| /* ---------------------------------------------------------------------- |
| * Copyright (C) 2010-2014 ARM Limited. All rights reserved. |
| * |
| * $Date: 19. March 2015 |
| * $Revision: V.1.4.5 |
| * |
| * Project: CMSIS DSP Library |
| * Title: arm_lms_f32.c |
| * |
| * Description: Processing function for the floating-point LMS filter. |
| * |
| * Target Processor: Cortex-M4/Cortex-M3/Cortex-M0 |
| * |
| * Redistribution and use in source and binary forms, with or without |
| * modification, are permitted provided that the following conditions |
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| * distribution. |
| * - Neither the name of ARM LIMITED nor the names of its contributors |
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| * software without specific prior written permission. |
| * |
| * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS |
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| |
| #include "arm_math.h" |
| |
| /** |
| * @ingroup groupFilters |
| */ |
| |
| /** |
| * @defgroup LMS Least Mean Square (LMS) Filters |
| * |
| * LMS filters are a class of adaptive filters that are able to "learn" an unknown transfer functions. |
| * LMS filters use a gradient descent method in which the filter coefficients are updated based on the instantaneous error signal. |
| * Adaptive filters are often used in communication systems, equalizers, and noise removal. |
| * The CMSIS DSP Library contains LMS filter functions that operate on Q15, Q31, and floating-point data types. |
| * The library also contains normalized LMS filters in which the filter coefficient adaptation is indepedent of the level of the input signal. |
| * |
| * An LMS filter consists of two components as shown below. |
| * The first component is a standard transversal or FIR filter. |
| * The second component is a coefficient update mechanism. |
| * The LMS filter has two input signals. |
| * The "input" feeds the FIR filter while the "reference input" corresponds to the desired output of the FIR filter. |
| * That is, the FIR filter coefficients are updated so that the output of the FIR filter matches the reference input. |
| * The filter coefficient update mechanism is based on the difference between the FIR filter output and the reference input. |
| * This "error signal" tends towards zero as the filter adapts. |
| * The LMS processing functions accept the input and reference input signals and generate the filter output and error signal. |
| * \image html LMS.gif "Internal structure of the Least Mean Square filter" |
| * |
| * The functions operate on blocks of data and each call to the function processes |
| * <code>blockSize</code> samples through the filter. |
| * <code>pSrc</code> points to input signal, <code>pRef</code> points to reference signal, |
| * <code>pOut</code> points to output signal and <code>pErr</code> points to error signal. |
| * All arrays contain <code>blockSize</code> values. |
| * |
| * The functions operate on a block-by-block basis. |
| * Internally, the filter coefficients <code>b[n]</code> are updated on a sample-by-sample basis. |
| * The convergence of the LMS filter is slower compared to the normalized LMS algorithm. |
| * |
| * \par Algorithm: |
| * The output signal <code>y[n]</code> is computed by a standard FIR filter: |
| * <pre> |
| * y[n] = b[0] * x[n] + b[1] * x[n-1] + b[2] * x[n-2] + ...+ b[numTaps-1] * x[n-numTaps+1] |
| * </pre> |
| * |
| * \par |
| * The error signal equals the difference between the reference signal <code>d[n]</code> and the filter output: |
| * <pre> |
| * e[n] = d[n] - y[n]. |
| * </pre> |
| * |
| * \par |
