tmk_core/tool/mbed/mbed-sdk/libraries/dsp/cmsis_dsp/FilteringFunctions/arm_lms_norm_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_norm_f32.c
   9 *
  10 * Description:  Processing function for the floating-point Normalised LMS.
  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
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  19 *   - Redistributions in binary form must reproduce the above copyright
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  23 *   - Neither the name of ARM LIMITED nor the names of its contributors
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  25 *     software without specific prior written permission.
  26 *
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  40
  41 #include "arm_math.h"
  42
  43 /**
  44  * @ingroup groupFilters
  45  */
  46
  47 /**
  48  * @defgroup LMS_NORM Normalized LMS Filters
  49  *
  50  * This set of functions implements a commonly used adaptive filter.
  51  * It is related to the Least Mean Square (LMS) adaptive filter and includes an additional normalization
  52  * factor which increases the adaptation rate of the filter.
  53  * The CMSIS DSP Library contains normalized LMS filter functions that operate on Q15, Q31, and floating-point data types.
  54  *
  55  * A normalized least mean square (NLMS) filter consists of two components as shown below.
  56  * The first component is a standard transversal or FIR filter.
  57  * The second component is a coefficient update mechanism.
  58  * The NLMS filter has two input signals.
  59  * The "input" feeds the FIR filter while the "reference input" corresponds to the desired output of the FIR filter.
  60  * That is, the FIR filter coefficients are updated so that the output of the FIR filter matches the reference input.
  61  * The filter coefficient update mechanism is based on the difference between the FIR filter output and the reference input.
  62  * This "error signal" tends towards zero as the filter adapts.
  63  * The NLMS processing functions accept the input and reference input signals and generate the filter output and error signal.
  64  * \image html LMS.gif "Internal structure of the NLMS adaptive filter"
  65  *
  66  * The functions operate on blocks of data and each call to the function processes
  67  * <code>blockSize</code> samples through the filter.
  68  * <code>pSrc</code> points to input signal, <code>pRef</code> points to reference signal,
  69  * <code>pOut</code> points to output signal and <code>pErr</code> points to error signal.
  70  * All arrays contain <code>blockSize</code> values.
  71  *
  72  * The functions operate on a block-by-block basis.
  73  * Internally, the filter coefficients <code>b[n]</code> are updated on a sample-by-sample basis.
  74  * The convergence of the LMS filter is slower compared to the normalized LMS algorithm.
  75  *
  76  * \par Algorithm:
  77  * The output signal <code>y[n]</code> is computed by a standard FIR filter:
  78  * <pre>
  79  *     y[n] = b[0] * x[n] + b[1] * x[n-1] + b[2] * x[n-2] + ...+ b[numTaps-1] * x[n-numTaps+1]
  80  * </pre>
  81  *
  82  * \par
  83  * The error signal equals the difference between the reference signal <code>d[n]</code> and the filter output:
  84  * <pre>
  85  *     e[n] = d[n] - y[n].
  86  * </pre>
  87  *
  88  * \par
  89  * After each sample of the error signal is computed the instanteous energy of the filter state variables is calculated:
  90  * <pre>
  91  *    E = x[n]^2 + x[n-1]^2 + ... + x[n-numTaps+1]^2.
  92  * </pre>
  93  * The filter coefficients <code>b[k]</code> are then updated on a sample-by-sample basis:
  94  * <pre>
  95  *     b[k] = b[k] + e[n] * (mu/E) * x[n-k],  for k=0, 1, ..., numTaps-1
  96  * </pre>
  97  * where <code>mu</code> is the step size and controls the rate of coefficient convergence.
  98  *\par
  99  * In the APIs, <code>pCoeffs</code> points to a coefficient array of size <code>numTaps</code>.
 100  * Coefficients are stored in time reversed order.
 101  * \par
 102  * <pre>
 103  *    {b[numTaps-1], b[numTaps-2], b[N-2], ..., b[1], b[0]}
 104  * </pre>
 105  * \par
 106  * <code>pState</code> points to a state array of size <code>numTaps + blockSize - 1</code>.
