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/* ----------------------------------------------------------------------
* Copyright (C) 2010 ARM Limited. All rights reserved.
*
* $Date: 15. July 2011
* $Revision: V1.0.10
*
* Project: CMSIS DSP Library
* Title: arm_lms_norm_f32.c
*
* Description: Processing function for the floating-point Normalised LMS.
*
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
*
* Version 1.0.10 2011/7/15
* Big Endian support added and Merged M0 and M3/M4 Source code.
*
* Version 1.0.3 2010/11/29
* Re-organized the CMSIS folders and updated documentation.
*
* Version 1.0.2 2010/11/11
* Documentation updated.
*
* Version 1.0.1 2010/10/05
* Production release and review comments incorporated.
*
* Version 1.0.0 2010/09/20
* Production release and review comments incorporated
*
* Version 0.0.7 2010/06/10
* Misra-C changes done
* -------------------------------------------------------------------- */
#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
* <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 instanteous energy of the filter state variables is calculated:
* <pre>
* E = x[n]^2 + x[n-1]^2 + ... + x[n-numTaps+1]^2.
* </pre>
* The filter coefficients <code>b[k]</code> are then updated on a sample-by-sample basis:
* <pre>
* b[k] = b[k] + e[n] * (mu/E) * 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.
* \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 <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_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;
#ifndef ARM_MATH_CM0
/* 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 /* #ifndef ARM_MATH_CM0 */
}
/**
* @} end of LMS_NORM group
*/
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