arm_lms_f32.c

00001 /* ----------------------------------------------------------------------    
00002 * Copyright (C) 2010-2014 ARM Limited. All rights reserved.    
00003 *    
00004 * $Date:        19. March 2015
00005 * $Revision:    V.1.4.5
00006 *    
00007 * Project:      CMSIS DSP Library    
00008 * Title:        arm_lms_f32.c    
00009 *    
00010 * Description:  Processing function for the floating-point LMS filter.    
00011 *    
00012 * Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
00013 *  
00014 * Redistribution and use in source and binary forms, with or without 
00015 * modification, are permitted provided that the following conditions
00016 * are met:
00017 *   - Redistributions of source code must retain the above copyright
00018 *     notice, this list of conditions and the following disclaimer.
00019 *   - Redistributions in binary form must reproduce the above copyright
00020 *     notice, this list of conditions and the following disclaimer in
00021 *     the documentation and/or other materials provided with the 
00022 *     distribution.
00023 *   - Neither the name of ARM LIMITED nor the names of its contributors
00024 *     may be used to endorse or promote products derived from this
00025 *     software without specific prior written permission.
00026 *
00027 * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
00028 * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
00029 * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
00030 * FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE 
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00032 * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
00033 * BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
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00035 * CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
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00037 * ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
00038 * POSSIBILITY OF SUCH DAMAGE.    
00039 * -------------------------------------------------------------------- */
00040 
00041 #include "arm_math.h"
00042 
00043 /**    
00044  * @ingroup groupFilters    
00045  */
00046 
00047 /**    
00048  * @defgroup LMS Least Mean Square (LMS) Filters    
00049  *    
00050  * LMS filters are a class of adaptive filters that are able to "learn" an unknown transfer functions.    
00051  * LMS filters use a gradient descent method in which the filter coefficients are updated based on the instantaneous error signal.    
00052  * Adaptive filters are often used in communication systems, equalizers, and noise removal.    
00053  * The CMSIS DSP Library contains LMS filter functions that operate on Q15, Q31, and floating-point data types.    
00054  * The library also contains normalized LMS filters in which the filter coefficient adaptation is indepedent of the level of the input signal.    
00055  *    
00056  * An LMS filter consists of two components as shown below.    
00057  * The first component is a standard transversal or FIR filter.    
00058  * The second component is a coefficient update mechanism.    
00059  * The LMS filter has two input signals.    
00060  * The "input" feeds the FIR filter while the "reference input" corresponds to the desired output of the FIR filter.    
00061  * That is, the FIR filter coefficients are updated so that the output of the FIR filter matches the reference input.    
00062  * The filter coefficient update mechanism is based on the difference between the FIR filter output and the reference input.    
00063  * This "error signal" tends towards zero as the filter adapts.    
00064  * The LMS processing functions accept the input and reference input signals and generate the filter output and error signal.    
00065  * \image html LMS.gif "Internal structure of the Least Mean Square filter"    
00066  *    
00067  * The functions operate on blocks of data and each call to the function processes    
00068  * <code>blockSize</code> samples through the filter.    
00069  * <code>pSrc</code> points to input signal, <code>pRef</code> points to reference signal,    
00070  * <code>pOut</code> points to output signal and <code>pErr</code> points to error signal.    
00071  * All arrays contain <code>blockSize</code> values.    
00072  *    
00073  * The functions operate on a block-by-block basis.    
00074  * Internally, the filter coefficients <code>b[n]</code> are updated on a sample-by-sample basis.    
00075  * The convergence of the LMS filter is slower compared to the normalized LMS algorithm.    
00076  *    
00077  * \par Algorithm:    
00078  * The output signal <code>y[n]</code> is computed by a standard FIR filter:    
00079  * <pre>    
00080  *     y[n] = b[0] * x[n] + b[1] * x[n-1] + b[2] * x[n-2] + ...+ b[numTaps-1] * x[n-numTaps+1]    
00081  * </pre>    
00082  *    
00083  * \par    
00084  * The error signal equals the difference between the reference signal <code>d[n]</code> and the filter output:    
00085  * <pre>    
00086  *     e[n] = d[n] - y[n].    
00087  * </pre>    
00088  *    
00089  * \par    
00090  * After each sample of the error signal is computed, the filter coefficients <code>b[k]</code> are updated on a sample-by-sample basis:    
00091  * <pre>    
00092  *     b[k] = b[k] + e[n] * mu * x[n-k],  for k=0, 1, ..., numTaps-1    
00093  * </pre>    
00094  * where <code>mu</code> is the step size and controls the rate of coefficient convergence.    
