arm_lms_norm_f32.c

00001 /* ----------------------------------------------------------------------    
00002 * Copyright (C) 2010-2014 ARM Limited. All rights reserved.    
00003 *    
00004 * $Date:        12. March 2014
00005 * $Revision:    V1.4.3
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/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 
00031 * COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
00032 * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
00033 * BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
00034 * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
00035 * CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
00036 * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
00037 * ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
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00039 * -------------------------------------------------------------------- */
00040 
00041 #include "arm_math.h"
00042 
00043 /**    
00044  * @ingroup groupFilters    
00045  */
00046 
00047 /**    
00048  * @defgroup LMS_NORM Normalized LMS Filters    
00049  *    
00050  * This set of functions implements a commonly used adaptive filter.    
00051  * It is related to the Least Mean Square (LMS) adaptive filter and includes an additional normalization    
00052  * factor which increases the adaptation rate of the filter.    
00053  * The CMSIS DSP Library contains normalized LMS filter functions that operate on Q15, Q31, and floating-point data types.    
00054  *    
00055  * A normalized least mean square (NLMS) filter consists of two components as shown below.    
00056  * The first component is a standard transversal or FIR filter.    
00057  * The second component is a coefficient update mechanism.    
00058  * The NLMS filter has two input signals.    
00059  * The "input" feeds the FIR filter while the "reference input" corresponds to the desired output of the FIR filter.    
00060  * That is, the FIR filter coefficients are updated so that the output of the FIR filter matches the reference input.    
00061  * The filter coefficient update mechanism is based on the difference between the FIR filter output and the reference input.    
00062  * This "error signal" tends towards zero as the filter adapts.    
00063  * The NLMS processing functions accept the input and reference input signals and generate the filter output and error signal.    
00064  * \image html LMS.gif "Internal structure of the NLMS adaptive filter"    
00065  *    
00066  * The functions operate on blocks of data and each call to the function processes    
00067  * <code>blockSize</code> samples through the filter.    
00068  * <code>pSrc</code> points to input signal, <code>pRef</code> points to reference signal,    
00069  * <code>pOut</code> points to output signal and <code>pErr</code> points to error signal.    
00070  * All arrays contain <code>blockSize</code> values.    
00071  *    
00072  * The functions operate on a block-by-block basis.    
00073  * Internally, the filter coefficients <code>b[n]</code> are updated on a sample-by-sample basis.    
00074  * The convergence of the LMS filter is slower compared to the normalized LMS algorithm.    
00075  *    
00076  * \par Algorithm:    
00077  * The output signal <code>y[n]</code> is computed by a standard FIR filter:    
00078  * <pre>    
00079  *     y[n] = b[0] * x[n] + b[1] * x[n-1] + b[2] * x[n-2] + ...+ b[numTaps-1] * x[n-numTaps+1]    
00080  * </pre>    
00081  *    
00082  * \par    
00083  * The error signal equals the difference between the reference signal <code>d[n]</code> and the filter output:    
00084  * <pre>    
00085  *     e[n] = d[n] - y[n].    
00086  * </pre>    
00087  *    
00088  * \par    
00089  * After each sample of the error signal is computed the instanteous energy of the filter state variables is calculated:    
00090  * <pre>    
00091  *    E = x[n]^2 + x[n-1]^2 + ... + x[n-numTaps+1]^2.    
00092  * </pre>    
00093  * The filter coefficients <code>b[k]</code> are then updated on a sample-by-sample basis:    
00094  * <pre>    
00095  *     b[k] = b[k] + e[n] * (mu/E) * x[n-k],  for k=0, 1, ..., numTaps-1    
00096  * </pre>    
00097  * where <code>mu</code> is the step size and controls the rate of coefficient convergence.    
00098  *\par    
00099  * In the APIs, <code>pCoeffs</code> points to a coefficient array of size <code>numTaps</code>.    
00100  * Coefficients are stored in time reversed order.    
00101  * \par    
00102  * <pre>    
00103  *    {b[numTaps-1], b[numTaps-2], b[N-2], ..., b[1], b[0]}    
00104  * </pre>    
00105  * \par    
00106  * <code>pState</code> points to a state array of size <code>numTaps + blockSize - 1</code>.    