 107  * Samples in the state buffer are stored in the order:
 108  * \par
 109  * <pre>
 110  *    {x[n-numTaps+1], x[n-numTaps], x[n-numTaps-1], x[n-numTaps-2]....x[0], x[1], ..., x[blockSize-1]}
 111  * </pre>
 112  * \par
 113  * Note that the length of the state buffer exceeds the length of the coefficient array by <code>blockSize-1</code> samples.
 114  * The increased state buffer length allows circular addressing, which is traditionally used in FIR filters,
 115  * to be avoided and yields a significant speed improvement.
 116  * The state variables are updated after each block of data is processed.
 117  * \par Instance Structure
 118  * The coefficients and state variables for a filter are stored together in an instance data structure.
 119  * A separate instance structure must be defined for each filter and
 120  * coefficient and state arrays cannot be shared among instances.
 121  * There are separate instance structure declarations for each of the 3 supported data types.
 122  *
 123  * \par Initialization Functions
 124  * There is also an associated initialization function for each data type.
 125  * The initialization function performs the following operations:
 126  * - Sets the values of the internal structure fields.
 127  * - Zeros out the values in the state buffer.
 128  * To do this manually without calling the init function, assign the follow subfields of the instance structure:
 129  * numTaps, pCoeffs, mu, energy, x0, pState. Also set all of the values in pState to zero.
 130  * For Q7, Q15, and Q31 the following fields must also be initialized;
 131  * recipTable, postShift
 132  *
 133  * \par
 134  * Instance structure cannot be placed into a const data section and it is recommended to use the initialization function.
 135  * \par Fixed-Point Behavior:
 136  * Care must be taken when using the Q15 and Q31 versions of the normalised LMS filter.
 137  * The following issues must be considered:
 138  * - Scaling of coefficients
 139  * - Overflow and saturation
 140  *
 141  * \par Scaling of Coefficients:
 142  * Filter coefficients are represented as fractional values and
 143  * coefficients are restricted to lie in the range <code>[-1 +1)</code>.
 144  * The fixed-point functions have an additional scaling parameter <code>postShift</code>.
 145  * At the output of the filter's accumulator is a shift register which shifts the result by <code>postShift</code> bits.
 146  * This essentially scales the filter coefficients by <code>2^postShift</code> and
 147  * allows the filter coefficients to exceed the range <code>[+1 -1)</code>.
 148  * The value of <code>postShift</code> is set by the user based on the expected gain through the system being modeled.
 149  *
 150  * \par Overflow and Saturation:
 151  * Overflow and saturation behavior of the fixed-point Q15 and Q31 versions are
 152  * described separately as part of the function specific documentation below.
 153  */
 154
 155
 156 /**
 157  * @addtogroup LMS_NORM
 158  * @{
 159  */
 160
 161
 162   /**
 163    * @brief Processing function for floating-point normalized LMS filter.
 164    * @param[in] *S points to an instance of the floating-point normalized LMS filter structure.
 165    * @param[in] *pSrc points to the block of input data.
 166    * @param[in] *pRef points to the block of reference data.
 167    * @param[out] *pOut points to the block of output data.
 168    * @param[out] *pErr points to the block of error data.
 169    * @param[in] blockSize number of samples to process.
 170    * @return none.