00095  *\par    
00096  * In the APIs, <code>pCoeffs</code> points to a coefficient array of size <code>numTaps</code>.    
00097  * Coefficients are stored in time reversed order.    
00098  * \par    
00099  * <pre>    
00100  *    {b[numTaps-1], b[numTaps-2], b[N-2], ..., b[1], b[0]}    
00101  * </pre>    
00102  * \par    
00103  * <code>pState</code> points to a state array of size <code>numTaps + blockSize - 1</code>.    
00104  * Samples in the state buffer are stored in the order:    
00105  * \par    
00106  * <pre>    
00107  *    {x[n-numTaps+1], x[n-numTaps], x[n-numTaps-1], x[n-numTaps-2]....x[0], x[1], ..., x[blockSize-1]}    
00108  * </pre>    
00109  * \par    
00110  * Note that the length of the state buffer exceeds the length of the coefficient array by <code>blockSize-1</code> samples.    
00111  * The increased state buffer length allows circular addressing, which is traditionally used in FIR filters,    
00112  * to be avoided and yields a significant speed improvement.    
00113  * The state variables are updated after each block of data is processed.    
00114  * \par Instance Structure    
00115  * The coefficients and state variables for a filter are stored together in an instance data structure.    
00116  * A separate instance structure must be defined for each filter and    
00117  * coefficient and state arrays cannot be shared among instances.    
00118  * There are separate instance structure declarations for each of the 3 supported data types.    
00119  *    
00120  * \par Initialization Functions    
00121  * There is also an associated initialization function for each data type.    
00122  * The initialization function performs the following operations:    
00123  * - Sets the values of the internal structure fields.    
00124  * - Zeros out the values in the state buffer.    
00125  * To do this manually without calling the init function, assign the follow subfields of the instance structure:
00126  * numTaps, pCoeffs, mu, postShift (not for f32), pState. Also set all of the values in pState to zero. 
00127  *
00128  * \par    
00129  * Use of the initialization function is optional.    
00130  * However, if the initialization function is used, then the instance structure cannot be placed into a const data section.    
00131  * To place an instance structure into a const data section, the instance structure must be manually initialized.    
00132  * Set the values in the state buffer to zeros before static initialization.    
00133  * The code below statically initializes each of the 3 different data type filter instance structures    
00134  * <pre>    
00135  *    arm_lms_instance_f32 S = {numTaps, pState, pCoeffs, mu};    
00136  *    arm_lms_instance_q31 S = {numTaps, pState, pCoeffs, mu, postShift};    
00137  *    arm_lms_instance_q15 S = {numTaps, pState, pCoeffs, mu, postShift};    
00138  * </pre>    
00139  * where <code>numTaps</code> is the number of filter coefficients in the filter; <code>pState</code> is the address of the state buffer;    
00140  * <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.    
00141  *    
00142  * \par Fixed-Point Behavior:    
00143  * Care must be taken when using the Q15 and Q31 versions of the LMS filter.    
00144  * The following issues must be considered:    
00145  * - Scaling of coefficients    
00146  * - Overflow and saturation    
00147  *    
00148  * \par Scaling of Coefficients:    
00149  * Filter coefficients are represented as fractional values and    
00150  * coefficients are restricted to lie in the range <code>[-1 +1)</code>.    
00151  * The fixed-point functions have an additional scaling parameter <code>postShift</code>.    
00152  * At the output of the filter's accumulator is a shift register which shifts the result by <code>postShift</code> bits.    
00153  * This essentially scales the filter coefficients by <code>2^postShift</code> and    
00154  * allows the filter coefficients to exceed the range <code>[+1 -1)</code>.    
00155  * The value of <code>postShift</code> is set by the user based on the expected gain through the system being modeled.    
00156  *    
00157  * \par Overflow and Saturation:    
00158  * Overflow and saturation behavior of the fixed-point Q15 and Q31 versions are    
00159  * described separately as part of the function specific documentation below.    
00160  */
00161 
00162 /**    
00163  * @addtogroup LMS    
00164  * @{    
00165  */
00166 
00167 /**           
00168  * @details           
00169  * This function operates on floating-point data types.       
00170  *    
00171  * @brief Processing function for floating-point LMS filter.    
00172  * @param[in]  *S points to an instance of the floating-point LMS filter structure.    
