arm_lms_norm_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_norm_f32.c  
00009 *  
00010 * Description:  Processing function for the floating-point Normalised LMS.  
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_NORM Normalized LMS Filters  
00038  *  
00039  * This set of functions implements a commonly used adaptive filter.  
00040  * It is related to the Least Mean Square (LMS) adaptive filter and includes an additional normalization  
00041  * factor which increases the adaptation rate of the filter.  
00042  * The CMSIS DSP Library contains normalized LMS filter functions that operate on Q15, Q31, and floating-point data types.  
00043  *  
00044  * A normalized least mean square (NLMS) filter consists of two components as shown below.  
00045  * The first component is a standard transversal or FIR filter.  
00046  * The second component is a coefficient update mechanism.  
00047  * The NLMS filter has two input signals.  
00048  * The "input" feeds the FIR filter while the "reference input" corresponds to the desired output of the FIR filter.  
00049  * That is, the FIR filter coefficients are updated so that the output of the FIR filter matches the reference input.  
00050  * The filter coefficient update mechanism is based on the difference between the FIR filter output and the reference input.  
00051  * This "error signal" tends towards zero as the filter adapts.  
00052  * The NLMS processing functions accept the input and reference input signals and generate the filter output and error signal.  
00053  * \image html LMS.gif "Internal structure of the NLMS adaptive filter"  
00054  *  
00055  * The functions operate on blocks of data and each call to the function processes  
00056  * <code>blockSize</code> samples through the filter.  
00057  * <code>pSrc</code> points to input signal, <code>pRef</code> points to reference signal,  
00058  * <code>pOut</code> points to output signal and <code>pErr</code> points to error signal.  
00059  * All arrays contain <code>blockSize</code> values.  
00060  *  
00061  * The API functions operate on a block-by-block basis.  
00062  * Internally, the filter coefficients <code>b[n]</code> are updated on a sample-by-sample basis.  
00063  * The convergence of the LMS filter is slower compared to the normalized LMS algorithm.  
00064  *  
00065  * \par Algorithm:  
00066  * The output signal <code>y[n]</code> is computed by a standard FIR filter:  
00067  * <pre>  
00068  *     y[n] = b[0] * x[n] + b[1] * x[n-1] + b[2] * x[n-2] + ...+ b[numTaps-1] * x[n-numTaps+1]  
00069  * </pre>  
00070  *  
00071  * \par  
00072  * The error signal equals the difference between the reference signal <code>d[n]</code> and the filter output:  
00073  * <pre>  
00074  *     e[n] = d[n] - y[n].  
00075  * </pre>  
00076  *  
00077  * \par  
00078  * After each sample of the error signal is computed the instanteous energy of the filter state variables is calculated:  
00079  * <pre>  
00080  *    E = x[n]^2 + x[n-1]^2 + ... + x[n-numTaps+1]^2.  
00081  * </pre>  
00082  * The filter coefficients <code>b[k]</code> are then updated on a sample-by-sample basis:  
00083  * <pre>  
00084  *     b[k] = b[k] + e[n] * (mu/E) * x[n-k],  for k=0, 1, ..., numTaps-1  
00085  * </pre>  
00086  * where <code>mu</code> is the step size and controls the rate of coefficient convergence.  
00087  *\par  
00088  * In the APIs, <code>pCoeffs</code> points to a coefficient array of size <code>numTaps</code>.  
00089  * Coefficients are stored in time reversed order.  
00090  * \par  
00091  * <pre>  
00092  *    {b[numTaps-1], b[numTaps-2], b[N-2], ..., b[1], b[0]}  
00093  * </pre>  
00094  * \par  
00095  * <code>pState</code> points to a state array of size <code>numTaps + blockSize - 1</code>.  
00096  * Samples in the state buffer are stored in the order:  
00097  * \par  
00098  * <pre>  
00099  *    {x[n-numTaps+1], x[n-numTaps], x[n-numTaps-1], x[n-numTaps-2]....x[0], x[1], ..., x[blockSize-1]}  
00100  * </pre>  
00101  * \par  
00102  * Note that the length of the state buffer exceeds the length of the coefficient array by <code>blockSize-1</code> samples.  
00103  * The increased state buffer length allows circular addressing, which is traditionally used in FIR filters,  
00104  * to be avoided and yields a significant speed improvement.  
00105  * The state variables are updated after each block of data is processed.  
00106  * \par Instance Structure  
00107  * The coefficients and state variables for a filter are stored together in an instance data structure.  
00108  * A separate instance structure must be defined for each filter and  
00109  * coefficient and state arrays cannot be shared among instances.  
