * </pre>
 146  * set the pCoeffs array to:
 147  * <pre>
 148  *    {0.75, -0.4, 0.6, 0.8, -0.45}
 149  * </pre>
 150  * and set <code>postShift=1</code>
 151  *
 152  * \par
 153  * <b>Filter gain: </b>
 154  * The frequency response of a Biquad filter is a function of its coefficients.
 155  * It is possible for the gain through the filter to exceed 1.0 meaning that the filter increases the amplitude of certain frequencies.
 156  * 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.
 157  * 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.
 158  *
 159  * \par
 160  * <b>Overflow and saturation: </b>
 161  * For Q15 and Q31 versions, it is described separately as part of the function specific documentation below.
 162  */
 163
 164 /**
 165  * @addtogroup BiquadCascadeDF1
 166  * @{
 167  */
 168
 169 /**
 170  * @param[in]  *S         points to an instance of the floating-point Biquad cascade structure.
 171  * @param[in]  *pSrc      points to the block of input data.
 172  * @param[out] *pDst      points to the block of output data.
 173  * @param[in]  blockSize  number of samples to process per call.
 174  * @return     none.
 175  *
 176  */
 177
 178 void arm_biquad_cascade_df1_f32(
 179   const arm_biquad_casd_df1_inst_f32 * S,
 180   float32_t * pSrc,
 181   float32_t * pDst,
 182   uint32_t blockSize)
 183 {
 184   float32_t *pIn = pSrc;                         /*  source pointer            */
 185   float32_t *pOut = pDst;                        /*  destination pointer       */
 186   float32_t *pState = S->pState;                 /*  pState pointer            */
 187   float32_t *pCoeffs = S->pCoeffs;               /*  coefficient pointer       */
 188   float32_t acc;                                 /*  Simulates the accumulator */
 189   float32_t b0, b1, b2, a1, a2;                  /*  Filter coefficients       */
 190   float32_t Xn1, Xn2, Yn1, Yn2;                  /*  Filter pState variables   */
 191   float32_t Xn;                                  /*  temporary input           */
 192   uint32_t sample, stage = S->numStages;         /*  loop counters             */
 193
 194
 195 #ifndef ARM_MATH_CM0_FAMILY
 196
 197   /* Run the below code for Cortex-M4 and Cortex-M3 */
 198
 199   do
 200   {
 201     /* Reading the coefficients */
 202     b0 = *pCoeffs++;
 203     b1 = *pCoeffs++;
 204     b2 = *pCoeffs++;
 205     a1 = *pCoeffs++;
 206     a2 = *pCoeffs++;
 207
 208     /* Reading the pState values */
 209     Xn1 = pState[0];
 210     Xn2 = pState[1];
 211     Yn1 = pState[2];
 212     Yn2 = pState[3];
 213
 214     /* Apply loop unrolling and compute 4 output values simultaneously. */
 215     /*      The variable acc hold output values that are being computed:
 216      *
 217      *    acc =  b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1]   + a2 * y[n-2]
 218      *    acc =  b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1]   + a2 * y[n-2]
 219      *    acc =  b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1]   + a2 * y[n-2]
 220      *    acc =  b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1]   + a2 * y[n-2]
 221      */
 222
 223     sample = blockSize >> 2u;
 224
 225     /* First part of the processing with loop unrolling.  Compute 4 outputs at a time.
 226      ** a second loop below computes the remaining 1 to 3 samples. */
 227     while(sample > 0u)
 228     {
 229       /* Read the first input */
 230       Xn = *pIn++;
 231
 232       /* acc =  b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] */
 233       Yn2 = (b0 * Xn) + (b1 * Xn1) + (b2 * Xn2) + (a1 * Yn1) + (a2 * Yn2);
 234
 235       /* Store the result in the accumulator in the destination buffer. */
 236       *pOut++ = Yn2;
 237
 238       /* Every time after the output is computed state should be updated. */
 239       /* The states should be updated as:  */
 240       /* Xn2 = Xn1    */
 241       /* Xn1 = Xn     */
 242       /* Yn2 = Yn1    */
 243       /* Yn1 = acc   */
 244
 245       /* Read the second input */
 246       Xn2 = *pIn++;
 247
 248       /* acc =  b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] */
 249       Yn1 = (b0 * Xn2) + (b1 * Xn) + (b2 * Xn1) + (a1 * Yn2) + (a2 * Yn1);
 250
 251       /* Store the result in the accumulator in the destination buffer. */
 252       *pOut++ = Yn1;
 253
 254       /* Every time after the output is computed state should be updated. */
 255       /* The states should be updated as:  */
 256       /* Xn2 = Xn1    */
 257       /* Xn1 = Xn     */
 258       /* Yn2 = Yn1    */
 259       /* Yn1 = acc   */
 260
 261       /* Read the third input */
 262       Xn1 = *pIn++;
 263
 264       /* acc =  b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] */
 265       Yn2 = (b0 * Xn1) + (b1 * Xn2) + (b2 * Xn) + (a1 * Yn1) + (a2 * Yn2);
 266
 267       /* Store the result in the accumulator in the destination buffer. */
 268       *pOut++ = Yn2;
 269
 270       /* Every time after the output is computed state should be updated. */
 271       /* The states should be updated as: */
 272       /* Xn2 = Xn1    */
 273       /* Xn1 = Xn     */
 274       /* Yn2 = Yn1    */
 275       /* Yn1 = acc   */
 276
 277       /* Read the forth input */
 278       Xn = *pIn++;
 279
 280       /* acc =  b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] */
 281       Yn1 = (b0 * Xn) + (b1 * Xn1) + (b2 * Xn2) + (a1 * Yn2) + (a2 * Yn1);
 282
 283       /* Store the result in the accumulator in the destination buffer. */
 284       *pOut++ = Yn1;
 285
 286       /* Every time after the output is computed state should be updated. */
 287       /* The states should be updated as:  */
 288       /* Xn2 = Xn1    */
 289       /* Xn1 = Xn     */
 290       /* Yn2 = Yn1    */
 291       /* Yn1 = acc   */
 292       Xn2 = Xn1;
 293       Xn1 = Xn;
 294
 295       /* decrement the loop counter */
 296       sample--;
 297
 298     }
 299
 300     /* If the blockSize is not a multiple of 4, compute any remaining output samples here.
