/* ----------------------------------------------------------------------
* Project: CMSIS DSP Library
* Title: arm_lms_norm_f32.c
* Description: Processing function for the floating-point Normalised LMS
*
* $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_NORM Normalized LMS Filters
*
* This set of functions implements a commonly used adaptive filter.
* It is related to the Least Mean Square (LMS) adaptive filter and includes an additional normalization
* factor which increases the adaptation rate of the filter.
* The CMSIS DSP Library contains normalized LMS filter functions that operate on Q15, Q31, and floating-point data types.
*
* A normalized least mean square (NLMS) 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 NLMS 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 NLMS 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 NLMS adaptive filter"
*
* The functions operate on blocks of data and each call to the function processes
* blockSize
samples through the filter.
* pSrc
points to input signal, pRef
points to reference signal,
* pOut
points to output signal and pErr
points to error signal.
* All arrays contain blockSize
values.
*
* The functions operate on a block-by-block basis.
* Internally, the filter coefficients b[n]
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 y[n]
is computed by a standard FIR filter:
*
* y[n] = b[0] * x[n] + b[1] * x[n-1] + b[2] * x[n-2] + ...+ b[numTaps-1] * x[n-numTaps+1] ** * \par * The error signal equals the difference between the reference signal
d[n]
and the filter output:
* * e[n] = d[n] - y[n]. ** * \par * After each sample of the error signal is computed the instanteous energy of the filter state variables is calculated: *
* E = x[n]^2 + x[n-1]^2 + ... + x[n-numTaps+1]^2. ** The filter coefficients
b[k]
are then updated on a sample-by-sample basis:
* * b[k] = b[k] + e[n] * (mu/E) * x[n-k], for k=0, 1, ..., numTaps-1 ** where
mu
is the step size and controls the rate of coefficient convergence.
*\par
* In the APIs, pCoeffs
points to a coefficient array of size numTaps
.
* Coefficients are stored in time reversed order.
* \par
* * {b[numTaps-1], b[numTaps-2], b[N-2], ..., b[1], b[0]} ** \par *
pState
points to a state array of size numTaps + blockSize - 1
.
* Samples in the state buffer are stored in the order:
* \par
* * {x[n-numTaps+1], x[n-numTaps], x[n-numTaps-1], x[n-numTaps-2]....x[0], x[1], ..., x[blockSize-1]} ** \par * Note that the length of the state buffer exceeds the length of the coefficient array by
blockSize-1
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, energy, x0, pState. Also set all of the values in pState to zero.
* For Q7, Q15, and Q31 the following fields must also be initialized;
* recipTable, postShift
*
* \par
* Instance structure cannot be placed into a const data section and it is recommended to use the initialization function.
* \par Fixed-Point Behavior:
* Care must be taken when using the Q15 and Q31 versions of the normalised 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 [-1 +1)
.
* The fixed-point functions have an additional scaling parameter postShift
.
* At the output of the filter's accumulator is a shift register which shifts the result by postShift
bits.
* This essentially scales the filter coefficients by 2^postShift
and
* allows the filter coefficients to exceed the range [+1 -1)
.
* The value of postShift
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_NORM
* @{
*/
/**
* @brief Processing function for floating-point normalized LMS filter.
* @param[in] *S points to an instance of the floating-point normalized 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_norm_f32(
arm_lms_norm_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 energy; /* Energy of the input */
float32_t sum, e, d; /* accumulator, error, reference data sample */
float32_t w, x0, in; /* weight factor, temporary variable to hold input sample and state */
/* Initializations of error, difference, Coefficient update */
e = 0.0f;
d = 0.0f;
w = 0.0f;
energy = S->energy;
x0 = S->x0;
/* S->pState points to buffer 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)]);
/* Loop over blockSize number of values */
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);
/* Read the sample from input buffer */
in = *pSrc++;
/* Update the energy calculation */
energy -= x0 * x0;
energy += in * in;
/* 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 updating filter coefficients */
/* epsilon value 0.000000119209289f */
w = (e * mu) / (energy + 0.000000119209289f);
/* 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 += w * (*px++);
pb++;
*pb += w * (*px++);
pb++;
*pb += w * (*px++);
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 += w * (*px++);
pb++;
/* Decrement the loop counter */
tapCnt--;
}
x0 = *pState;
/* Advance state pointer by 1 for the next sample */
pState = pState + 1;
/* Decrement the loop counter */
blkCnt--;
}
S->energy = energy;
S->x0 = x0;
/* 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)/4 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;
/* Read the sample from input buffer */
in = *pSrc++;
/* Update the energy calculation */
energy -= x0 * x0;
energy += in * in;
/* 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 in the accumulator is stored in the destination buffer. */
*pOut++ = sum;
/* Compute and store error */
d = (float32_t) (*pRef++);
e = d - sum;
*pErr++ = e;
/* Calculation of Weighting factor for updating filter coefficients */
/* epsilon value 0.000000119209289f */
w = (e * mu) / (energy + 0.000000119209289f);
/* Initialize pState pointer */
px = pState;
/* Initialize pCcoeffs pointer */
pb = pCoeffs;
/* Loop over numTaps number of values */
tapCnt = numTaps;
while (tapCnt > 0U)
{
/* Perform the multiply-accumulate */
*pb += w * (*px++);
pb++;
/* Decrement the loop counter */
tapCnt--;
}
x0 = *pState;
/* Advance state pointer by 1 for the next sample */
pState = pState + 1;
/* Decrement the loop counter */
blkCnt--;
}
S->energy = energy;
S->x0 = x0;
/* 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;
/* Copy (numTaps - 1U) samples */
tapCnt = (numTaps - 1U);
/* Copy the remaining q31_t data */
while (tapCnt > 0U)
{
*pStateCurnt++ = *pState++;
/* Decrement the loop counter */
tapCnt--;
}
#endif /* #if defined (ARM_MATH_DSP) */
}
/**
* @} end of LMS_NORM group
*/