00110  * There are separate instance structure declarations for each of the 3 supported data types.  
00111  *  
00112  * \par Initialization Functions  
00113  * There is also an associated initialization function for each data type.  
00114  * The initialization function performs the following operations:  
00115  * - Sets the values of the internal structure fields.  
00116  * - Zeros out the values in the state buffer.  
00117  * \par  
00118  * Instance structure cannot be placed into a const data section and it is recommended to use the initialization function.  
00119  * \par Fixed-Point Behavior:  
00120  * Care must be taken when using the Q15 and Q31 versions of the normalised LMS filter.  
00121  * The following issues must be considered:  
00122  * - Scaling of coefficients  
00123  * - Overflow and saturation  
00124  *  
00125  * \par Scaling of Coefficients:  
00126  * Filter coefficients are represented as fractional values and  
00127  * coefficients are restricted to lie in the range <code>[-1 +1)</code>.  
00128  * The fixed-point functions have an additional scaling parameter <code>postShift</code>.  
00129  * At the output of the filter's accumulator is a shift register which shifts the result by <code>postShift</code> bits.  
00130  * This essentially scales the filter coefficients by <code>2^postShift</code> and  
00131  * allows the filter coefficients to exceed the range <code>[+1 -1)</code>.  
00132  * The value of <code>postShift</code> is set by the user based on the expected gain through the system being modeled.  
00133  *  
00134  * \par Overflow and Saturation:  
00135  * Overflow and saturation behavior of the fixed-point Q15 and Q31 versions are  
00136  * described separately as part of the function specific documentation below.  
00137  */ 
00138  
00139  
00140 /**  
00141  * @addtogroup LMS_NORM  
00142  * @{  
00143  */ 
00144  
00145  
00146   /**  
00147    * @brief Processing function for floating-point normalized LMS filter.  
00148    * @param[in] *S points to an instance of the floating-point normalized LMS filter structure.  
00149    * @param[in] *pSrc points to the block of input data.  
00150    * @param[in] *pRef points to the block of reference data.  
00151    * @param[out] *pOut points to the block of output data.  
00152    * @param[out] *pErr points to the block of error data.  
00153    * @param[in] blockSize number of samples to process.  
00154    * @return none.  
00155    */ 
00156  
00157 void arm_lms_norm_f32( 
00158   arm_lms_norm_instance_f32 * S, 
00159   float32_t * pSrc, 
00160   float32_t * pRef, 
00161   float32_t * pOut, 
00162   float32_t * pErr, 
00163   uint32_t blockSize) 
00164 { 
00165   float32_t *pState = S->pState;                 /* State pointer */ 
00166   float32_t *pCoeffs = S->pCoeffs;               /* Coefficient pointer */ 
00167   float32_t *pStateCurnt;                        /* Points to the current sample of the state */ 
00168   float32_t *px, *pb;                            /* Temporary pointers for state and coefficient buffers */ 
00169   float32_t mu = S->mu;                          /* Adaptive factor */ 
00170   uint32_t numTaps = S->numTaps;                 /* Number of filter coefficients in the filter */ 
00171   uint32_t tapCnt, blkCnt;                       /* Loop counters */ 
00172   float32_t energy;                              /* Energy of the input */ 
00173   float32_t sum, e, d;                           /* accumulator, error, reference data sample */ 
00174   float32_t w, x0, in;                           /* weight factor, temporary variable to hold input sample and state */ 
00175  
00176   /* Initializations of error,  difference, Coefficient update */ 
00177   e = 0.0f; 
00178   d = 0.0f; 
00179   w = 0.0f; 
00180  
00181   energy = S->energy; 
00182   x0 = S->x0; 
00183  
00184   /* S->pState points to buffer which contains previous frame (numTaps - 1) samples */ 
00185   /* pStateCurnt points to the location where the new input data should be written */ 
00186   pStateCurnt = &(S->pState[(numTaps - 1u)]); 
00187  
00188   blkCnt = blockSize; 
00189  
00190   while(blkCnt > 0u) 
00191   { 
00192     /* Copy the new input sample into the state buffer */ 