 301      ** No loop unrolling is used. */
 302     sample = blockSize & 0x3u;
 303
 304     while(sample > 0u)
 305     {
 306       /* Read the input */
 307       Xn = *pIn++;
 308
 309       /* acc =  b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] */
 310       acc = (b0 * Xn) + (b1 * Xn1) + (b2 * Xn2) + (a1 * Yn1) + (a2 * Yn2);
 311
 312       /* Store the result in the accumulator in the destination buffer. */
 313       *pOut++ = acc;
 314
 315       /* Every time after the output is computed state should be updated. */
 316       /* The states should be updated as:    */
 317       /* Xn2 = Xn1    */
 318       /* Xn1 = Xn     */
 319       /* Yn2 = Yn1    */
 320       /* Yn1 = acc   */
 321       Xn2 = Xn1;
 322       Xn1 = Xn;
 323       Yn2 = Yn1;
 324       Yn1 = acc;
 325
 326       /* decrement the loop counter */
 327       sample--;
 328
 329     }
 330
 331     /*  Store the updated state variables back into the pState array */
 332     *pState++ = Xn1;
 333     *pState++ = Xn2;
 334     *pState++ = Yn1;
 335     *pState++ = Yn2;
 336
 337     /*  The first stage goes from the input buffer to the output buffer. */
 338     /*  Subsequent numStages  occur in-place in the output buffer */
 339     pIn = pDst;
 340
 341     /* Reset the output pointer */
 342     pOut = pDst;
 343
 344     /* decrement the loop counter */
 345     stage--;
 346
 347   } while(stage > 0u);
 348
 349 #else
 350
 351   /* Run the below code for Cortex-M0 */
 352
 353   do
 354   {
 355     /* Reading the coefficients */
 356     b0 = *pCoeffs++;
 357     b1 = *pCoeffs++;
 358     b2 = *pCoeffs++;
 359     a1 = *pCoeffs++;
 360     a2 = *pCoeffs++;
 361
 362     /* Reading the pState values */
 363     Xn1 = pState[0];
 364     Xn2 = pState[1];
 365     Yn1 = pState[2];
 366     Yn2 = pState[3];
 367
 368     /*      The variables acc holds the output value that is computed:
 369      *    acc =  b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1]   + a2 * y[n-2]
 370      */
 371
 372     sample = blockSize;
 373
 374     while(sample > 0u)
 375     {
 376       /* Read the input */
 377       Xn = *pIn++;
 378
 379       /* acc =  b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] */
 380       acc = (b0 * Xn) + (b1 * Xn1) + (b2 * Xn2) + (a1 * Yn1) + (a2 * Yn2);
 381
 382       /* Store the result in the accumulator in the destination buffer. */
 383       *pOut++ = acc;
 384
 385       /* Every time after the output is computed state should be updated. */
 386       /* The states should be updated as:    */
 387       /* Xn2 = Xn1    */
 388       /* Xn1 = Xn     */
 389       /* Yn2 = Yn1    */
 390       /* Yn1 = acc   */
 391       Xn2 = Xn1;
 392       Xn1 = Xn;
 393       Yn2 = Yn1;
 394       Yn1 = acc;
 395
 396       /* decrement the loop counter */
 397       sample--;
 398     }
 399
 400     /*  Store the updated state variables back into the pState array */
 401     *pState++ = Xn1;
 402     *pState++ = Xn2;
 403     *pState++ = Yn1;
 404     *pState++ = Yn2;
 405
 406     /*  The first stage goes from the input buffer to the output buffer. */
 407     /*  Subsequent numStages  occur in-place in the output buffer */
 408     pIn = pDst;
 409
 410     /* Reset the output pointer */
 411     pOut = pDst;
 412
 413     /* decrement the loop counter */
 414     stage--;
 415
 416   } while(stage > 0u);
 417
 418 #endif /*   #ifndef ARM_MATH_CM0_FAMILY         */
 419
 420 }
 421
 422
 423   /**
 424    * @} end of BiquadCascadeDF1 group
 425    */