00173  * @param[in]  *pSrc points to the block of input data.    
00174  * @param[in]  *pRef points to the block of reference data.    
00175  * @param[out] *pOut points to the block of output data.    
00176  * @param[out] *pErr points to the block of error data.    
00177  * @param[in]  blockSize number of samples to process.    
00178  * @return     none.    
00179  */
00180 
00181 void arm_lms_f32(
00182   const arm_lms_instance_f32 * S,
00183   float32_t * pSrc,
00184   float32_t * pRef,
00185   float32_t * pOut,
00186   float32_t * pErr,
00187   uint32_t blockSize)
00188 {
00189   float32_t *pState = S->pState;                 /* State pointer */
00190   float32_t *pCoeffs = S->pCoeffs;               /* Coefficient pointer */
00191   float32_t *pStateCurnt;                        /* Points to the current sample of the state */
00192   float32_t *px, *pb;                            /* Temporary pointers for state and coefficient buffers */
00193   float32_t mu = S->mu;                          /* Adaptive factor */
00194   uint32_t numTaps = S->numTaps;                 /* Number of filter coefficients in the filter */
00195   uint32_t tapCnt, blkCnt;                       /* Loop counters */
00196   float32_t sum, e, d;                           /* accumulator, error, reference data sample */
00197   float32_t w = 0.0f;                            /* weight factor */
00198 
00199   e = 0.0f;
00200   d = 0.0f;
00201 
00202   /* S->pState points to state array which contains previous frame (numTaps - 1) samples */
00203   /* pStateCurnt points to the location where the new input data should be written */
00204   pStateCurnt = &(S->pState[(numTaps - 1u)]);
00205 
00206   blkCnt = blockSize;
00207 
00208 
00209 #ifndef ARM_MATH_CM0_FAMILY
00210 
00211   /* Run the below code for Cortex-M4 and Cortex-M3 */
00212 
00213   while(blkCnt > 0u)
00214   {
00215     /* Copy the new input sample into the state buffer */
00216     *pStateCurnt++ = *pSrc++;
00217 
00218     /* Initialize pState pointer */
00219     px = pState;
00220 
00221     /* Initialize coeff pointer */
00222     pb = (pCoeffs);
00223 
00224     /* Set the accumulator to zero */
00225     sum = 0.0f;
00226 
00227     /* Loop unrolling.  Process 4 taps at a time. */
00228     tapCnt = numTaps >> 2;
00229 
00230     while(tapCnt > 0u)
00231     {
00232       /* Perform the multiply-accumulate */
00233       sum += (*px++) * (*pb++);
00234       sum += (*px++) * (*pb++);
00235       sum += (*px++) * (*pb++);
00236       sum += (*px++) * (*pb++);
00237 
00238       /* Decrement the loop counter */
00239       tapCnt--;
00240     }
00241 
00242     /* If the filter length is not a multiple of 4, compute the remaining filter taps */
00243     tapCnt = numTaps % 0x4u;
00244 
00245     while(tapCnt > 0u)
00246     {
00247       /* Perform the multiply-accumulate */
00248       sum += (*px++) * (*pb++);
00249 
00250       /* Decrement the loop counter */
00251       tapCnt--;
00252     }
00253 
00254     /* The result in the accumulator, store in the destination buffer. */
00255     *pOut++ = sum;
00256 
00257     /* Compute and store error */
00258     d = (float32_t) (*pRef++);
00259     e = d - sum;
00260     *pErr++ = e;
00261 
00262     /* Calculation of Weighting factor for the updating filter coefficients */
00263     w = e * mu;
00264 
00265     /* Initialize pState pointer */
00266     px = pState;
00267 
00268     /* Initialize coeff pointer */
00269     pb = (pCoeffs);
00270 
00271     /* Loop unrolling.  Process 4 taps at a time. */
00272     tapCnt = numTaps >> 2;
00273 
00274     /* Update filter coefficients */
00275     while(tapCnt > 0u)
00276     {
00277       /* Perform the multiply-accumulate */
00278       *pb = *pb + (w * (*px++));
00279       pb++;
00280 
00281       *pb = *pb + (w * (*px++));
00282       pb++;
00283 
00284       *pb = *pb + (w * (*px++));
00285       pb++;
00286 
00287       *pb = *pb + (w * (*px++));
00288       pb++;
00289 
00290       /* Decrement the loop counter */
