pigweed / third_party / github / STMicroelectronics / cmsis_core / refs/heads/cm4 / . / DSP / Source / FilteringFunctions / arm_biquad_cascade_df1_f32.c

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

* Project: CMSIS DSP Library | |

* Title: arm_biquad_cascade_df1_f32.c | |

* Description: Processing function for the floating-point Biquad cascade DirectFormI(DF1) 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 BiquadCascadeDF1 Biquad Cascade IIR Filters Using Direct Form I Structure | |

This set of functions implements arbitrary order recursive (IIR) filters. | |

The filters are implemented as a cascade of second order Biquad sections. | |

The functions support Q15, Q31 and floating-point data types. | |

Fast version of Q15 and Q31 also available. | |

The functions operate on blocks of input and output data and each call to the function | |

processes <code>blockSize</code> samples through the filter. | |

<code>pSrc</code> points to the array of input data and | |

<code>pDst</code> points to the array of output data. | |

Both arrays contain <code>blockSize</code> values. | |

@par Algorithm | |

Each Biquad stage implements a second order filter using the difference equation: | |

<pre> | |

y[n] = b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] | |

</pre> | |

A Direct Form I algorithm is used with 5 coefficients and 4 state variables per stage. | |

\image html Biquad.gif "Single Biquad filter stage" | |

Coefficients <code>b0, b1 and b2 </code> multiply the input signal <code>x[n]</code> and are referred to as the feedforward coefficients. | |

Coefficients <code>a1</code> and <code>a2</code> multiply the output signal <code>y[n]</code> and are referred to as the feedback coefficients. | |

Pay careful attention to the sign of the feedback coefficients. | |

Some design tools use the difference equation | |

<pre> | |

y[n] = b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] - a1 * y[n-1] - a2 * y[n-2] | |

</pre> | |

In this case the feedback coefficients <code>a1</code> and <code>a2</code> | |

must be negated when used with the CMSIS DSP Library. | |

@par | |

Higher order filters are realized as a cascade of second order sections. | |

<code>numStages</code> refers to the number of second order stages used. | |

For example, an 8th order filter would be realized with <code>numStages=4</code> second order stages. | |

\image html BiquadCascade.gif "8th order filter using a cascade of Biquad stages" | |

A 9th order filter would be realized with <code>numStages=5</code> second order stages with the coefficients for one of the stages configured as a first order filter (<code>b2=0</code> and <code>a2=0</code>). | |

@par | |

The <code>pState</code> points to state variables array. | |

Each Biquad stage has 4 state variables <code>x[n-1], x[n-2], y[n-1],</code> and <code>y[n-2]</code>. | |

The state variables are arranged in the <code>pState</code> array as: | |

<pre> | |

{x[n-1], x[n-2], y[n-1], y[n-2]} | |

</pre> | |

@par | |

The 4 state variables for stage 1 are first, then the 4 state variables for stage 2, and so on. | |

The state array has a total length of <code>4*numStages</code> values. | |

The state variables are updated after each block of data is processed, the coefficients are untouched. | |

@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. | |

Coefficient arrays may be shared among several instances while state variable arrays cannot be shared. | |

There are separate instance structure declarations for each of the 3 supported data types. | |

@par Init Function | |

There is also an associated initialization function for each data type. | |

The initialization function performs 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: | |

numStages, pCoeffs, 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_biquad_casd_df1_inst_f32 S1 = {numStages, pState, pCoeffs}; | |

arm_biquad_casd_df1_inst_q15 S2 = {numStages, pState, pCoeffs, postShift}; | |

arm_biquad_casd_df1_inst_q31 S3 = {numStages, pState, pCoeffs, postShift}; | |

</pre> | |

where <code>numStages</code> is the number of Biquad stages in the filter; | |

<code>pState</code> is the address of the state buffer; | |

<code>pCoeffs</code> is the address of the coefficient buffer; | |

<code>postShift</code> shift to be applied. | |

@par Fixed-Point Behavior | |

Care must be taken when using the Q15 and Q31 versions of the Biquad Cascade filter functions. | |

Following issues must be considered: | |

- Scaling of coefficients | |

- Filter gain | |

- 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> | |

which allow the filter coefficients to exceed the range <code>[+1 -1)</code>. | |

At the output of the filter's accumulator is a shift register which shifts the result by <code>postShift</code> bits. | |

