arm_lms_f32.c

00001 /* ----------------------------------------------------------------------  
00002 * Copyright (C) 2010 ARM Limited. All rights reserved.  
00003 *  
00004 * $Date:        29. November 2010  
00005 * $Revision:    V1.0.3  
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
00013 *  
00014 * Version 1.0.3 2010/11/29 
00015 *    Re-organized the CMSIS folders and updated documentation.  
00016 *   
00017 * Version 1.0.2 2010/11/11  
00018 *    Documentation updated.   
00019 *  
00020 * Version 1.0.1 2010/10/05   
00021 *    Production release and review comments incorporated.  
00022 *  
00023 * Version 1.0.0 2010/09/20   
00024 *    Production release and review comments incorporated  
00025 *  
00026 * Version 0.0.7  2010/06/10   
00027 *    Misra-C changes done  
00028 * -------------------------------------------------------------------- */ 
00029  
00030 #include "arm_math.h" 
00031  
00032 /**  
00033  * @ingroup groupFilters  
00034  */ 
00035  
00036 /**  
00037  * @defgroup LMS Least Mean Square (LMS) Filters  
00038  *  
00039  * LMS filters are a class of adaptive filters that are able to "learn" an unknown transfer functions.  
00040  * LMS filters use a gradient descent method in which the filter coefficients are updated based on the instantaneous error signal.  
00041  * Adaptive filters are often used in communication systems, equalizers, and noise removal.  
00042  * The CMSIS DSP Library contains LMS filter functions that operate on Q15, Q31, and floating-point data types.  
00043  * The library also contains normalized LMS filters in which the filter coefficient adaptation is indepedent of the level of the input signal.  
00044  *  
00045  * An LMS filter consists of two components as shown below.  
00046  * The first component is a standard transversal or FIR filter.  
00047  * The second component is a coefficient update mechanism.  
00048  * The LMS filter has two input signals.  
00049  * The "input" feeds the FIR filter while the "reference input" corresponds to the desired output of the FIR filter.  
00050  * That is, the FIR filter coefficients are updated so that the output of the FIR filter matches the reference input.  
00051  * The filter coefficient update mechanism is based on the difference between the FIR filter output and the reference input.  
00052  * This "error signal" tends towards zero as the filter adapts.  
00053  * The LMS processing functions accept the input and reference input signals and generate the filter output and error signal.  
00054  * \image html LMS.gif "Internal structure of the Least Mean Square filter"  
00055  *  
00056  * The functions operate on blocks of data and each call to the function processes  
00057  * <code>blockSize</code> samples through the filter.  
00058  * <code>pSrc</code> points to input signal, <code>pRef</code> points to reference signal,  
00059  * <code>pOut</code> points to output signal and <code>pErr</code> points to error signal.  
00060  * All arrays contain <code>blockSize</code> values.  
00061  *  
00062  * The API functions operate on a block-by-block basis.  
00063  * Internally, the filter coefficients <code>b[n]</code> are updated on a sample-by-sample basis.  
00064  * The convergence of the LMS filter is slower compared to the normalized LMS algorithm.  
00065  *  
00066  * \par Algorithm:  
00067  * The output signal <code>y[n]</code> is computed by a standard FIR filter:  
00068  * <pre>  
00069  *     y[n] = b[0] * x[n] + b[1] * x[n-1] + b[2] * x[n-2] + ...+ b[numTaps-1] * x[n-numTaps+1]  
00070  * </pre>  
00071  *  
00072  * \par  
00073  * The error signal equals the difference between the reference signal <code>d[n]</code> and the filter output:  
00074  * <pre>  
00075  *     e[n] = d[n] - y[n].  
00076  * </pre>  
00077  *  
00078  * \par  
00079  * After each sample of the error signal is computed, the filter coefficients <code>b[k]</code> are updated on a sample-by-sample basis:  
00080  * <pre>  
00081  *     b[k] = b[k] + e[n] * mu * x[n-k],  for k=0, 1, ..., numTaps-1  
00082  * </pre>  
00083  * where <code>mu</code> is the step size and controls the rate of coefficient convergence.  
00084  *\par  
00085  * In the APIs, <code>pCoeffs</code> points to a coefficient array of size <code>numTaps</code>.  
00086  * Coefficients are stored in time reversed order.  
00087  * \par  
00088  * <pre>  
00089  *    {b[numTaps-1], b[numTaps-2], b[N-2], ..., b[1], b[0]}  
00090  * </pre>  
00091  * \par  
00092  * <code>pState</code> points to a state array of size <code>numTaps + blockSize - 1</code>.  
00093  * Samples in the state buffer are stored in the order:  
00094  * \par  
00095  * <pre>  
00096  *    {x[n-numTaps+1], x[n-numTaps], x[n-numTaps-1], x[n-numTaps-2]....x[0], x[1], ..., x[blockSize-1]}  
00097  * </pre>  
00098  * \par  
00099  * Note that the length of the state buffer exceeds the length of the coefficient array by <code>blockSize-1</code> samples.  