00107  * Samples in the state buffer are stored in the order:    
00108  * \par    
00109  * <pre>    
00110  *    {x[n-numTaps+1], x[n-numTaps], x[n-numTaps-1], x[n-numTaps-2]....x[0], x[1], ..., x[blockSize-1]}    
00111  * </pre>    
00112  * \par    
00113  * Note that the length of the state buffer exceeds the length of the coefficient array by <code>blockSize-1</code> samples.    
00114  * The increased state buffer length allows circular addressing, which is traditionally used in FIR filters,    
00115  * to be avoided and yields a significant speed improvement.    
00116  * The state variables are updated after each block of data is processed.    
00117  * \par Instance Structure    
00118  * The coefficients and state variables for a filter are stored together in an instance data structure.    
00119  * A separate instance structure must be defined for each filter and    
00120  * coefficient and state arrays cannot be shared among instances.    
00121  * There are separate instance structure declarations for each of the 3 supported data types.    
00122  *    
00123  * \par Initialization Functions    
00124  * There is also an associated initialization function for each data type.    
00125  * The initialization function performs the following operations:    
00126  * - Sets the values of the internal structure fields.    
00127  * - Zeros out the values in the state buffer.    
00128  * To do this manually without calling the init function, assign the follow subfields of the instance structure:
00129  * numTaps, pCoeffs, mu, energy, x0, pState. Also set all of the values in pState to zero. 
00130  * For Q7, Q15, and Q31 the following fields must also be initialized;
00131  * recipTable, postShift
00132  *
00133  * \par    
00134  * Instance structure cannot be placed into a const data section and it is recommended to use the initialization function.    
00135  * \par Fixed-Point Behavior:    
00136  * Care must be taken when using the Q15 and Q31 versions of the normalised LMS filter.    
00137  * The following issues must be considered:    
00138  * - Scaling of coefficients    
00139  * - Overflow and saturation    
00140  *    
00141  * \par Scaling of Coefficients:    
00142  * Filter coefficients are represented as fractional values and    
00143  * coefficients are restricted to lie in the range <code>[-1 +1)</code>.    
00144  * The fixed-point functions have an additional scaling parameter <code>postShift</code>.    
00145  * At the output of the filter's accumulator is a shift register which shifts the result by <code>postShift</code> bits.    
00146  * This essentially scales the filter coefficients by <code>2^postShift</code> and    
00147  * allows the filter coefficients to exceed the range <code>[+1 -1)</code>.    
00148  * The value of <code>postShift</code> is set by the user based on the expected gain through the system being modeled.    
00149  *    
00150  * \par Overflow and Saturation:    
00151  * Overflow and saturation behavior of the fixed-point Q15 and Q31 versions are    
00152  * described separately as part of the function specific documentation below.    
00153  */
00154 
00155 
00156 /**    
00157  * @addtogroup LMS_NORM    
00158  * @{    
00159  */
00160 
00161 
00162   /**    
00163    * @brief Processing function for floating-point normalized LMS filter.    
00164    * @param[in] *S points to an instance of the floating-point normalized LMS filter structure.    
00165    * @param[in] *pSrc points to the block of input data.    
00166    * @param[in] *pRef points to the block of reference data.    
00167    * @param[out] *pOut points to the block of output data.    
00168    * @param[out] *pErr points to the block of error data.    
00169    * @param[in] blockSize number of samples to process.    
00170    * @return none.    
