tmk_core/tool/mbed/mbed-sdk/libraries/dsp/cmsis_dsp/FilteringFunctions/arm_lms_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_lms_f32.c
   9 *
  10 * Description:  Processing function for the floating-point LMS filter.
  11 *
  12 * Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
  13 *
  14 * Redistribution and use in source and binary forms, with or without
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  23 *   - Neither the name of ARM LIMITED nor the names of its contributors
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  40
  41 #include "arm_math.h"
  42
  43 /**
  44  * @ingroup groupFilters
  45  */
  46
  47 /**
  48  * @defgroup LMS Least Mean Square (LMS) Filters
  49  *
  50  * LMS filters are a class of adaptive filters that are able to "learn" an unknown transfer functions.
  51  * LMS filters use a gradient descent method in which the filter coefficients are updated based on the instantaneous error signal.
  52  * Adaptive filters are often used in communication systems, equalizers, and noise removal.
  53  * The CMSIS DSP Library contains LMS filter functions that operate on Q15, Q31, and floating-point data types.
  54  * The library also contains normalized LMS filters in which the filter coefficient adaptation is indepedent of the level of the input signal.
  55  *
  56  * An LMS filter consists of two components as shown below.
  57  * The first component is a standard transversal or FIR filter.
  58  * The second component is a coefficient update mechanism.
  59  * The LMS filter has two input signals.
  60  * The "input" feeds the FIR filter while the "reference input" corresponds to the desired output of the FIR filter.
  61  * That is, the FIR filter coefficients are updated so that the output of the FIR filter matches the reference input.
  62  * The filter coefficient update mechanism is based on the difference between the FIR filter output and the reference input.
  63  * This "error signal" tends towards zero as the filter adapts.
  64  * The LMS processing functions accept the input and reference input signals and generate the filter output and error signal.
  65  * \image html LMS.gif "Internal structure of the Least Mean Square filter"
  66  *
  67  * The functions operate on blocks of data and each call to the function processes
  68  * <code>blockSize</code> samples through the filter.
  69  * <code>pSrc</code> points to input signal, <code>pRef</code> points to reference signal,
  70  * <code>pOut</code> points to output signal and <code>pErr</code> points to error signal.
  71  * All arrays contain <code>blockSize</code> values.
  72  *
  73  * The functions operate on a block-by-block basis.
  74  * Internally, the filter coefficients <code>b[n]</code> are updated on a sample-by-sample basis.
  75  * The convergence of the LMS filter is slower compared to the normalized LMS algorithm.
  76  *
  77  * \par Algorithm:
  78  * The output signal <code>y[n]</code> is computed by a standard FIR filter:
  79  * <pre>
  80  *     y[n] = b[0] * x[n] + b[1] * x[n-1] + b[2] * x[n-2] + ...+ b[numTaps-1] * x[n-numTaps+1]
  81  * </pre>
  82  *
  83  * \par
  84  * The error signal equals the difference between the reference signal <code>d[n]</code> and the filter output:
  85  * <pre>
  86  *     e[n] = d[n] - y[n].
  87  * </pre>
  88  *
  89  * \par
  90  * After each sample of the error signal is computed, the filter coefficients <code>b[k]</code> are updated on a sample-by-sample basis:
  91  * <pre>
  92  *     b[k] = b[k] + e[n] * mu * x[n-k],  for k=0, 1, ..., numTaps-1
  93  * </pre>
  94  * where <code>mu</code> is the step size and controls the rate of coefficient convergence.
  95  *\par
  96  * In the APIs, <code>pCoeffs</code> points to a coefficient array of size <code>numTaps</code>.
  97  * Coefficients are stored in time reversed order.
  98  * \par
  99  * <pre>
 100  *    {b[numTaps-1], b[numTaps-2], b[N-2], ..., b[1], b[0]}
 101  * </pre>
 102  * \par
 103  * <code>pState</code> points to a state array of size <code>numTaps + blockSize - 1</code>.
