455 lines
15 KiB
C
455 lines
15 KiB
C
/* ----------------------------------------------------------------------
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* Project: CMSIS DSP Library
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* Title: arm_lms_norm_f32.c
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* Description: Processing function for the floating-point Normalised LMS
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*
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* $Date: 27. January 2017
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* $Revision: V.1.5.1
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*
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* Target Processor: Cortex-M cores
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* -------------------------------------------------------------------- */
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/*
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* Copyright (C) 2010-2017 ARM Limited or its affiliates. All rights reserved.
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*
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* SPDX-License-Identifier: Apache-2.0
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*
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* Licensed under the Apache License, Version 2.0 (the License); you may
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* not use this file except in compliance with the License.
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* You may obtain a copy of the License at
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*
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* www.apache.org/licenses/LICENSE-2.0
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*
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* Unless required by applicable law or agreed to in writing, software
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* distributed under the License is distributed on an AS IS BASIS, WITHOUT
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* WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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* See the License for the specific language governing permissions and
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* limitations under the License.
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*/
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#include "arm_math.h"
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/**
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* @ingroup groupFilters
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*/
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/**
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* @defgroup LMS_NORM Normalized LMS Filters
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*
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* This set of functions implements a commonly used adaptive filter.
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* It is related to the Least Mean Square (LMS) adaptive filter and includes an additional normalization
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* factor which increases the adaptation rate of the filter.
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* The CMSIS DSP Library contains normalized LMS filter functions that operate on Q15, Q31, and floating-point data types.
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*
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* A normalized least mean square (NLMS) filter consists of two components as shown below.
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* The first component is a standard transversal or FIR filter.
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* The second component is a coefficient update mechanism.
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* The NLMS filter has two input signals.
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* The "input" feeds the FIR filter while the "reference input" corresponds to the desired output of the FIR filter.
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* That is, the FIR filter coefficients are updated so that the output of the FIR filter matches the reference input.
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* The filter coefficient update mechanism is based on the difference between the FIR filter output and the reference input.
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* This "error signal" tends towards zero as the filter adapts.
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* The NLMS processing functions accept the input and reference input signals and generate the filter output and error signal.
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* \image html LMS.gif "Internal structure of the NLMS adaptive filter"
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*
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* The functions operate on blocks of data and each call to the function processes
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* <code>blockSize</code> samples through the filter.
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* <code>pSrc</code> points to input signal, <code>pRef</code> points to reference signal,
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* <code>pOut</code> points to output signal and <code>pErr</code> points to error signal.
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* All arrays contain <code>blockSize</code> values.
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*
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* The functions operate on a block-by-block basis.
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* Internally, the filter coefficients <code>b[n]</code> are updated on a sample-by-sample basis.
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* The convergence of the LMS filter is slower compared to the normalized LMS algorithm.
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*
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* \par Algorithm:
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* The output signal <code>y[n]</code> is computed by a standard FIR filter:
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* <pre>
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* y[n] = b[0] * x[n] + b[1] * x[n-1] + b[2] * x[n-2] + ...+ b[numTaps-1] * x[n-numTaps+1]
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* </pre>
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*
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* \par
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* The error signal equals the difference between the reference signal <code>d[n]</code> and the filter output:
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* <pre>
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* e[n] = d[n] - y[n].
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* </pre>
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*
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* \par
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* After each sample of the error signal is computed the instanteous energy of the filter state variables is calculated:
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* <pre>
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* E = x[n]^2 + x[n-1]^2 + ... + x[n-numTaps+1]^2.
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* </pre>
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* The filter coefficients <code>b[k]</code> are then updated on a sample-by-sample basis:
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* <pre>
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* b[k] = b[k] + e[n] * (mu/E) * x[n-k], for k=0, 1, ..., numTaps-1
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* </pre>
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* where <code>mu</code> is the step size and controls the rate of coefficient convergence.
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*\par
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* In the APIs, <code>pCoeffs</code> points to a coefficient array of size <code>numTaps</code>.
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* Coefficients are stored in time reversed order.
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* \par
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* <pre>
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* {b[numTaps-1], b[numTaps-2], b[N-2], ..., b[1], b[0]}
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* </pre>
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* \par
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* <code>pState</code> points to a state array of size <code>numTaps + blockSize - 1</code>.
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* Samples in the state buffer are stored in the order:
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* \par
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* <pre>
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* {x[n-numTaps+1], x[n-numTaps], x[n-numTaps-1], x[n-numTaps-2]....x[0], x[1], ..., x[blockSize-1]}
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* </pre>
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* \par
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* Note that the length of the state buffer exceeds the length of the coefficient array by <code>blockSize-1</code> samples.
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* The increased state buffer length allows circular addressing, which is traditionally used in FIR filters,
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* to be avoided and yields a significant speed improvement.
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* The state variables are updated after each block of data is processed.
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* \par Instance Structure
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* The coefficients and state variables for a filter are stored together in an instance data structure.