00171    */
00172 
00173 void arm_lms_norm_f32(
00174   arm_lms_norm_instance_f32 * S,
00175   float32_t * pSrc,
00176   float32_t * pRef,
00177   float32_t * pOut,
00178   float32_t * pErr,
00179   uint32_t blockSize)
00180 {
00181   float32_t *pState = S->pState;                 /* State pointer */
00182   float32_t *pCoeffs = S->pCoeffs;               /* Coefficient pointer */
00183   float32_t *pStateCurnt;                        /* Points to the current sample of the state */
00184   float32_t *px, *pb;                            /* Temporary pointers for state and coefficient buffers */
00185   float32_t mu = S->mu;                          /* Adaptive factor */
00186   uint32_t numTaps = S->numTaps;                 /* Number of filter coefficients in the filter */
00187   uint32_t tapCnt, blkCnt;                       /* Loop counters */
00188   float32_t energy;                              /* Energy of the input */
00189   float32_t sum, e, d;                           /* accumulator, error, reference data sample */
00190   float32_t w, x0, in;                           /* weight factor, temporary variable to hold input sample and state */
00191 
00192   /* Initializations of error,  difference, Coefficient update */
00193   e = 0.0f;
00194   d = 0.0f;
00195   w = 0.0f;
00196 
00197   energy = S->energy;
00198   x0 = S->x0;
00199 
00200   /* S->pState points to buffer which contains previous frame (numTaps - 1) samples */
00201   /* pStateCurnt points to the location where the new input data should be written */
00202   pStateCurnt = &(S->pState[(numTaps - 1u)]);
00203 
00204   /* Loop over blockSize number of values */
00205   blkCnt = blockSize;
00206 
00207 
00208 #ifndef ARM_MATH_CM0_FAMILY
00209 
00210   /* Run the below code for Cortex-M4 and Cortex-M3 */
00211 
00212   while(blkCnt > 0u)
00213   {
00214     /* Copy the new input sample into the state buffer */
00215     *pStateCurnt++ = *pSrc;
00216 
00217     /* Initialize pState pointer */
00218     px = pState;
00219 
00220     /* Initialize coeff pointer */
00221     pb = (pCoeffs);
00222 
00223     /* Read the sample from input buffer */
00224     in = *pSrc++;
00225 
00226     /* Update the energy calculation */
00227     energy -= x0 * x0;
00228     energy += in * in;
00229 
00230     /* Set the accumulator to zero */
00231     sum = 0.0f;
00232 
00233     /* Loop unrolling.  Process 4 taps at a time. */
00234     tapCnt = numTaps >> 2;
00235 
00236     while(tapCnt > 0u)
00237     {
00238       /* Perform the multiply-accumulate */
00239       sum += (*px++) * (*pb++);
00240       sum += (*px++) * (*pb++);
00241       sum += (*px++) * (*pb++);
00242       sum += (*px++) * (*pb++);
00243 
00244       /* Decrement the loop counter */
00245       tapCnt--;
00246     }
00247 
00248     /* If the filter length is not a multiple of 4, compute the remaining filter taps */
00249     tapCnt = numTaps % 0x4u;
00250 
00251     while(tapCnt > 0u)
00252     {
00253       /* Perform the multiply-accumulate */
00254       sum += (*px++) * (*pb++);
00255 
00256       /* Decrement the loop counter */
00257       tapCnt--;
00258     }
00259 
00260     /* The result in the accumulator, store in the destination buffer. */
00261     *pOut++ = sum;
00262 
00263     /* Compute and store error */
00264     d = (float32_t) (*pRef++);
00265     e = d - sum;
00266     *pErr++ = e;
00267 
00268     /* Calculation of Weighting factor for updating filter coefficients */
00269     /* epsilon value 0.000000119209289f */
00270     w = (e * mu) / (energy + 0.000000119209289f);
00271 
00272     /* Initialize pState pointer */
00273     px = pState;
00274 
00275     /* Initialize coeff pointer */
00276     pb = (pCoeffs);
00277 
00278     /* Loop unrolling.  Process 4 taps at a time. */
00279     tapCnt = numTaps >> 2;
00280 
00281     /* Update filter coefficients */
00282     while(tapCnt > 0u)
00283     {
00284       /* Perform the multiply-accumulate */
00285       *pb += w * (*px++);
00286       pb++;
00287 
00288       *pb += w * (*px++);
00289       pb++;
00290 
00291       *pb += w * (*px++);
00292       pb++;
00293 
00294       *pb += w * (*px++);
00295       pb++;
00296 
00297 
00298       /* Decrement the loop counter */
00299       tapCnt--;
00300     }
00301 
00302     /* If the filter length is not a multiple of 4, compute the remaining filter taps */
