/* ----------------------------------------------------------------------
* Project: CMSIS DSP Library
* Title: arm_lms_f32.c
* Description: Processing function for the floating-point LMS filter
*
* $Date: 27. January 2017
* $Revision: V.1.5.1
*
* Target Processor: Cortex-M cores
* -------------------------------------------------------------------- */
/*
* Copyright (C) 2010-2017 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
* @{
*/
/**
* @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;
#if defined (ARM_MATH_DSP)
/* 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 /* #if defined (ARM_MATH_DSP) */
}
/**
* @} end of LMS group
*/