| /* ---------------------------------------------------------------------- |
| * Project: CMSIS DSP Library |
| * Title: arm_lms_f32.c |
| * Description: Processing function for the floating-point LMS filter |
| * |
| * $Date: 18. March 2019 |
| * $Revision: V1.6.0 |
| * |
| * Target Processor: Cortex-M cores |
| * -------------------------------------------------------------------- */ |
| /* |
| * Copyright (C) 2010-2019 ARM Limited or its affiliates. All rights reserved. |
| * |
| * SPDX-License-Identifier: Apache-2.0 |
| * |
| * Licensed under the Apache License, Version 2.0 (the License); you may |
| * not use this file except in compliance with the License. |
| * You may obtain a copy of the License at |
| * |
| * www.apache.org/licenses/LICENSE-2.0 |
| * |
| * Unless required by applicable law or agreed to in writing, software |
| * distributed under the License is distributed on an AS IS BASIS, WITHOUT |
| * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. |
| * See the License for the specific language governing permissions and |
| * limitations under the License. |
| */ |
| |
| #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 |
| @{ |
| */ |
| |
| /** |
| @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 |
| */ |
| #if defined(ARM_MATH_NEON) |
| void arm_lms_f32( |
| const arm_lms_instance_f32 * S, |
| const 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 */ |
| |
| float32x4_t tempV, sumV, xV, bV; |
| float32x2_t tempV2; |
| |
| 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; |
| |
| 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; |
| sumV = vdupq_n_f32(0.0); |
| |
| /* Process 4 taps at a time. */ |
| tapCnt = numTaps >> 2; |
| |
| while (tapCnt > 0U) |
| { |
| /* Perform the multiply-accumulate */ |
| xV = vld1q_f32(px); |
| bV = vld1q_f32(pb); |
| sumV = vmlaq_f32(sumV, xV, bV); |
| |
| px += 4; |
| pb += 4; |
| |
| /* Decrement the loop counter */ |
| tapCnt--; |
| } |
| tempV2 = vpadd_f32(vget_low_f32(sumV),vget_high_f32(sumV)); |
| sum = tempV2[0] + tempV2[1]; |
| |
| |
| /* 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); |
| |
| /* Process 4 taps at a time. */ |
| tapCnt = numTaps >> 2; |
| |
| /* Update filter coefficients */ |
| while (tapCnt > 0U) |
| { |
| /* Perform the multiply-accumulate */ |
| xV = vld1q_f32(px); |
| bV = vld1q_f32(pb); |
| px += 4; |
| bV = vmlaq_n_f32(bV,xV,w); |
| |
| vst1q_f32(pb,bV); |
| pb += 4; |
| |
| |
| /* 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; |
| |
| /* Process 4 taps at a time for (numTaps - 1U) samples copy */ |
| tapCnt = (numTaps - 1U) >> 2U; |
| |
| /* copy data */ |
| while (tapCnt > 0U) |
| { |
| tempV = vld1q_f32(pState); |
| vst1q_f32(pStateCurnt,tempV); |
| pState += 4; |
| pStateCurnt += 4; |
| |
| /* 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 |
| void arm_lms_f32( |
| const arm_lms_instance_f32 * S, |
| const 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 */ |
| float32_t acc, e; /* Accumulator, error */ |
| float32_t w; /* Weight factor */ |
| uint32_t numTaps = S->numTaps; /* Number of filter coefficients in the filter */ |
| uint32_t tapCnt, blkCnt; /* Loop counters */ |
| |
| /* Initializations of error, difference, Coefficient update */ |
| e = 0.0f; |
| w = 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)]); |
| |