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* A separate instance structure must be defined for each filter and
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* coefficient and state arrays cannot be shared among instances.
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* There are separate instance structure declarations for each of the 3 supported data types.
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*
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* \par Initialization Functions
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* There is also an associated initialization function for each data type.
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* The initialization function performs the following operations:
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* - Sets the values of the internal structure fields.
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* - Zeros out the values in the state buffer.
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* To do this manually without calling the init function, assign the follow subfields of the instance structure:
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* numTaps, pCoeffs, mu, energy, x0, pState. Also set all of the values in pState to zero.
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* For Q7, Q15, and Q31 the following fields must also be initialized;
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* recipTable, postShift
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*
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* \par
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* Instance structure cannot be placed into a const data section and it is recommended to use the initialization function.
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* \par Fixed-Point Behavior:
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* Care must be taken when using the Q15 and Q31 versions of the normalised LMS filter.
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* The following issues must be considered:
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* - Scaling of coefficients
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* - Overflow and saturation
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*
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* \par Scaling of Coefficients:
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* Filter coefficients are represented as fractional values and
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* coefficients are restricted to lie in the range <code>[-1 +1)</code>.
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* The fixed-point functions have an additional scaling parameter <code>postShift</code>.
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* At the output of the filter's accumulator is a shift register which shifts the result by <code>postShift</code> bits.
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* This essentially scales the filter coefficients by <code>2^postShift</code> and
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* allows the filter coefficients to exceed the range <code>[+1 -1)</code>.
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* The value of <code>postShift</code> is set by the user based on the expected gain through the system being modeled.
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*
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* \par Overflow and Saturation:
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* Overflow and saturation behavior of the fixed-point Q15 and Q31 versions are
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* described separately as part of the function specific documentation below.
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*/
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/**
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* @addtogroup LMS_NORM
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* @{
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*/
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/**
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* @brief Processing function for floating-point normalized LMS filter.
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* @param[in] *S points to an instance of the floating-point normalized LMS filter structure.
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* @param[in] *pSrc points to the block of input data.
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* @param[in] *pRef points to the block of reference data.
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* @param[out] *pOut points to the block of output data.
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* @param[out] *pErr points to the block of error data.
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* @param[in] blockSize number of samples to process.
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* @return none.
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*/
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void arm_lms_norm_f32(
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arm_lms_norm_instance_f32 * S,
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float32_t * pSrc,
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float32_t * pRef,
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float32_t * pOut,
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float32_t * pErr,
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uint32_t blockSize)
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{
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float32_t *pState = S->pState; /* State pointer */
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float32_t *pCoeffs = S->pCoeffs; /* Coefficient pointer */
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float32_t *pStateCurnt; /* Points to the current sample of the state */
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float32_t *px, *pb; /* Temporary pointers for state and coefficient buffers */
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float32_t mu = S->mu; /* Adaptive factor */
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uint32_t numTaps = S->numTaps; /* Number of filter coefficients in the filter */
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uint32_t tapCnt, blkCnt; /* Loop counters */
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float32_t energy; /* Energy of the input */
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float32_t sum, e, d; /* accumulator, error, reference data sample */
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float32_t w, x0, in; /* weight factor, temporary variable to hold input sample and state */
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/* Initializations of error, difference, Coefficient update */
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e = 0.0f;
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d = 0.0f;
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w = 0.0f;
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energy = S->energy;
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x0 = S->x0;
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/* S->pState points to buffer which contains previous frame (numTaps - 1) samples */
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/* pStateCurnt points to the location where the new input data should be written */
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pStateCurnt = &(S->pState[(numTaps - 1U)]);
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/* Loop over blockSize number of values */
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blkCnt = blockSize;
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#if defined (ARM_MATH_DSP)
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/* Run the below code for Cortex-M4 and Cortex-M3 */
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while (blkCnt > 0U)
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{
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/* Copy the new input sample into the state buffer */
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*pStateCurnt++ = *pSrc;
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/* Initialize pState pointer */
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px = pState;
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/* Initialize coeff pointer */
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pb = (pCoeffs);
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/* Read the sample from input buffer */
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in = *pSrc++;
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/* Update the energy calculation */
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energy -= x0 * x0;
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energy += in * in;
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/* Set the accumulator to zero */
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sum = 0.0f;
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/* Loop unrolling. Process 4 taps at a time. */
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tapCnt = numTaps >> 2;
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while (tapCnt > 0U)
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{
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/* Perform the multiply-accumulate */
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sum += (*px++) * (*pb++);
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sum += (*px++) * (*pb++);
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sum += (*px++) * (*pb++);
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sum += (*px++) * (*pb++);
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/* Decrement the loop counter */
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tapCnt--;
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}
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/* If the filter length is not a multiple of 4, compute the remaining filter taps */
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tapCnt = numTaps % 0x4U;
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while (tapCnt > 0U)
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{
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/* Perform the multiply-accumulate */
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sum += (*px++) * (*pb++);
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/* Decrement the loop counter */
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tapCnt--;
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}
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/* The result in the accumulator, store in the destination buffer. */
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*pOut++ = sum;
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/* Compute and store error */
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d = (float32_t) (*pRef++);
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e = d - sum;
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*pErr++ = e;