 104  * Samples in the state buffer are stored in the order:
 105  * \par
 106  * <pre>
 107  *    {x[n-numTaps+1], x[n-numTaps], x[n-numTaps-1], x[n-numTaps-2]....x[0], x[1], ..., x[blockSize-1]}
 108  * </pre>
 109  * \par
 110  * Note that the length of the state buffer exceeds the length of the coefficient array by <code>blockSize-1</code> samples.
 111  * The increased state buffer length allows circular addressing, which is traditionally used in FIR filters,
 112  * to be avoided and yields a significant speed improvement.
 113  * The state variables are updated after each block of data is processed.
 114  * \par Instance Structure
 115  * The coefficients and state variables for a filter are stored together in an instance data structure.
 116  * A separate instance structure must be defined for each filter and
 117  * coefficient and state arrays cannot be shared among instances.
 118  * There are separate instance structure declarations for each of the 3 supported data types.
 119  *
 120  * \par Initialization Functions
 121  * There is also an associated initialization function for each data type.
 122  * The initialization function performs the following operations:
 123  * - Sets the values of the internal structure fields.
 124  * - Zeros out the values in the state buffer.
 125  * To do this manually without calling the init function, assign the follow subfields of the instance structure:
 126  * numTaps, pCoeffs, mu, postShift (not for f32), pState. Also set all of the values in pState to zero.
 127  *
 128  * \par
 129  * Use of the initialization function is optional.
 130  * However, if the initialization function is used, then the instance structure cannot be placed into a const data section.
 131  * To place an instance structure into a const data section, the instance structure must be manually initialized.
 132  * Set the values in the state buffer to zeros before static initialization.
 133  * The code below statically initializes each of the 3 different data type filter instance structures
 134  * <pre>
 135  *    arm_lms_instance_f32 S = {numTaps, pState, pCoeffs, mu};
 136  *    arm_lms_instance_q31 S = {numTaps, pState, pCoeffs, mu, postShift};
 137  *    arm_lms_instance_q15 S = {numTaps, pState, pCoeffs, mu, postShift};
 138  * </pre>
 139  * where <code>numTaps</code> is the number of filter coefficients in the filter; <code>pState</code> is the address of the state buffer;
 140  * <code>pCoeffs</code> is the address of the coefficient buffer; <code>mu</code> is the step size parameter; and <code>postShift</code> is the shift applied to coefficients.
 141  *
 142  * \par Fixed-Point Behavior:
 143  * Care must be taken when using the Q15 and Q31 versions of the LMS filter.
 144  * The following issues must be considered:
 145  * - Scaling of coefficients
 146  * - Overflow and saturation
 147  *
 148  * \par Scaling of Coefficients:
 149  * Filter coefficients are represented as fractional values and
 150  * coefficients are restricted to lie in the range <code>[-1 +1)</code>.
 151  * The fixed-point functions have an additional scaling parameter <code>postShift</code>.
 152  * At the output of the filter's accumulator is a shift register which shifts the result by <code>postShift</code> bits.
 153  * This essentially scales the filter coefficients by <code>2^postShift</code> and
 154  * allows the filter coefficients to exceed the range <code>[+1 -1)</code>.
 155  * The value of <code>postShift</code> is set by the user based on the expected gain through the system being modeled.
 156  *
 157  * \par Overflow and Saturation:
 158  * Overflow and saturation behavior of the fixed-point Q15 and Q31 versions are
 159  * described separately as part of the function specific documentation below.
 160  */
 161
 162 /**
 163  * @addtogroup LMS
 164  * @{
 165  */
 166
 167 /**
 168  * @details
 169  * This function operates on floating-point data types.
 170  *
 171  * @brief Processing function for floating-point LMS filter.
 172  * @param[in]  *S points to an instance of the floating-point LMS filter structure.
 173  * @param[in]  *pSrc points to the block of input data.
 174  * @param[in]  *pRef points to the block of reference data.
 175  * @param[out] *pOut points to the block of output data.
 176  * @param[out] *pErr points to the block of error data.
 177  * @param[in]  blockSize number of samples to process.
 178  * @return     none.
