/* ----------------------------------------------------------------------
* Copyright (C) 2010 ARM Limited. All rights reserved.
*
* $Date: 29. November 2010
* $Revision: V1.0.3
*
* Project: CMSIS DSP Library
* Title: arm_lms_f32.c
*
* Description: Processing function for the floating-point LMS filter.
*
* Target Processor: Cortex-M4/Cortex-M3
*
* 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 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
* 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 API 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 filter coefficients
b[k]
are updated on a sample-by-sample basis:
* * b[k] = b[k] + e[n] * mu * 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.
* \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
* * 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}; ** where
numTaps
is the number of filter coefficients in the filter; pState
is the address of the state buffer;
* pCoeffs
is the address of the coefficient buffer; mu
is the step size parameter; and postShift
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 [-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
* @{
*/
/**
* @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;
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--;
}
}
/**
* @} end of LMS group
*/