 171    */
 172
 173 void arm_lms_norm_f32(
 174   arm_lms_norm_instance_f32 * S,
 175   float32_t * pSrc,
 176   float32_t * pRef,
 177   float32_t * pOut,
 178   float32_t * pErr,
 179   uint32_t blockSize)
 180 {
 181   float32_t *pState = S->pState;                 /* State pointer */
 182   float32_t *pCoeffs = S->pCoeffs;               /* Coefficient pointer */
 183   float32_t *pStateCurnt;                        /* Points to the current sample of the state */
 184   float32_t *px, *pb;                            /* Temporary pointers for state and coefficient buffers */
 185   float32_t mu = S->mu;                          /* Adaptive factor */
 186   uint32_t numTaps = S->numTaps;                 /* Number of filter coefficients in the filter */
 187   uint32_t tapCnt, blkCnt;                       /* Loop counters */
 188   float32_t energy;                              /* Energy of the input */
 189   float32_t sum, e, d;                           /* accumulator, error, reference data sample */
 190   float32_t w, x0, in;                           /* weight factor, temporary variable to hold input sample and state */
 191
 192   /* Initializations of error,  difference, Coefficient update */
 193   e = 0.0f;
 194   d = 0.0f;
 195   w = 0.0f;
 196
 197   energy = S->energy;
 198   x0 = S->x0;
 199
 200   /* S->pState points to buffer which contains previous frame (numTaps - 1) samples */
 201   /* pStateCurnt points to the location where the new input data should be written */
 202   pStateCurnt = &(S->pState[(numTaps - 1u)]);
 203
 204   /* Loop over blockSize number of values */
 205   blkCnt = blockSize;
 206
 207
 208 #ifndef ARM_MATH_CM0_FAMILY
 209
 210   /* Run the below code for Cortex-M4 and Cortex-M3 */
 211
 212   while(blkCnt > 0u)
 213   {
 214     /* Copy the new input sample into the state buffer */
 215     *pStateCurnt++ = *pSrc;
 216
 217     /* Initialize pState pointer */
 218     px = pState;
 219
 220     /* Initialize coeff pointer */
 221     pb = (pCoeffs);
 222
 223     /* Read the sample from input buffer */
 224     in = *pSrc++;
 225
 226     /* Update the energy calculation */
 227     energy -= x0 * x0;
 228     energy += in * in;
 229
 230     /* Set the accumulator to zero */
 231     sum = 0.0f;
 232
 233     /* Loop unrolling.  Process 4 taps at a time. */
 234     tapCnt = numTaps >> 2;
 235
 236     while(tapCnt > 0u)
 237     {
 238       /* Perform the multiply-accumulate */
 239       sum += (*px++) * (*pb++);
 240       sum += (*px++) * (*pb++);
 241       sum += (*px++) * (*pb++);
 242       sum += (*px++) * (*pb++);
 243
 244       /* Decrement the loop counter */
 245       tapCnt--;
 246     }
 247
 248     /* If the filter length is not a multiple of 4, compute the remaining filter taps */
 249     tapCnt = numTaps % 0x4u;
 250
 251     while(tapCnt > 0u)
 252     {
 253       /* Perform the multiply-accumulate */
 254       sum += (*px++) * (*pb++);
 255
 256       /* Decrement the loop counter */
 257       tapCnt--;
 258     }
 259
 260     /* The result in the accumulator, store in the destination buffer. */
 261     *pOut++ = sum;
 262
 263     /* Compute and store error */
 264     d = (float32_t) (*pRef++);
 265     e = d - sum;
 266     *pErr++ = e;
 267
 268     /* Calculation of Weighting factor for updating filter coefficients */
 269     /* epsilon value 0.000000119209289f */
 270     w = (e * mu) / (energy + 0.000000119209289f);
 271
 272     /* Initialize pState pointer */
 273     px = pState;
 274
 275     /* Initialize coeff pointer */
 276     pb = (pCoeffs);
 277
 278     /* Loop unrolling.  Process 4 taps at a time. */
 279     tapCnt = numTaps >> 2;
 280
 281     /* Update filter coefficients */
 282     while(tapCnt > 0u)
 283     {
 284       /* Perform the multiply-accumulate */
 285       *pb += w * (*px++);
 286       pb++;
 287
 288       *pb += w * (*px++);
 289       pb++;
 290
 291       *pb += w * (*px++);
 292       pb++;
 293
 294       *pb += w * (*px++);
 295       pb++;
 296
 297
 298       /* Decrement the loop counter */
 299       tapCnt--;
 300     }
 301
 302     /* If the filter length is not a multiple of 4, compute the remaining filter taps */