00303     tapCnt = numTaps % 0x4u;
00304 
00305     while(tapCnt > 0u)
00306     {
00307       /* Perform the multiply-accumulate */
00308       *pb += w * (*px++);
00309       pb++;
00310 
00311       /* Decrement the loop counter */
00312       tapCnt--;
00313     }
00314 
00315     x0 = *pState;
00316 
00317     /* Advance state pointer by 1 for the next sample */
00318     pState = pState + 1;
00319 
00320     /* Decrement the loop counter */
00321     blkCnt--;
00322   }
00323 
00324   S->energy = energy;
00325   S->x0 = x0;
00326 
00327   /* Processing is complete. Now copy the last numTaps - 1 samples to the    
00328      satrt of the state buffer. This prepares the state buffer for the    
00329      next function call. */
00330 
00331   /* Points to the start of the pState buffer */
00332   pStateCurnt = S->pState;
00333 
00334   /* Loop unrolling for (numTaps - 1u)/4 samples copy */
00335   tapCnt = (numTaps - 1u) >> 2u;
00336 
00337   /* copy data */
00338   while(tapCnt > 0u)
00339   {
00340     *pStateCurnt++ = *pState++;
00341     *pStateCurnt++ = *pState++;
00342     *pStateCurnt++ = *pState++;
00343     *pStateCurnt++ = *pState++;
00344 
00345     /* Decrement the loop counter */
00346     tapCnt--;
00347   }
00348 
00349   /* Calculate remaining number of copies */
00350   tapCnt = (numTaps - 1u) % 0x4u;
00351 
00352   /* Copy the remaining q31_t data */
00353   while(tapCnt > 0u)
00354   {
00355     *pStateCurnt++ = *pState++;
00356 
00357     /* Decrement the loop counter */
00358     tapCnt--;
00359   }
00360 
00361 #else
00362 
00363   /* Run the below code for Cortex-M0 */
00364 
00365   while(blkCnt > 0u)
00366   {
00367     /* Copy the new input sample into the state buffer */
00368     *pStateCurnt++ = *pSrc;
00369 
00370     /* Initialize pState pointer */
00371     px = pState;
00372 
00373     /* Initialize pCoeffs pointer */
00374     pb = pCoeffs;
00375 
00376     /* Read the sample from input buffer */
00377     in = *pSrc++;
00378 
00379     /* Update the energy calculation */
00380     energy -= x0 * x0;
00381     energy += in * in;
00382 
00383     /* Set the accumulator to zero */
00384     sum = 0.0f;
00385 
00386     /* Loop over numTaps number of values */
00387     tapCnt = numTaps;
00388 
00389     while(tapCnt > 0u)
00390     {
00391       /* Perform the multiply-accumulate */
00392       sum += (*px++) * (*pb++);
00393 
00394       /* Decrement the loop counter */
00395       tapCnt--;
00396     }
00397 
00398     /* The result in the accumulator is stored in the destination buffer. */
00399     *pOut++ = sum;
00400 
00401     /* Compute and store error */
00402     d = (float32_t) (*pRef++);
00403     e = d - sum;
00404     *pErr++ = e;
00405 
00406     /* Calculation of Weighting factor for updating filter coefficients */
00407     /* epsilon value 0.000000119209289f */
00408     w = (e * mu) / (energy + 0.000000119209289f);
00409 
00410     /* Initialize pState pointer */
00411     px = pState;
00412 
00413     /* Initialize pCcoeffs pointer */
00414     pb = pCoeffs;
00415 
00416     /* Loop over numTaps number of values */
00417     tapCnt = numTaps;
00418 
00419     while(tapCnt > 0u)
00420     {
00421       /* Perform the multiply-accumulate */
00422       *pb += w * (*px++);
00423       pb++;
00424 
00425       /* Decrement the loop counter */
00426       tapCnt--;
00427     }
00428 
00429     x0 = *pState;
00430 
00431     /* Advance state pointer by 1 for the next sample */
00432     pState = pState + 1;
00433 
00434     /* Decrement the loop counter */
00435     blkCnt--;
00436   }
00437 
00438   S->energy = energy;
00439   S->x0 = x0;
00440 
00441   /* Processing is complete. Now copy the last numTaps - 1 samples to the        
00442      satrt of the state buffer. This prepares the state buffer for the        
00443      next function call. */
00444 
00445   /* Points to the start of the pState buffer */
00446   pStateCurnt = S->pState;
00447 
00448   /* Copy (numTaps - 1u) samples  */
00449   tapCnt = (numTaps - 1u);
00450 
00451   /* Copy the remaining q31_t data */
00452   while(tapCnt > 0u)
00453   {
00454     *pStateCurnt++ = *pState++;
00455 
00456     /* Decrement the loop counter */
00457     tapCnt--;
00458   }
00459 
00460 #endif /*   #ifndef ARM_MATH_CM0_FAMILY */
00461 
00462 }
00463 
00464 /**    
00465    * @} end of LMS_NORM group    
00466    */