| * After each sample of the error signal is computed, the filter coefficients <code>b[k]</code> are updated on a sample-by-sample basis: |
| * <pre> |
| * b[k] = b[k] + e[n] * mu * x[n-k], for k=0, 1, ..., numTaps-1 |
| * </pre> |
| * where <code>mu</code> is the step size and controls the rate of coefficient convergence. |
| *\par |
| * In the APIs, <code>pCoeffs</code> points to a coefficient array of size <code>numTaps</code>. |
| * Coefficients are stored in time reversed order. |
| * \par |
| * <pre> |
| * {b[numTaps-1], b[numTaps-2], b[N-2], ..., b[1], b[0]} |
| * </pre> |
| * \par |
| * <code>pState</code> points to a state array of size <code>numTaps + blockSize - 1</code>. |
| * Samples in the state buffer are stored in the order: |
| * \par |
| * <pre> |
| * {x[n-numTaps+1], x[n-numTaps], x[n-numTaps-1], x[n-numTaps-2]....x[0], x[1], ..., x[blockSize-1]} |
| * </pre> |
| * \par |
| * Note that the length of the state buffer exceeds the length of the coefficient array by <code>blockSize-1</code> samples. |
| * The increased state buffer length allows circular addressing, which is traditionally used in FIR filters, |
| * to be avoided and yields a significant speed improvement. |
| * The state variables are updated after each block of data is processed. |
| * \par Instance Structure |
| * The coefficients and state variables for a filter are stored together in an instance data structure. |
| * A separate instance structure must be defined for each filter and |
| * coefficient and state arrays cannot be shared among instances. |
| * There are separate instance structure declarations for each of the 3 supported data types. |
| * |
| * \par Initialization Functions |
| * There is also an associated initialization function for each data type. |
| * The initialization function performs the following operations: |
| * - Sets the values of the internal structure fields. |
| * - Zeros out the values in the state buffer. |
| * To do this manually without calling the init function, assign the follow subfields of the instance structure: |
| * numTaps, pCoeffs, mu, postShift (not for f32), pState. Also set all of the values in pState to zero. |
| * |
| * \par |
| * Use of the initialization function is optional. |
| * However, if the initialization function is used, then the instance structure cannot be placed into a const data section. |
| * To place an instance structure into a const data section, the instance structure must be manually initialized. |
| * Set the values in the state buffer to zeros before static initialization. |
| * The code below statically initializes each of the 3 different data type filter instance structures |
| * <pre> |
| * arm_lms_instance_f32 S = {numTaps, pState, pCoeffs, mu}; |
| * arm_lms_instance_q31 S = {numTaps, pState, pCoeffs, mu, postShift}; |
| * arm_lms_instance_q15 S = {numTaps, pState, pCoeffs, mu, postShift}; |
| * </pre> |
| * where <code>numTaps</code> is the number of filter coefficients in the filter; <code>pState</code> is the address of the state buffer; |
| * <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. |
| * |
| * \par Fixed-Point Behavior: |
| * Care must be taken when using the Q15 and Q31 versions of the LMS filter. |
| * The following issues must be considered: |
| * - Scaling of coefficients |
| * - Overflow and saturation |
| * |
| * \par Scaling of Coefficients: |
| * Filter coefficients are represented as fractional values and |
| * coefficients are restricted to lie in the range <code>[-1 +1)</code>. |
| * The fixed-point functions have an additional scaling parameter <code>postShift</code>. |
| * At the output of the filter's accumulator is a shift register which shifts the result by <code>postShift</code> bits. |