00100  * The increased state buffer length allows circular addressing, which is traditionally used in FIR filters,  
00101  * to be avoided and yields a significant speed improvement.  
00102  * The state variables are updated after each block of data is processed.  
00103  * \par Instance Structure  
00104  * The coefficients and state variables for a filter are stored together in an instance data structure.  
00105  * A separate instance structure must be defined for each filter and  
00106  * coefficient and state arrays cannot be shared among instances.  
00107  * There are separate instance structure declarations for each of the 3 supported data types.  
00108  *  
00109  * \par Initialization Functions  
00110  * There is also an associated initialization function for each data type.  
00111  * The initialization function performs the following operations:  
00112  * - Sets the values of the internal structure fields.  
00113  * - Zeros out the values in the state buffer.  
00114  * \par  
00115  * Use of the initialization function is optional.  
00116  * However, if the initialization function is used, then the instance structure cannot be placed into a const data section.  
00117  * To place an instance structure into a const data section, the instance structure must be manually initialized.  
00118  * Set the values in the state buffer to zeros before static initialization.  
00119  * The code below statically initializes each of the 3 different data type filter instance structures  
00120  * <pre>  
00121  *    arm_lms_instance_f32 S = {numTaps, pState, pCoeffs, mu};  
00122  *    arm_lms_instance_q31 S = {numTaps, pState, pCoeffs, mu, postShift};  
00123  *    arm_lms_instance_q15 S = {numTaps, pState, pCoeffs, mu, postShift};  
00124  * </pre>  
00125  * where <code>numTaps</code> is the number of filter coefficients in the filter; <code>pState</code> is the address of the state buffer;  
00126  * <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.  
00127  *  
00128  * \par Fixed-Point Behavior:  
00129  * Care must be taken when using the Q15 and Q31 versions of the LMS filter.  
00130  * The following issues must be considered:  
00131  * - Scaling of coefficients  
00132  * - Overflow and saturation  
00133  *  
00134  * \par Scaling of Coefficients:  
00135  * Filter coefficients are represented as fractional values and  
00136  * coefficients are restricted to lie in the range <code>[-1 +1)</code>.  
00137  * The fixed-point functions have an additional scaling parameter <code>postShift</code>.  
00138  * At the output of the filter's accumulator is a shift register which shifts the result by <code>postShift</code> bits.  
00139  * This essentially scales the filter coefficients by <code>2^postShift</code> and  
00140  * allows the filter coefficients to exceed the range <code>[+1 -1)</code>.  
00141  * The value of <code>postShift</code> is set by the user based on the expected gain through the system being modeled.  
00142  *  
00143  * \par Overflow and Saturation:  
00144  * Overflow and saturation behavior of the fixed-point Q15 and Q31 versions are  
00145  * described separately as part of the function specific documentation below.  
00146  */ 
00147  
00148 /**  
00149  * @addtogroup LMS  
00150  * @{  
00151  */ 
00152  
00153   /**  
00154    * @brief Processing function for floating-point LMS filter.  
00155    * @param[in]  *S points to an instance of the floating-point LMS filter structure.  
00156    * @param[in]  *pSrc points to the block of input data.  
00157    * @param[in]  *pRef points to the block of reference data.  
00158    * @param[out] *pOut points to the block of output data.  
00159    * @param[out] *pErr points to the block of error data.  
00160    * @param[in]  blockSize number of samples to process.  
00161    * @return     none.  