\image html BiquadPostshift.gif "Fixed-point Biquad with shift by postShift bits after accumulator" | |

This essentially scales the filter coefficients by <code>2^postShift</code>. | |

For example, to realize the coefficients | |

<pre> | |

{1.5, -0.8, 1.2, 1.6, -0.9} | |

</pre> | |

set the pCoeffs array to: | |

<pre> | |

{0.75, -0.4, 0.6, 0.8, -0.45} | |

</pre> | |

and set <code>postShift=1</code> | |

@par Filter gain | |

The frequency response of a Biquad filter is a function of its coefficients. | |

It is possible for the gain through the filter to exceed 1.0 meaning that the filter increases the amplitude of certain frequencies. | |

This means that an input signal with amplitude < 1.0 may result in an output > 1.0 and these are saturated or overflowed based on the implementation of the filter. | |

To avoid this behavior the filter needs to be scaled down such that its peak gain < 1.0 or the input signal must be scaled down so that the combination of input and filter are never overflowed. | |

@par Overflow and saturation | |

For Q15 and Q31 versions, it is described separately as part of the function specific documentation below. | |

*/ | |

/** | |

@addtogroup BiquadCascadeDF1 | |

@{ | |

*/ | |

/** | |

@brief Processing function for the floating-point Biquad cascade filter. | |

@param[in] S points to an instance of the floating-point Biquad cascade structure | |

@param[in] pSrc points to the block of input data | |

@param[out] pDst points to the block of output data | |

@param[in] blockSize number of samples to process | |

@return none | |

*/ | |

#if defined(ARM_MATH_NEON) | |

void arm_biquad_cascade_df1_f32( | |

const arm_biquad_casd_df1_inst_f32 * S, | |

const float32_t * pSrc, | |

float32_t * pDst, | |

uint32_t blockSize) | |

{ | |

const float32_t *pIn = pSrc; /* source pointer */ | |

float32_t *pOut = pDst; /* destination pointer */ | |

float32_t *pState = S->pState; /* pState pointer */ | |

const float32_t *pCoeffs = S->pCoeffs; /* coefficient pointer */ | |

float32_t acc; /* Simulates the accumulator */ | |

uint32_t sample, stage = S->numStages; /* loop counters */ | |

float32x4_t Xn; | |

float32x2_t Yn; | |

float32x2_t a; | |

float32x4_t b; | |

float32x4_t x,tmp; | |

float32x2_t t; | |

float32x2x2_t y; | |

float32_t Xns; | |

while (stage > 0U) | |

{ | |

/* Reading the coefficients */ | |

Xn = vld1q_f32(pState); | |

Yn = vld1_f32(pState + 2); | |

b = vld1q_f32(pCoeffs); | |

b = vrev64q_f32(b); | |

b = vcombine_f32(vget_high_f32(b), vget_low_f32(b)); | |

a = vld1_f32(pCoeffs + 3); | |

a = vrev64_f32(a); | |

b[0] = 0.0; | |

pCoeffs += 5; | |

/* Reading the pState values */ | |

/* Apply loop unrolling and compute 4 output values simultaneously. */ | |

/* The variable acc hold output values that are being computed: | |

* | |

* acc = b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] | |

* acc = b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] | |

* acc = b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] | |

* acc = b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] | |

*/ | |

/* First part of the processing with loop unrolling. Compute 4 outputs at a time. | |