| /* initialise loop count */ |
| blkCnt = blockSize; |
| |
| while (blkCnt > 0U) |
| { |
| /* Copy the new input sample into the state buffer */ |
| *pStateCurnt++ = *pSrc++; |
| |
| /* Initialize pState pointer */ |
| px = pState; |
| |
| /* Initialize coefficient pointer */ |
| pb = pCoeffs; |
| |
| /* Set the accumulator to zero */ |
| acc = 0.0f; |
| |
| #if defined (ARM_MATH_LOOPUNROLL) |
| |
| /* Loop unrolling: Compute 4 taps at a time. */ |
| tapCnt = numTaps >> 2U; |
| |
| while (tapCnt > 0U) |
| { |
| /* Perform the multiply-accumulate */ |
| acc += (*px++) * (*pb++); |
| |
| acc += (*px++) * (*pb++); |
| |
| acc += (*px++) * (*pb++); |
| |
| acc += (*px++) * (*pb++); |
| |
| /* Decrement loop counter */ |
| tapCnt--; |
| } |
| |
| /* Loop unrolling: Compute remaining taps */ |
| tapCnt = numTaps % 0x4U; |
| |
| #else |
| |
| /* Initialize tapCnt with number of samples */ |
| tapCnt = numTaps; |
| |
| #endif /* #if defined (ARM_MATH_LOOPUNROLL) */ |
| |
| while (tapCnt > 0U) |
| { |
| /* Perform the multiply-accumulate */ |
| acc += (*px++) * (*pb++); |
| |
| /* Decrement the loop counter */ |
| tapCnt--; |
| } |
| |
| /* Store the result from accumulator into the destination buffer. */ |
| *pOut++ = acc; |
| |
| /* Compute and store error */ |
| e = (float32_t) *pRef++ - acc; |
| *pErr++ = e; |
| |
| /* Calculation of Weighting factor for updating filter coefficients */ |
| w = e * mu; |
| |
| /* Initialize pState pointer */ |
| /* Advance state pointer by 1 for the next sample */ |
| px = pState++; |
| |
| /* Initialize coefficient pointer */ |
| pb = pCoeffs; |
| |
| #if defined (ARM_MATH_LOOPUNROLL) |
| |
| /* Loop unrolling: Compute 4 taps at a time. */ |
| tapCnt = numTaps >> 2U; |
| |
| /* Update filter coefficients */ |
| while (tapCnt > 0U) |
| { |
| /* Perform the multiply-accumulate */ |
| *pb += w * (*px++); |
| pb++; |
| |
| *pb += w * (*px++); |
| pb++; |
| |
| *pb += w * (*px++); |
| pb++; |
| |
| *pb += w * (*px++); |
| pb++; |
| |
| /* Decrement loop counter */ |
| tapCnt--; |
| } |
| |
| /* Loop unrolling: Compute remaining taps */ |
| tapCnt = numTaps % 0x4U; |
| |
| #else |
| |
| /* Initialize tapCnt with number of samples */ |
| tapCnt = numTaps; |
| |
| #endif /* #if defined (ARM_MATH_LOOPUNROLL) */ |
| |
| while (tapCnt > 0U) |
| { |
| /* Perform the multiply-accumulate */ |
| *pb += w * (*px++); |
| pb++; |
| |
| /* Decrement loop counter */ |
| tapCnt--; |
| } |
| |
| /* Decrement 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 data */ |
| #if defined (ARM_MATH_LOOPUNROLL) |
| |
| /* Loop unrolling: Compute 4 taps at a time. */ |
| tapCnt = (numTaps - 1U) >> 2U; |
| |
| while (tapCnt > 0U) |
| { |
| *pStateCurnt++ = *pState++; |
| *pStateCurnt++ = *pState++; |
| *pStateCurnt++ = *pState++; |
| *pStateCurnt++ = *pState++; |
| |
| /* Decrement loop counter */ |
| tapCnt--; |
| } |
| |
| /* Loop unrolling: Compute remaining taps */ |
| tapCnt = (numTaps - 1U) % 0x4U; |
| |
| #else |
| |
| /* Initialize tapCnt with number of samples */ |
| tapCnt = (numTaps - 1U); |
| |
| #endif /* #if defined (ARM_MATH_LOOPUNROLL) */ |
| |
| while (tapCnt > 0U) |
| { |
| *pStateCurnt++ = *pState++; |
| |
| /* Decrement loop counter */ |
| tapCnt--; |
| } |
| |
| } |
| #endif /* #if defined(ARM_MATH_NEON) */ |
| |
| /** |
| @} end of LMS group |
| */ |