00162    */ 
00163  
00164 void arm_lms_f32( 
00165   const arm_lms_instance_f32 * S, 
00166   float32_t * pSrc, 
00167   float32_t * pRef, 
00168   float32_t * pOut, 
00169   float32_t * pErr, 
00170   uint32_t blockSize) 
00171 { 
00172   float32_t *pState = S->pState;                 /* State pointer */ 
00173   float32_t *pCoeffs = S->pCoeffs;               /* Coefficient pointer */ 
00174   float32_t *pStateCurnt;                        /* Points to the current sample of the state */ 
00175   float32_t *px, *pb;                            /* Temporary pointers for state and coefficient buffers */ 
00176   float32_t mu = S->mu;                          /* Adaptive factor */ 
00177   uint32_t numTaps = S->numTaps;                 /* Number of filter coefficients in the filter */ 
00178   uint32_t tapCnt, blkCnt;                       /* Loop counters */ 
00179   float32_t sum, e, d;                           /* accumulator, error, reference data sample */ 
00180   float32_t w = 0.0f;                            /* weight factor */ 
00181  
00182   e = 0.0f; 
00183   d = 0.0f; 
00184  
00185   /* S->pState points to state array which contains previous frame (numTaps - 1) samples */ 
00186   /* pStateCurnt points to the location where the new input data should be written */ 
00187   pStateCurnt = &(S->pState[(numTaps - 1u)]); 
00188  
00189   blkCnt = blockSize; 
00190  
00191   while(blkCnt > 0u) 
00192   { 
00193     /* Copy the new input sample into the state buffer */ 
00194     *pStateCurnt++ = *pSrc++; 
00195  
00196     /* Initialize pState pointer */ 
00197     px = pState; 
00198  
00199     /* Initialize coeff pointer */ 
00200     pb = (pCoeffs); 
00201  
00202     /* Set the accumulator to zero */ 
00203     sum = 0.0f; 
00204  
00205     /* Loop unrolling.  Process 4 taps at a time. */ 
00206     tapCnt = numTaps >> 2; 
00207  
00208     while(tapCnt > 0u) 
00209     { 
00210       /* Perform the multiply-accumulate */ 
00211       sum += (*px++) * (*pb++); 
00212       sum += (*px++) * (*pb++); 
00213       sum += (*px++) * (*pb++); 
00214       sum += (*px++) * (*pb++); 
00215  
00216       /* Decrement the loop counter */ 
00217       tapCnt--; 
00218     } 
00219  
00220     /* If the filter length is not a multiple of 4, compute the remaining filter taps */ 
00221     tapCnt = numTaps % 0x4u; 
00222  
00223     while(tapCnt > 0u) 
00224     { 
00225       /* Perform the multiply-accumulate */ 
00226       sum += (*px++) * (*pb++); 
00227  
00228       /* Decrement the loop counter */ 
00229       tapCnt--; 
00230     } 
00231  
00232     /* The result in the accumulator, store in the destination buffer. */ 
00233     *pOut++ = sum; 
00234  
00235     /* Compute and store error */ 
00236     d = (float32_t) (*pRef++); 
00237     e = d - sum; 
00238     *pErr++ = e; 
00239  
00240     /* Calculation of Weighting factor for the updating filter coefficients */ 
00241     w = e * mu; 
00242  
00243     /* Initialize pState pointer */ 
00244     px = pState; 
00245  
00246     /* Initialize coeff pointer */ 
00247     pb = (pCoeffs); 
00248  
00249     /* Loop unrolling.  Process 4 taps at a time. */ 
00250     tapCnt = numTaps >> 2; 
00251  
00252     /* Update filter coefficients */ 
00253     while(tapCnt > 0u) 
00254     { 
00255       /* Perform the multiply-accumulate */ 
00256       *pb = *pb + (w * (*px++)); 
00257       pb++; 
00258  
00259       *pb = *pb + (w * (*px++)); 
00260       pb++; 
00261  
00262       *pb = *pb + (w * (*px++)); 
00263       pb++; 
00264  
00265       *pb = *pb + (w * (*px++)); 
00266       pb++; 
00267  
00268       /* Decrement the loop counter */ 
00269       tapCnt--; 
00270     } 
00271  
00272     /* If the filter length is not a multiple of 4, compute the remaining filter taps */ 
00273     tapCnt = numTaps % 0x4u; 
00274  
00275     while(tapCnt > 0u) 
00276     { 
00277       /* Perform the multiply-accumulate */ 
00278       *pb = *pb + (w * (*px++)); 
00279       pb++; 
00280  
00281       /* Decrement the loop counter */ 
00282       tapCnt--; 
00283     } 
00284  
00285     /* Advance state pointer by 1 for the next sample */ 
00286     pState = pState + 1; 
00287  
00288     /* Decrement the loop counter */ 
00289     blkCnt--; 
00290   } 
00291  
00292  
00293   /* Processing is complete. Now copy the last numTaps - 1 samples to the  
00294      satrt of the state buffer. This prepares the state buffer for the  
00295      next function call. */ 
00296  
00297   /* Points to the start of the pState buffer */ 
00298   pStateCurnt = S->pState; 
00299  
00300   /* Loop unrolling for (numTaps - 1u) samples copy */ 
00301   tapCnt = (numTaps - 1u) >> 2u; 
00302  
00303   /* copy data */ 
00304   while(tapCnt > 0u) 
00305   { 
00306     *pStateCurnt++ = *pState++; 
00307     *pStateCurnt++ = *pState++; 
00308     *pStateCurnt++ = *pState++; 
00309     *pStateCurnt++ = *pState++; 
00310  
00311     /* Decrement the loop counter */ 
00312     tapCnt--; 
00313   } 
00314  
00315   /* Calculate remaining number of copies */ 
00316   tapCnt = (numTaps - 1u) % 0x4u; 
00317  
00318   /* Copy the remaining q31_t data */ 
00319   while(tapCnt > 0u) 
00320   { 
00321     *pStateCurnt++ = *pState++; 
00322  
00323     /* Decrement the loop counter */ 
00324     tapCnt--; 
00325   } 
00326 } 
00327  
00328 /**  
00329    * @} end of LMS group  
00330    */