** a second loop below computes the remaining 1 to 3 samples. */ | |

sample = blockSize >> 2U; | |

while (sample > 0U) | |

{ | |

/* Read the first 4 inputs */ | |

x = vld1q_f32(pIn); | |

pIn += 4; | |

tmp = vextq_f32(Xn, x, 1); | |

t = vmul_f32(vget_high_f32(b), vget_high_f32(tmp)); | |

t = vmla_f32(t, vget_low_f32(b), vget_low_f32(tmp)); | |

t = vmla_f32(t, a, Yn); | |

t = vpadd_f32(t, t); | |

Yn = vext_f32(Yn, t, 1); | |

tmp = vextq_f32(Xn, x, 2); | |

t = vmul_f32(vget_high_f32(b), vget_high_f32(tmp)); | |

t = vmla_f32(t, vget_low_f32(b), vget_low_f32(tmp)); | |

t = vmla_f32(t, a, Yn); | |

t = vpadd_f32(t, t); | |

Yn = vext_f32(Yn, t, 1); | |

y.val[0] = Yn; | |

tmp = vextq_f32(Xn, x, 3); | |

t = vmul_f32(vget_high_f32(b), vget_high_f32(tmp)); | |

t = vmla_f32(t, vget_low_f32(b), vget_low_f32(tmp)); | |

t = vmla_f32(t, a, Yn); | |

t = vpadd_f32(t, t); | |

Yn = vext_f32(Yn, t, 1); | |

Xn = x; | |

t = vmul_f32(vget_high_f32(b), vget_high_f32(Xn)); | |

t = vmla_f32(t, vget_low_f32(b), vget_low_f32(Xn)); | |

t = vmla_f32(t, a, Yn); | |

t = vpadd_f32(t, t); | |

Yn = vext_f32(Yn, t, 1); | |

y.val[1] = Yn; | |

tmp = vcombine_f32(y.val[0], y.val[1]); | |

/* Store the 4 outputs and increment the pointer */ | |

vst1q_f32(pOut, tmp); | |

pOut += 4; | |

/* Decrement the loop counter */ | |

sample--; | |

} | |

/* If the block size is not a multiple of 4, compute any remaining output samples here. | |

** No loop unrolling is used. */ | |

sample = blockSize & 0x3U; | |

while (sample > 0U) | |

{ | |

/* Read the input */ | |

Xns = *pIn++; | |

/* acc = b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] */ | |

acc = (b[1] * Xn[2]) + (b[2] * Xn[3]) + (b[3] * Xns) + (a[0] * Yn[0]) + (a[1] * Yn[1]); | |

/* Store the result in the accumulator in the destination buffer. */ | |

*pOut++ = acc; | |

/* Every time after the output is computed state should be updated. */ | |

/* The states should be updated as: */ | |

/* Xn2 = Xn1 */ | |

/* Xn1 = Xn */ | |

/* Yn2 = Yn1 */ | |

/* Yn1 = acc */ | |

Xn[2] = Xn[3]; | |

Xn[3] = Xns; | |

Yn[0] = Yn[1]; | |

Yn[1] = acc; | |

/* Decrement the loop counter */ | |

sample--; | |

} | |

vst1q_f32(pState,vcombine_f32(vrev64_f32(vget_high_f32(Xn)),vrev64_f32(Yn))); | |