00193     *pStateCurnt++ = *pSrc; 
00194  
00195     /* Initialize pState pointer */ 
00196     px = pState; 
00197  
00198     /* Initialize coeff pointer */ 
00199     pb = (pCoeffs); 
00200  
00201     /* Read the sample from input buffer */ 
00202     in = *pSrc++; 
00203  
00204     /* Update the energy calculation */ 
00205     energy -= x0 * x0; 
00206     energy += in * in; 
00207  
00208     /* Set the accumulator to zero */ 
00209     sum = 0.0f; 
00210  
00211     /* Loop unrolling.  Process 4 taps at a time. */ 
00212     tapCnt = numTaps >> 2; 
00213  
00214     while(tapCnt > 0u) 
00215     { 
00216       /* Perform the multiply-accumulate */ 
00217       sum += (*px++) * (*pb++); 
00218       sum += (*px++) * (*pb++); 
00219       sum += (*px++) * (*pb++); 
00220       sum += (*px++) * (*pb++); 
00221  
00222       /* Decrement the loop counter */ 
00223       tapCnt--; 
00224     } 
00225  
00226     /* If the filter length is not a multiple of 4, compute the remaining filter taps */ 
00227     tapCnt = numTaps % 0x4u; 
00228  
00229     while(tapCnt > 0u) 
00230     { 
00231       /* Perform the multiply-accumulate */ 
00232       sum += (*px++) * (*pb++); 
00233  
00234       /* Decrement the loop counter */ 
00235       tapCnt--; 
00236     } 
00237  
00238     /* The result in the accumulator, store in the destination buffer. */ 
00239     *pOut++ = sum; 
00240  
00241     /* Compute and store error */ 
00242     d = (float32_t) (*pRef++); 
00243     e = d - sum; 
00244     *pErr++ = e; 
00245  
00246     /* Calculation of Weighting factor for updating filter coefficients */ 
00247     /* epsilon value 0.000000119209289f */ 
00248     w = (e * mu) / (energy + 0.000000119209289f); 
00249  
00250     /* Initialize pState pointer */ 
00251     px = pState; 
00252  
00253     /* Initialize coeff pointer */ 
00254     pb = (pCoeffs); 
00255  
00256     /* Loop unrolling.  Process 4 taps at a time. */ 
00257     tapCnt = numTaps >> 2; 
00258  
00259     /* Update filter coefficients */ 
00260     while(tapCnt > 0u) 
00261     { 
00262       /* Perform the multiply-accumulate */ 
00263       *pb += w * (*px++); 
00264       pb++; 
00265  
00266       *pb += w * (*px++); 
00267       pb++; 
00268  
00269       *pb += w * (*px++); 
00270       pb++; 
00271  
00272       *pb += w * (*px++); 
00273       pb++; 
00274  
00275  
00276       /* Decrement the loop counter */ 
00277       tapCnt--; 
00278     } 
00279  
00280     /* If the filter length is not a multiple of 4, compute the remaining filter taps */ 
00281     tapCnt = numTaps % 0x4u; 
00282  
00283     while(tapCnt > 0u) 
00284     { 
00285       /* Perform the multiply-accumulate */ 
00286       *pb += w * (*px++); 
00287       pb++; 
00288  
00289       /* Decrement the loop counter */ 
00290       tapCnt--; 
00291     } 
00292  
00293     x0 = *pState; 
00294  
00295     /* Advance state pointer by 1 for the next sample */ 
00296     pState = pState + 1; 
00297  
00298     /* Decrement the loop counter */ 
00299     blkCnt--; 
00300   } 
00301  
00302   S->energy = energy; 
00303   S->x0 = x0; 
00304  
00305   /* Processing is complete. Now copy the last numTaps - 1 samples to the  
00306      satrt of the state buffer. This prepares the state buffer for the  
00307      next function call. */ 
00308  
00309   /* Points to the start of the pState buffer */ 
00310   pStateCurnt = S->pState; 
00311  
00312   /* Loop unrolling for (numTaps - 1u)/4 samples copy */ 
00313   tapCnt = (numTaps - 1u) >> 2u; 
00314  
00315   /* copy data */ 
00316   while(tapCnt > 0u) 
00317   { 
00318     *pStateCurnt++ = *pState++; 
00319     *pStateCurnt++ = *pState++; 
00320     *pStateCurnt++ = *pState++; 
00321     *pStateCurnt++ = *pState++; 
00322  
00323     /* Decrement the loop counter */ 
00324     tapCnt--; 
00325   } 
00326  
00327   /* Calculate remaining number of copies */ 
00328   tapCnt = (numTaps - 1u) % 0x4u; 
00329  
00330   /* Copy the remaining q31_t data */ 
00331   while(tapCnt > 0u) 
00332   { 
00333     *pStateCurnt++ = *pState++; 
00334  
00335     /* Decrement the loop counter */ 
00336     tapCnt--; 
00337   } 
00338  
00339  
00340 } 
00341  
00342 /**  
00343    * @} end of LMS_NORM group  
00344    */