| * This essentially scales the filter coefficients by <code>2^postShift</code> and |
| * allows the filter coefficients to exceed the range <code>[+1 -1)</code>. |
| * The value of <code>postShift</code> is set by the user based on the expected gain through the system being modeled. |
| * |
| * \par Overflow and Saturation: |
| * Overflow and saturation behavior of the fixed-point Q15 and Q31 versions are |
| * described separately as part of the function specific documentation below. |
| */ |
| |
| /** |
| * @addtogroup LMS |
| * @{ |
| */ |
| |
| /** |
| * @details |
| * This function operates on floating-point data types. |
| * |
| * @brief Processing function for floating-point LMS filter. |
| * @param[in] *S points to an instance of the floating-point LMS filter structure. |
| * @param[in] *pSrc points to the block of input data. |
| * @param[in] *pRef points to the block of reference data. |
| * @param[out] *pOut points to the block of output data. |
| * @param[out] *pErr points to the block of error data. |
| * @param[in] blockSize number of samples to process. |
| * @return none. |
| */ |
| |
| void arm_lms_f32( |
| const arm_lms_instance_f32 * S, |
| float32_t * pSrc, |
| float32_t * pRef, |
| float32_t * pOut, |
| float32_t * pErr, |
| uint32_t blockSize) |
| { |
| float32_t *pState = S->pState; /* State pointer */ |
| float32_t *pCoeffs = S->pCoeffs; /* Coefficient pointer */ |
| float32_t *pStateCurnt; /* Points to the current sample of the state */ |
| float32_t *px, *pb; /* Temporary pointers for state and coefficient buffers */ |
| float32_t mu = S->mu; /* Adaptive factor */ |
| uint32_t numTaps = S->numTaps; /* Number of filter coefficients in the filter */ |
| uint32_t tapCnt, blkCnt; /* Loop counters */ |
| float32_t sum, e, d; /* accumulator, error, reference data sample */ |
| float32_t w = 0.0f; /* weight factor */ |
| |
| e = 0.0f; |
| d = 0.0f; |
| |
| /* S->pState points to state array which contains previous frame (numTaps - 1) samples */ |
| /* pStateCurnt points to the location where the new input data should be written */ |
| pStateCurnt = &(S->pState[(numTaps - 1u)]); |
| |
| blkCnt = blockSize; |
| |
| |
| #ifndef ARM_MATH_CM0_FAMILY |
| |
| /* Run the below code for Cortex-M4 and Cortex-M3 */ |
| |
| while(blkCnt > 0u) |
| { |
| /* Copy the new input sample into the state buffer */ |
| *pStateCurnt++ = *pSrc++; |
| |
| /* Initialize pState pointer */ |
| px = pState; |
| |
| /* Initialize coeff pointer */ |
| pb = (pCoeffs); |
| |
| /* Set the accumulator to zero */ |
| sum = 0.0f; |
| |
| /* Loop unrolling. Process 4 taps at a time. */ |
| tapCnt = numTaps >> 2; |
| |
| while(tapCnt > 0u) |
| { |
| /* Perform the multiply-accumulate */ |
| sum += (*px++) * (*pb++); |
| sum += (*px++) * (*pb++); |
| sum += (*px++) * (*pb++); |
| sum += (*px++) * (*pb++); |
| |
| /* Decrement the loop counter */ |
| tapCnt--; |
| } |
| |
| /* If the filter length is not a multiple of 4, compute the remaining filter taps */ |
| tapCnt = numTaps % 0x4u; |
| |
| while(tapCnt > 0u) |
| { |
| /* Perform the multiply-accumulate */ |
| sum += (*px++) * (*pb++); |
| |
| /* Decrement the loop counter */ |
| tapCnt--; |
| } |
| |
| /* The result in the accumulator, store in the destination buffer. */ |
| *pOut++ = sum; |
| |
| /* Compute and store error */ |
| d = (float32_t) (*pRef++); |
| e = d - sum; |
| *pErr++ = e; |
| |
| /* Calculation of Weighting factor for the updating filter coefficients */ |
| w = e * mu; |
| |
| /* Initialize pState pointer */ |
| px = pState; |
| |
| /* Initialize coeff pointer */ |
| pb = (pCoeffs); |
| |