 179  */
 180
 181 void arm_lms_f32(
 182   const arm_lms_instance_f32 * S,
 183   float32_t * pSrc,
 184   float32_t * pRef,
 185   float32_t * pOut,
 186   float32_t * pErr,
 187   uint32_t blockSize)
 188 {
 189   float32_t *pState = S->pState;                 /* State pointer */
 190   float32_t *pCoeffs = S->pCoeffs;               /* Coefficient pointer */
 191   float32_t *pStateCurnt;                        /* Points to the current sample of the state */
 192   float32_t *px, *pb;                            /* Temporary pointers for state and coefficient buffers */
 193   float32_t mu = S->mu;                          /* Adaptive factor */
 194   uint32_t numTaps = S->numTaps;                 /* Number of filter coefficients in the filter */
 195   uint32_t tapCnt, blkCnt;                       /* Loop counters */
 196   float32_t sum, e, d;                           /* accumulator, error, reference data sample */
 197   float32_t w = 0.0f;                            /* weight factor */
 198
 199   e = 0.0f;
 200   d = 0.0f;
 201
 202   /* S->pState points to state array which contains previous frame (numTaps - 1) samples */
 203   /* pStateCurnt points to the location where the new input data should be written */
 204   pStateCurnt = &(S->pState[(numTaps - 1u)]);
 205
 206   blkCnt = blockSize;
 207
 208
 209 #ifndef ARM_MATH_CM0_FAMILY
 210
 211   /* Run the below code for Cortex-M4 and Cortex-M3 */
 212
 213   while(blkCnt > 0u)
 214   {
 215     /* Copy the new input sample into the state buffer */
 216     *pStateCurnt++ = *pSrc++;
 217
 218     /* Initialize pState pointer */
 219     px = pState;
 220
 221     /* Initialize coeff pointer */
 222     pb = (pCoeffs);
 223
 224     /* Set the accumulator to zero */
 225     sum = 0.0f;
 226
 227     /* Loop unrolling.  Process 4 taps at a time. */
 228     tapCnt = numTaps >> 2;
 229
 230     while(tapCnt > 0u)
 231     {
 232       /* Perform the multiply-accumulate */
 233       sum += (*px++) * (*pb++);
 234       sum += (*px++) * (*pb++);
 235       sum += (*px++) * (*pb++);
 236       sum += (*px++) * (*pb++);
 237
 238       /* Decrement the loop counter */
 239       tapCnt--;
 240     }
 241
 242     /* If the filter length is not a multiple of 4, compute the remaining filter taps */
 243     tapCnt = numTaps % 0x4u;
 244
 245     while(tapCnt > 0u)
 246     {
 247       /* Perform the multiply-accumulate */
 248       sum += (*px++) * (*pb++);
 249
 250       /* Decrement the loop counter */
 251       tapCnt--;
 252     }
 253
 254     /* The result in the accumulator, store in the destination buffer. */
 255     *pOut++ = sum;
 256
 257     /* Compute and store error */
 258     d = (float32_t) (*pRef++);
 259     e = d - sum;
 260     *pErr++ = e;
 261
 262     /* Calculation of Weighting factor for the updating filter coefficients */
 263     w = e * mu;
 264
 265     /* Initialize pState pointer */
 266     px = pState;
 267
 268     /* Initialize coeff pointer */
 269     pb = (pCoeffs);
 270
 271     /* Loop unrolling.  Process 4 taps at a time. */
 272     tapCnt = numTaps >> 2;
 273
 274     /* Update filter coefficients */
 275     while(tapCnt > 0u)
 276     {
 277       /* Perform the multiply-accumulate */
 278       *pb = *pb + (w * (*px++));
 279       pb++;
 280
 281       *pb = *pb + (w * (*px++));
 282       pb++;
 283
 284       *pb = *pb + (w * (*px++));
 285       pb++;
 286
 287       *pb = *pb + (w * (*px++));
 288       pb++;
 289
 290       /* Decrement the loop counter */
 291       tapCnt--;
 292     }
 293
 294     /* If the filter length is not a multiple of 4, compute the remaining filter taps */
