pigweed / third_party / github / STMicroelectronics / cmsis_core / refs/heads/cm4 / . / DSP / Source / FilteringFunctions / arm_lms_f32.c

/* ---------------------------------------------------------------------- | |

* Project: CMSIS DSP Library | |

* Title: arm_lms_f32.c | |

* Description: Processing function for the floating-point LMS filter | |

* | |

* $Date: 18. March 2019 | |

* $Revision: V1.6.0 | |

* | |

* Target Processor: Cortex-M cores | |

* -------------------------------------------------------------------- */ | |

/* | |

* Copyright (C) 2010-2019 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 | |

@{ | |

*/ | |

/** | |

@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 | |

*/ | |

#if defined(ARM_MATH_NEON) | |

void arm_lms_f32( | |

const arm_lms_instance_f32 * S, | |

const 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 */ | |

float32x4_t tempV, sumV, xV, bV; | |

float32x2_t tempV2; | |

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; | |

sumV = vdupq_n_f32(0.0); | |

/* Process 4 taps at a time. */ | |

tapCnt = numTaps >> 2; | |

while (tapCnt > 0U) | |

{ | |

/* Perform the multiply-accumulate */ | |

xV = vld1q_f32(px); | |

bV = vld1q_f32(pb); | |

sumV = vmlaq_f32(sumV, xV, bV); | |

px += 4; | |

pb += 4; | |

/* Decrement the loop counter */ | |

tapCnt--; | |

} | |

tempV2 = vpadd_f32(vget_low_f32(sumV),vget_high_f32(sumV)); | |

sum = tempV2[0] + tempV2[1]; | |

/* 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); | |

/* Process 4 taps at a time. */ | |

tapCnt = numTaps >> 2; | |

/* Update filter coefficients */ | |

while (tapCnt > 0U) | |

{ | |

/* Perform the multiply-accumulate */ | |

xV = vld1q_f32(px); | |

bV = vld1q_f32(pb); | |

px += 4; | |

bV = vmlaq_n_f32(bV,xV,w); | |

vst1q_f32(pb,bV); | |

pb += 4; | |

/* 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; | |

/* Process 4 taps at a time for (numTaps - 1U) samples copy */ | |

tapCnt = (numTaps - 1U) >> 2U; | |

/* copy data */ | |

while (tapCnt > 0U) | |

{ | |

tempV = vld1q_f32(pState); | |

vst1q_f32(pStateCurnt,tempV); | |

pState += 4; | |

pStateCurnt += 4; | |

/* 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 | |

void arm_lms_f32( | |

const arm_lms_instance_f32 * S, | |

const 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 */ | |

float32_t acc, e; /* Accumulator, error */ | |

float32_t w; /* Weight factor */ | |

uint32_t numTaps = S->numTaps; /* Number of filter coefficients in the filter */ | |

uint32_t tapCnt, blkCnt; /* Loop counters */ | |

/* Initializations of error, difference, Coefficient update */ | |

e = 0.0f; | |

w = 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)]); | |

/* initialise loop count */ | |

blkCnt = blockSize; | |

while (blkCnt > 0U) | |

{ | |

/* Copy the new input sample into the state buffer */ | |

*pStateCurnt++ = *pSrc++; | |

/* Initialize pState pointer */ | |

px = pState; | |

/* Initialize coefficient pointer */ | |

pb = pCoeffs; | |

/* Set the accumulator to zero */ | |

acc = 0.0f; | |

#if defined (ARM_MATH_LOOPUNROLL) | |

/* Loop unrolling: Compute 4 taps at a time. */ | |

tapCnt = numTaps >> 2U; | |

while (tapCnt > 0U) | |

{ | |

/* Perform the multiply-accumulate */ | |

acc += (*px++) * (*pb++); | |

acc += (*px++) * (*pb++); | |

acc += (*px++) * (*pb++); | |

acc += (*px++) * (*pb++); | |

/* Decrement loop counter */ | |

tapCnt--; | |

} | |

/* Loop unrolling: Compute remaining taps */ | |

tapCnt = numTaps % 0x4U; | |

#else | |

/* Initialize tapCnt with number of samples */ | |

tapCnt = numTaps; | |

#endif /* #if defined (ARM_MATH_LOOPUNROLL) */ | |

while (tapCnt > 0U) | |

{ | |

/* Perform the multiply-accumulate */ | |

acc += (*px++) * (*pb++); | |

/* Decrement the loop counter */ | |

tapCnt--; | |

} | |

/* Store the result from accumulator into the destination buffer. */ | |

*pOut++ = acc; | |

/* Compute and store error */ | |

e = (float32_t) *pRef++ - acc; | |

*pErr++ = e; | |

/* Calculation of Weighting factor for updating filter coefficients */ | |

w = e * mu; | |

/* Initialize pState pointer */ | |

/* Advance state pointer by 1 for the next sample */ | |

px = pState++; | |

/* Initialize coefficient pointer */ | |

pb = pCoeffs; | |

#if defined (ARM_MATH_LOOPUNROLL) | |

/* Loop unrolling: Compute 4 taps at a time. */ | |

tapCnt = numTaps >> 2U; | |

/* 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 loop counter */ | |

tapCnt--; | |

} | |

/* Loop unrolling: Compute remaining taps */ | |

tapCnt = numTaps % 0x4U; | |

#else | |

/* Initialize tapCnt with number of samples */ | |

tapCnt = numTaps; | |

#endif /* #if defined (ARM_MATH_LOOPUNROLL) */ | |

while (tapCnt > 0U) | |

{ | |

/* Perform the multiply-accumulate */ | |

*pb += w * (*px++); | |

pb++; | |

/* Decrement loop counter */ | |

tapCnt--; | |

} | |

/* Decrement 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 data */ | |

#if defined (ARM_MATH_LOOPUNROLL) | |

/* Loop unrolling: Compute 4 taps at a time. */ | |

tapCnt = (numTaps - 1U) >> 2U; | |

while (tapCnt > 0U) | |

{ | |

*pStateCurnt++ = *pState++; | |

*pStateCurnt++ = *pState++; | |

*pStateCurnt++ = *pState++; | |

*pStateCurnt++ = *pState++; | |

/* Decrement loop counter */ | |

tapCnt--; | |

} | |

/* Loop unrolling: Compute remaining taps */ | |

tapCnt = (numTaps - 1U) % 0x4U; | |

#else | |

/* Initialize tapCnt with number of samples */ | |

tapCnt = (numTaps - 1U); | |

#endif /* #if defined (ARM_MATH_LOOPUNROLL) */ | |

while (tapCnt > 0U) | |

{ | |

*pStateCurnt++ = *pState++; | |

/* Decrement loop counter */ | |

tapCnt--; | |

} | |

} | |

#endif /* #if defined(ARM_MATH_NEON) */ | |

/** | |

@} end of LMS group | |

*/ |