| /* Loop unrolling. Process 4 taps at a time. */ |
| tapCnt = numTaps >> 2; |
| |
| /* Update filter coefficients */ |
| while(tapCnt > 0u) |
| { |
| /* Perform the multiply-accumulate */ |
| *pb = *pb + (w * (*px++)); |
| pb++; |
| |
| *pb = *pb + (w * (*px++)); |
| pb++; |
| |
| *pb = *pb + (w * (*px++)); |
| pb++; |
| |
| *pb = *pb + (w * (*px++)); |
| pb++; |
| |
| /* Decrement the loop counter */ |
| tapCnt--; |
| } |
| |
| /* If the filter length is not a multiple of 4, compute the remaining filter taps */ |
| tapCnt = numTaps % 0x4u; |
| |
| while(tapCnt > 0u) |
| { |
| /* Perform the multiply-accumulate */ |
| *pb = *pb + (w * (*px++)); |
| pb++; |
| |
| /* Decrement the loop counter */ |
| tapCnt--; |
| } |
| |
| /* Advance state pointer by 1 for the next sample */ |
| pState = pState + 1; |
| |
| /* Decrement the loop counter */ |
| blkCnt--; |
| } |
| |
| |
| /* Processing is complete. Now copy the last numTaps - 1 samples to the |
| satrt of the state buffer. This prepares the state buffer for the |
| next function call. */ |
| |
| /* Points to the start of the pState buffer */ |
| pStateCurnt = S->pState; |
| |
| /* Loop unrolling for (numTaps - 1u) samples copy */ |
| tapCnt = (numTaps - 1u) >> 2u; |
| |
| /* copy data */ |
| while(tapCnt > 0u) |
| { |
| *pStateCurnt++ = *pState++; |
| *pStateCurnt++ = *pState++; |
| *pStateCurnt++ = *pState++; |
| *pStateCurnt++ = *pState++; |
| |
| /* Decrement the loop counter */ |
| tapCnt--; |
| } |
| |
| /* Calculate remaining number of copies */ |
| tapCnt = (numTaps - 1u) % 0x4u; |
| |
| /* Copy the remaining q31_t data */ |
| while(tapCnt > 0u) |
| { |
| *pStateCurnt++ = *pState++; |
| |
| /* Decrement the loop counter */ |
| tapCnt--; |
| } |
| |
| #else |
| |
| /* Run the below code for Cortex-M0 */ |
| |
| while(blkCnt > 0u) |
| { |
| /* Copy the new input sample into the state buffer */ |
| *pStateCurnt++ = *pSrc++; |
| |
| /* Initialize pState pointer */ |
| px = pState; |
| |
| /* Initialize pCoeffs pointer */ |
| pb = pCoeffs; |
| |
| /* Set the accumulator to zero */ |
| sum = 0.0f; |
| |
| /* Loop over numTaps number of values */ |
| tapCnt = numTaps; |
| |
| while(tapCnt > 0u) |
| { |
| /* Perform the multiply-accumulate */ |
| sum += (*px++) * (*pb++); |
| |
| /* Decrement the loop counter */ |
| tapCnt--; |
| } |
| |
| /* The result is stored in the destination buffer. */ |
| *pOut++ = sum; |
| |
| /* Compute and store error */ |
| d = (float32_t) (*pRef++); |
| e = d - sum; |
| *pErr++ = e; |
| |
| /* Weighting factor for the LMS version */ |
| w = e * mu; |
| |
| /* Initialize pState pointer */ |
| px = pState; |
| |
| /* Initialize pCoeffs pointer */ |
| pb = pCoeffs; |
| |
| /* Loop over numTaps number of values */ |
| tapCnt = numTaps; |
| |
| while(tapCnt > 0u) |
| { |
| /* Perform the multiply-accumulate */ |
| *pb = *pb + (w * (*px++)); |
| pb++; |
| |
| /* Decrement the loop counter */ |
| tapCnt--; |
| } |
| |
| /* Advance state pointer by 1 for the next sample */ |
| pState = pState + 1; |
| |
| /* Decrement the loop counter */ |
| blkCnt--; |
| } |
| |
| |
| /* Processing is complete. Now copy the last numTaps - 1 samples to the |
| * start of the state buffer. This prepares the state buffer for the |
| * next function call. */ |
| |
| /* Points to the start of the pState buffer */ |
| pStateCurnt = S->pState; |
| |
| /* Copy (numTaps - 1u) samples */ |
| tapCnt = (numTaps - 1u); |
| |
| /* Copy the data */ |
| while(tapCnt > 0u) |
| { |
| *pStateCurnt++ = *pState++; |
| |
| /* Decrement the loop counter */ |
| tapCnt--; |
| } |
| |
| #endif /* #ifndef ARM_MATH_CM0_FAMILY */ |
| |
| } |
| |
| /** |
| * @} end of LMS group |
| */ |