 303     tapCnt = numTaps % 0x4u;
 304
 305     while(tapCnt > 0u)
 306     {
 307       /* Perform the multiply-accumulate */
 308       *pb += w * (*px++);
 309       pb++;
 310
 311       /* Decrement the loop counter */
 312       tapCnt--;
 313     }
 314
 315     x0 = *pState;
 316
 317     /* Advance state pointer by 1 for the next sample */
 318     pState = pState + 1;
 319
 320     /* Decrement the loop counter */
 321     blkCnt--;
 322   }
 323
 324   S->energy = energy;
 325   S->x0 = x0;
 326
 327   /* Processing is complete. Now copy the last numTaps - 1 samples to the
 328      satrt of the state buffer. This prepares the state buffer for the
 329      next function call. */
 330
 331   /* Points to the start of the pState buffer */
 332   pStateCurnt = S->pState;
 333
 334   /* Loop unrolling for (numTaps - 1u)/4 samples copy */
 335   tapCnt = (numTaps - 1u) >> 2u;
 336
 337   /* copy data */
 338   while(tapCnt > 0u)
 339   {
 340     *pStateCurnt++ = *pState++;
 341     *pStateCurnt++ = *pState++;
 342     *pStateCurnt++ = *pState++;
 343     *pStateCurnt++ = *pState++;
 344
 345     /* Decrement the loop counter */
 346     tapCnt--;
 347   }
 348
 349   /* Calculate remaining number of copies */
 350   tapCnt = (numTaps - 1u) % 0x4u;
 351
 352   /* Copy the remaining q31_t data */
 353   while(tapCnt > 0u)
 354   {
 355     *pStateCurnt++ = *pState++;
 356
 357     /* Decrement the loop counter */
 358     tapCnt--;
 359   }
 360
 361 #else
 362
 363   /* Run the below code for Cortex-M0 */
 364
 365   while(blkCnt > 0u)
 366   {
 367     /* Copy the new input sample into the state buffer */
 368     *pStateCurnt++ = *pSrc;
 369
 370     /* Initialize pState pointer */
 371     px = pState;
 372
 373     /* Initialize pCoeffs pointer */
 374     pb = pCoeffs;
 375
 376     /* Read the sample from input buffer */
 377     in = *pSrc++;
 378
 379     /* Update the energy calculation */
 380     energy -= x0 * x0;
 381     energy += in * in;
 382
 383     /* Set the accumulator to zero */
 384     sum = 0.0f;
 385
 386     /* Loop over numTaps number of values */
 387     tapCnt = numTaps;
 388
 389     while(tapCnt > 0u)
 390     {
 391       /* Perform the multiply-accumulate */
 392       sum += (*px++) * (*pb++);
 393
 394       /* Decrement the loop counter */
 395       tapCnt--;
 396     }
 397
 398     /* The result in the accumulator is stored in the destination buffer. */
 399     *pOut++ = sum;
 400
 401     /* Compute and store error */
 402     d = (float32_t) (*pRef++);
 403     e = d - sum;
 404     *pErr++ = e;
 405
 406     /* Calculation of Weighting factor for updating filter coefficients */
 407     /* epsilon value 0.000000119209289f */
 408     w = (e * mu) / (energy + 0.000000119209289f);
 409
 410     /* Initialize pState pointer */
 411     px = pState;
 412
 413     /* Initialize pCcoeffs pointer */
 414     pb = pCoeffs;
 415
 416     /* Loop over numTaps number of values */
 417     tapCnt = numTaps;
 418
 419     while(tapCnt > 0u)
 420     {
 421       /* Perform the multiply-accumulate */
 422       *pb += w * (*px++);
 423       pb++;
 424
 425       /* Decrement the loop counter */
 426       tapCnt--;
 427     }
 428
 429     x0 = *pState;
 430
 431     /* Advance state pointer by 1 for the next sample */
 432     pState = pState + 1;
 433
 434     /* Decrement the loop counter */
 435     blkCnt--;
 436   }
 437
 438   S->energy = energy;
 439   S->x0 = x0;
 440
 441   /* Processing is complete. Now copy the last numTaps - 1 samples to the
 442      satrt of the state buffer. This prepares the state buffer for the
 443      next function call. */
 444
 445   /* Points to the start of the pState buffer */
 446   pStateCurnt = S->pState;
 447
 448   /* Copy (numTaps - 1u) samples  */
 449   tapCnt = (numTaps - 1u);
 450
 451   /* Copy the remaining q31_t data */
 452   while(tapCnt > 0u)
 453   {
 454     *pStateCurnt++ = *pState++;
 455
 456     /* Decrement the loop counter */
 457     tapCnt--;
 458   }
 459
 460 #endif /*   #ifndef ARM_MATH_CM0_FAMILY */
 461
 462 }
 463
 464 /**
 465    * @} end of LMS_NORM group
 466    */