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/* Calculation of Weighting factor for updating filter coefficients */
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/* epsilon value 0.000000119209289f */
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w = (e * mu) / (energy + 0.000000119209289f);
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/* Initialize pState pointer */
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px = pState;
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/* Initialize coeff pointer */
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pb = (pCoeffs);
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/* Loop unrolling. Process 4 taps at a time. */
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tapCnt = numTaps >> 2;
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/* Update filter coefficients */
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while (tapCnt > 0U)
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{
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/* Perform the multiply-accumulate */
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*pb += w * (*px++);
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pb++;
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*pb += w * (*px++);
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pb++;
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*pb += w * (*px++);
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pb++;
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*pb += w * (*px++);
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pb++;
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/* Decrement the loop counter */
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tapCnt--;
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}
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/* If the filter length is not a multiple of 4, compute the remaining filter taps */
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tapCnt = numTaps % 0x4U;
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while (tapCnt > 0U)
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{
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/* Perform the multiply-accumulate */
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*pb += w * (*px++);
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pb++;
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/* Decrement the loop counter */
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tapCnt--;
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}
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x0 = *pState;
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/* Advance state pointer by 1 for the next sample */
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pState = pState + 1;
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/* Decrement the loop counter */
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blkCnt--;
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}
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S->energy = energy;
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S->x0 = x0;
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/* Processing is complete. Now copy the last numTaps - 1 samples to the
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satrt of the state buffer. This prepares the state buffer for the
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next function call. */
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/* Points to the start of the pState buffer */
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pStateCurnt = S->pState;
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/* Loop unrolling for (numTaps - 1U)/4 samples copy */
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tapCnt = (numTaps - 1U) >> 2U;
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/* copy data */
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while (tapCnt > 0U)
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{
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*pStateCurnt++ = *pState++;
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*pStateCurnt++ = *pState++;
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*pStateCurnt++ = *pState++;
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*pStateCurnt++ = *pState++;
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/* Decrement the loop counter */
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tapCnt--;
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}
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/* Calculate remaining number of copies */
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tapCnt = (numTaps - 1U) % 0x4U;
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/* Copy the remaining q31_t data */
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while (tapCnt > 0U)
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{
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*pStateCurnt++ = *pState++;
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/* Decrement the loop counter */
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tapCnt--;
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}
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#else
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/* Run the below code for Cortex-M0 */
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while (blkCnt > 0U)
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{
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/* Copy the new input sample into the state buffer */
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*pStateCurnt++ = *pSrc;
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/* Initialize pState pointer */
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px = pState;
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/* Initialize pCoeffs pointer */
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pb = pCoeffs;
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/* Read the sample from input buffer */
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in = *pSrc++;
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/* Update the energy calculation */
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energy -= x0 * x0;
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energy += in * in;
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/* Set the accumulator to zero */
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sum = 0.0f;
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/* Loop over numTaps number of values */
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tapCnt = numTaps;
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while (tapCnt > 0U)
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{
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/* Perform the multiply-accumulate */
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sum += (*px++) * (*pb++);
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/* Decrement the loop counter */
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tapCnt--;
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}
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/* The result in the accumulator is stored in the destination buffer. */
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*pOut++ = sum;
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/* Compute and store error */
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d = (float32_t) (*pRef++);
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e = d - sum;
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*pErr++ = e;
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/* Calculation of Weighting factor for updating filter coefficients */
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/* epsilon value 0.000000119209289f */
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w = (e * mu) / (energy + 0.000000119209289f);
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/* Initialize pState pointer */
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px = pState;
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/* Initialize pCcoeffs pointer */
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pb = pCoeffs;
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/* Loop over numTaps number of values */
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tapCnt = numTaps;
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while (tapCnt > 0U)
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{
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/* Perform the multiply-accumulate */
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*pb += w * (*px++);
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pb++;
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/* Decrement the loop counter */
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tapCnt--;
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}
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x0 = *pState;
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/* Advance state pointer by 1 for the next sample */
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pState = pState + 1;
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/* Decrement the loop counter */
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blkCnt--;
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}
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S->energy = energy;
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S->x0 = x0;
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/* Processing is complete. Now copy the last numTaps - 1 samples to the
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satrt of the state buffer. This prepares the state buffer for the
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next function call. */
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/* Points to the start of the pState buffer */
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pStateCurnt = S->pState;
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/* Copy (numTaps - 1U) samples */
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tapCnt = (numTaps - 1U);
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/* Copy the remaining q31_t data */
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while (tapCnt > 0U)
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{
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*pStateCurnt++ = *pState++;
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/* Decrement the loop counter */
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tapCnt--;
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}
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#endif /* #if defined (ARM_MATH_DSP) */
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}
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/**
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* @} end of LMS_NORM group
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*/
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