pState += 4; | |

/* Store the updated state variables back into the pState array */ | |

/* The first stage goes from the input buffer to the output buffer. */ | |

/* Subsequent numStages occur in-place in the output buffer */ | |

pIn = pDst; | |

/* Reset the output pointer */ | |

pOut = pDst; | |

/* Decrement the loop counter */ | |

stage--; | |

} | |

} | |

#else | |

void arm_biquad_cascade_df1_f32( | |

const arm_biquad_casd_df1_inst_f32 * S, | |

const float32_t * pSrc, | |

float32_t * pDst, | |

uint32_t blockSize) | |

{ | |

const float32_t *pIn = pSrc; /* Source pointer */ | |

float32_t *pOut = pDst; /* Destination pointer */ | |

float32_t *pState = S->pState; /* pState pointer */ | |

const float32_t *pCoeffs = S->pCoeffs; /* Coefficient pointer */ | |

float32_t acc; /* Accumulator */ | |

float32_t b0, b1, b2, a1, a2; /* Filter coefficients */ | |

float32_t Xn1, Xn2, Yn1, Yn2; /* Filter pState variables */ | |

float32_t Xn; /* Temporary input */ | |

uint32_t sample, stage = S->numStages; /* Loop counters */ | |

do | |

{ | |

/* Reading the coefficients */ | |

b0 = *pCoeffs++; | |

b1 = *pCoeffs++; | |

b2 = *pCoeffs++; | |

a1 = *pCoeffs++; | |

a2 = *pCoeffs++; | |

/* Reading the pState values */ | |

Xn1 = pState[0]; | |

Xn2 = pState[1]; | |

Yn1 = pState[2]; | |

Yn2 = pState[3]; | |

#if defined (ARM_MATH_LOOPUNROLL) | |

/* Apply loop unrolling and compute 4 output values simultaneously. */ | |

/* Variable acc hold output values that are being computed: | |

* | |

* acc = b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] | |

* acc = b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] | |

* acc = b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] | |

* acc = b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] | |

*/ | |

/* Loop unrolling: Compute 4 outputs at a time */ | |

sample = blockSize >> 2U; | |

while (sample > 0U) | |

{ | |

/* Read the first input */ | |

Xn = *pIn++; | |

/* acc = b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] */ | |

Yn2 = (b0 * Xn) + (b1 * Xn1) + (b2 * Xn2) + (a1 * Yn1) + (a2 * Yn2); | |

/* Store output in destination buffer. */ | |

*pOut++ = Yn2; | |

/* Every time after the output is computed state should be updated. */ | |

/* The states should be updated as: */ | |

/* Xn2 = Xn1 */ | |

/* Xn1 = Xn */ | |

/* Yn2 = Yn1 */ | |

/* Yn1 = acc */ | |

/* Read the second input */ | |

Xn2 = *pIn++; | |

/* acc = b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] */ | |

Yn1 = (b0 * Xn2) + (b1 * Xn) + (b2 * Xn1) + (a1 * Yn2) + (a2 * Yn1); | |

/* Store output in destination buffer. */ | |

*pOut++ = Yn1; | |

/* Every time after the output is computed state should be updated. */ | |

/* The states should be updated as: */ | |

/* Xn2 = Xn1 */ | |

/* Xn1 = Xn */ | |

/* Yn2 = Yn1 */ | |

/* Yn1 = acc */ | |

/* Read the third input */ | |

Xn1 = *pIn++; | |

/* acc = b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] */ | |

Yn2 = (b0 * Xn1) + (b1 * Xn2) + (b2 * Xn) + (a1 * Yn1) + (a2 * Yn2); | |

/* Store output in destination buffer. */ | |

*pOut++ = Yn2; | |

/* Every time after the output is computed state should be updated. */ | |

/* The states should be updated as: */ | |

/* Xn2 = Xn1 */ | |

/* Xn1 = Xn */ | |

/* Yn2 = Yn1 */ | |

/* Yn1 = acc */ | |

/* Read the forth input */ | |

Xn = *pIn++; | |

/* acc = b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] */ | |

Yn1 = (b0 * Xn) + (b1 * Xn1) + (b2 * Xn2) + (a1 * Yn2) + (a2 * Yn1); | |

/* Store output in destination buffer. */ | |

*pOut++ = Yn1; | |

/* Every time after the output is computed state should be updated. */ | |

/* The states should be updated as: */ | |

/* Xn2 = Xn1 */ | |

/* Xn1 = Xn */ | |

/* Yn2 = Yn1 */ | |

/* Yn1 = acc */ | |

Xn2 = Xn1; | |

Xn1 = Xn; | |

/* decrement loop counter */ | |

sample--; | |

} | |

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

sample = blockSize & 0x3U; | |

#else | |

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

sample = blockSize; | |

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

while (sample > 0U) | |

{ | |

/* Read the input */ | |

Xn = *pIn++; | |

/* acc = b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] */ | |

acc = (b0 * Xn) + (b1 * Xn1) + (b2 * Xn2) + (a1 * Yn1) + (a2 * Yn2); | |

/* Store output in destination buffer. */ | |

*pOut++ = acc; | |

/* Every time after the output is computed state should be updated. */ | |

/* The states should be updated as: */ | |

/* Xn2 = Xn1 */ | |

/* Xn1 = Xn */ | |

/* Yn2 = Yn1 */ | |

/* Yn1 = acc */ | |

Xn2 = Xn1; | |

Xn1 = Xn; | |

Yn2 = Yn1; | |

Yn1 = acc; | |

/* decrement loop counter */ | |

sample--; | |

} | |

/* Store the updated state variables back into the pState array */ | |

*pState++ = Xn1; | |

*pState++ = Xn2; | |

*pState++ = Yn1; | |

*pState++ = Yn2; | |

/* The first stage goes from the input buffer to the output buffer. */ | |

/* Subsequent numStages occur in-place in the output buffer */ | |

pIn = pDst; | |

/* Reset output pointer */ | |

pOut = pDst; | |

/* decrement loop counter */ | |

stage--; | |

} while (stage > 0U); | |

} | |

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

/** | |

@} end of BiquadCascadeDF1 group | |

*/ |