00291       tapCnt--;
00292     }
00293 
00294     /* If the filter length is not a multiple of 4, compute the remaining filter taps */
00295     tapCnt = numTaps % 0x4u;
00296 
00297     while(tapCnt > 0u)
00298     {
00299       /* Perform the multiply-accumulate */
00300       *pb = *pb + (w * (*px++));
00301       pb++;
00302 
00303       /* Decrement the loop counter */
00304       tapCnt--;
00305     }
00306 
00307     /* Advance state pointer by 1 for the next sample */
00308     pState = pState + 1;
00309 
00310     /* Decrement the loop counter */
00311     blkCnt--;
00312   }
00313 
00314 
00315   /* Processing is complete. Now copy the last numTaps - 1 samples to the    
00316      satrt of the state buffer. This prepares the state buffer for the    
00317      next function call. */
00318 
00319   /* Points to the start of the pState buffer */
00320   pStateCurnt = S->pState;
00321 
00322   /* Loop unrolling for (numTaps - 1u) samples copy */
00323   tapCnt = (numTaps - 1u) >> 2u;
00324 
00325   /* copy data */
00326   while(tapCnt > 0u)
00327   {
00328     *pStateCurnt++ = *pState++;
00329     *pStateCurnt++ = *pState++;
00330     *pStateCurnt++ = *pState++;
00331     *pStateCurnt++ = *pState++;
00332 
00333     /* Decrement the loop counter */
00334     tapCnt--;
00335   }
00336 
00337   /* Calculate remaining number of copies */
00338   tapCnt = (numTaps - 1u) % 0x4u;
00339 
00340   /* Copy the remaining q31_t data */
00341   while(tapCnt > 0u)
00342   {
00343     *pStateCurnt++ = *pState++;
00344 
00345     /* Decrement the loop counter */
00346     tapCnt--;
00347   }
00348 
00349 #else
00350 
00351   /* Run the below code for Cortex-M0 */
00352 
00353   while(blkCnt > 0u)
00354   {
00355     /* Copy the new input sample into the state buffer */
00356     *pStateCurnt++ = *pSrc++;
00357 
00358     /* Initialize pState pointer */
00359     px = pState;
00360 
00361     /* Initialize pCoeffs pointer */
00362     pb = pCoeffs;
00363 
00364     /* Set the accumulator to zero */
00365     sum = 0.0f;
00366 
00367     /* Loop over numTaps number of values */
00368     tapCnt = numTaps;
00369 
00370     while(tapCnt > 0u)
00371     {
00372       /* Perform the multiply-accumulate */
00373       sum += (*px++) * (*pb++);
00374 
00375       /* Decrement the loop counter */
00376       tapCnt--;
00377     }
00378 
00379     /* The result is stored in the destination buffer. */
00380     *pOut++ = sum;
00381 
00382     /* Compute and store error */
00383     d = (float32_t) (*pRef++);
00384     e = d - sum;
00385     *pErr++ = e;
00386 
00387     /* Weighting factor for the LMS version */
00388     w = e * mu;
00389 
00390     /* Initialize pState pointer */
00391     px = pState;
00392 
00393     /* Initialize pCoeffs pointer */
00394     pb = pCoeffs;
00395 
00396     /* Loop over numTaps number of values */
00397     tapCnt = numTaps;
00398 
00399     while(tapCnt > 0u)
00400     {
00401       /* Perform the multiply-accumulate */
00402       *pb = *pb + (w * (*px++));
00403       pb++;
00404 
00405       /* Decrement the loop counter */
00406       tapCnt--;
00407     }
00408 
00409     /* Advance state pointer by 1 for the next sample */
00410     pState = pState + 1;
00411 
00412     /* Decrement the loop counter */
00413     blkCnt--;
00414   }
00415 
00416 
00417   /* Processing is complete. Now copy the last numTaps - 1 samples to the        
00418    * start of the state buffer. This prepares the state buffer for the        
00419    * next function call. */
00420 
00421   /* Points to the start of the pState buffer */
00422   pStateCurnt = S->pState;
00423 
00424   /*  Copy (numTaps - 1u) samples  */
00425   tapCnt = (numTaps - 1u);
00426 
00427   /* Copy the data */
00428   while(tapCnt > 0u)
00429   {
00430     *pStateCurnt++ = *pState++;
00431 
00432     /* Decrement the loop counter */
00433     tapCnt--;
00434   }
00435 
00436 #endif /*   #ifndef ARM_MATH_CM0_FAMILY */
00437 
00438 }
00439 
00440 /**    
00441    * @} end of LMS group    
00442    */