 295     tapCnt = numTaps % 0x4u;
 296
 297     while(tapCnt > 0u)
 298     {
 299       /* Perform the multiply-accumulate */
 300       *pb = *pb + (w * (*px++));
 301       pb++;
 302
 303       /* Decrement the loop counter */
 304       tapCnt--;
 305     }
 306
 307     /* Advance state pointer by 1 for the next sample */
 308     pState = pState + 1;
 309
 310     /* Decrement the loop counter */
 311     blkCnt--;
 312   }
 313
 314
 315   /* Processing is complete. Now copy the last numTaps - 1 samples to the
 316      satrt of the state buffer. This prepares the state buffer for the
 317      next function call. */
 318
 319   /* Points to the start of the pState buffer */
 320   pStateCurnt = S->pState;
 321
 322   /* Loop unrolling for (numTaps - 1u) samples copy */
 323   tapCnt = (numTaps - 1u) >> 2u;
 324
 325   /* copy data */
 326   while(tapCnt > 0u)
 327   {
 328     *pStateCurnt++ = *pState++;
 329     *pStateCurnt++ = *pState++;
 330     *pStateCurnt++ = *pState++;
 331     *pStateCurnt++ = *pState++;
 332
 333     /* Decrement the loop counter */
 334     tapCnt--;
 335   }
 336
 337   /* Calculate remaining number of copies */
 338   tapCnt = (numTaps - 1u) % 0x4u;
 339
 340   /* Copy the remaining q31_t data */
 341   while(tapCnt > 0u)
 342   {
 343     *pStateCurnt++ = *pState++;
 344
 345     /* Decrement the loop counter */
 346     tapCnt--;
 347   }
 348
 349 #else
 350
 351   /* Run the below code for Cortex-M0 */
 352
 353   while(blkCnt > 0u)
 354   {
 355     /* Copy the new input sample into the state buffer */
 356     *pStateCurnt++ = *pSrc++;
 357
 358     /* Initialize pState pointer */
 359     px = pState;
 360
 361     /* Initialize pCoeffs pointer */
 362     pb = pCoeffs;
 363
 364     /* Set the accumulator to zero */
 365     sum = 0.0f;
 366
 367     /* Loop over numTaps number of values */
 368     tapCnt = numTaps;
 369
 370     while(tapCnt > 0u)
 371     {
 372       /* Perform the multiply-accumulate */
 373       sum += (*px++) * (*pb++);
 374
 375       /* Decrement the loop counter */
 376       tapCnt--;
 377     }
 378
 379     /* The result is stored in the destination buffer. */
 380     *pOut++ = sum;
 381
 382     /* Compute and store error */
 383     d = (float32_t) (*pRef++);
 384     e = d - sum;
 385     *pErr++ = e;
 386
 387     /* Weighting factor for the LMS version */
 388     w = e * mu;
 389
 390     /* Initialize pState pointer */
 391     px = pState;
 392
 393     /* Initialize pCoeffs pointer */
 394     pb = pCoeffs;
 395
 396     /* Loop over numTaps number of values */
 397     tapCnt = numTaps;
 398
 399     while(tapCnt > 0u)
 400     {
 401       /* Perform the multiply-accumulate */
 402       *pb = *pb + (w * (*px++));
 403       pb++;
 404
 405       /* Decrement the loop counter */
 406       tapCnt--;
 407     }
 408
 409     /* Advance state pointer by 1 for the next sample */
 410     pState = pState + 1;
 411
 412     /* Decrement the loop counter */
 413     blkCnt--;
 414   }
 415
 416
 417   /* Processing is complete. Now copy the last numTaps - 1 samples to the
 418    * start of the state buffer. This prepares the state buffer for the
 419    * next function call. */
 420
 421   /* Points to the start of the pState buffer */
 422   pStateCurnt = S->pState;
 423
 424   /*  Copy (numTaps - 1u) samples  */
 425   tapCnt = (numTaps - 1u);
 426
 427   /* Copy the data */
 428   while(tapCnt > 0u)
 429   {
 430     *pStateCurnt++ = *pState++;
 431
 432     /* Decrement the loop counter */
 433     tapCnt--;
 434   }
 435
 436 #endif /*   #ifndef ARM_MATH_CM0_FAMILY */
 437
 438 }
 439
 440 /**
 441    * @} end of LMS group
 442    */