360 lines
13 KiB
C
360 lines
13 KiB
C
/* ----------------------------------------------------------------------
|
|
* Copyright (C) 2010-2013 ARM Limited. All rights reserved.
|
|
*
|
|
* $Date: 17. January 2013
|
|
*
|
|
* Project: CMSIS DSP Library
|
|
* Title: arm_biquad_cascade_df2T_f32.c
|
|
*
|
|
* Description: Processing function for the floating-point transposed
|
|
* direct form II Biquad cascade filter.
|
|
*
|
|
* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
|
|
*
|
|
* Redistribution and use in source and binary forms, with or without
|
|
* modification, are permitted provided that the following conditions
|
|
* are met:
|
|
* - Redistributions of source code must retain the above copyright
|
|
* notice, this list of conditions and the following disclaimer.
|
|
* - Redistributions in binary form must reproduce the above copyright
|
|
* notice, this list of conditions and the following disclaimer in
|
|
* the documentation and/or other materials provided with the
|
|
* distribution.
|
|
* - Neither the name of ARM LIMITED nor the names of its contributors
|
|
* may be used to endorse or promote products derived from this
|
|
* software without specific prior written permission.
|
|
*
|
|
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
|
|
* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
|
|
* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
|
|
* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
|
|
* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
|
|
* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
|
|
* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
|
|
* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
|
|
* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
|
|
* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
|
|
* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
|
|
* POSSIBILITY OF SUCH DAMAGE.
|
|
* -------------------------------------------------------------------- */
|
|
|
|
#include "arm_math.h"
|
|
|
|
/**
|
|
* @ingroup groupFilters
|
|
*/
|
|
|
|
/**
|
|
* @defgroup BiquadCascadeDF2T Biquad Cascade IIR Filters Using a Direct Form II Transposed Structure
|
|
*
|
|
* This set of functions implements arbitrary order recursive (IIR) filters using a transposed direct form II structure.
|
|
* The filters are implemented as a cascade of second order Biquad sections.
|
|
* These functions provide a slight memory savings as compared to the direct form I Biquad filter functions.
|
|
* Only floating-point data is supported.
|
|
*
|
|
* This function 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] + d1
|
|
* d1 = b1 * x[n] + a1 * y[n] + d2
|
|
* d2 = b2 * x[n] + a2 * y[n]
|
|
* </pre>
|
|
* where d1 and d2 represent the two state values.
|
|
*
|
|
* \par
|
|
* A Biquad filter using a transposed Direct Form II structure is shown below.
|
|
* \image html BiquadDF2Transposed.gif "Single transposed Direct Form II Biquad"
|
|
* 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 flip the sign of the feedback coefficients:
|
|
* <pre>
|
|
* y[n] = b0 * x[n] + d1;
|
|
* d1 = b1 * x[n] - a1 * y[n] + d2;
|
|
* d2 = b2 * x[n] - a2 * y[n];
|
|
* </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.
|
|
* 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
|
|
* <code>pState</code> points to the state variable array.
|
|
* Each Biquad stage has 2 state variables <code>d1</code> and <code>d2</code>.
|
|
* The state variables are arranged in the <code>pState</code> array as:
|
|
* <pre>
|
|
* {d11, d12, d21, d22, ...}
|
|
* </pre>
|
|
* where <code>d1x</code> refers to the state variables for the first Biquad and
|
|
* <code>d2x</code> refers to the state variables for the second Biquad.
|
|
* The state array has a total length of <code>2*numStages</code> values.
|
|
* The state variables are updated after each block of data is processed; the coefficients are untouched.
|
|
*
|
|
* \par
|
|
* The CMSIS library contains Biquad filters in both Direct Form I and transposed Direct Form II.
|
|
* The advantage of the Direct Form I structure is that it is numerically more robust for fixed-point data types.
|
|
* That is why the Direct Form I structure supports Q15 and Q31 data types.
|
|
* The transposed Direct Form II structure, on the other hand, requires a wide dynamic range for the state variables <code>d1</code> and <code>d2</code>.
|
|
* Because of this, the CMSIS library only has a floating-point version of the Direct Form II Biquad.
|
|
* The advantage of the Direct Form II Biquad is that it requires half the number of state variables, 2 rather than 4, per Biquad stage.
|
|
*
|
|
* \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.
|
|
*
|
|
* \par Init Functions
|
|
* There is also an associated initialization function.
|
|
* 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.
|
|
* For example, to statically initialize the instance structure use
|
|
* <pre>
|
|
* arm_biquad_cascade_df2T_instance_f32 S1 = {numStages, pState, pCoeffs};
|
|
* </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;
|
|
*
|
|
*/
|
|
|
|
/**
|
|
* @addtogroup BiquadCascadeDF2T
|
|
* @{
|
|
*/
|
|
|
|
/**
|
|
* @brief Processing function for the floating-point transposed direct form II Biquad cascade filter.
|
|
* @param[in] *S points to an instance of the filter data 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.
|
|
*/
|
|
|
|
|
|
LOW_OPTIMIZATION_ENTER
|
|
void arm_biquad_cascade_df2T_f32(
|
|
const arm_biquad_cascade_df2T_instance_f32 * S,
|
|
float32_t * pSrc,
|
|
float32_t * pDst,
|
|
uint32_t blockSize)
|
|
{
|
|
|
|
float32_t *pIn = pSrc; /* source pointer */
|
|
float32_t *pOut = pDst; /* destination pointer */
|
|
float32_t *pState = S->pState; /* State pointer */
|
|
float32_t *pCoeffs = S->pCoeffs; /* coefficient pointer */
|
|
float32_t acc1; /* accumulator */
|
|
float32_t b0, b1, b2, a1, a2; /* Filter coefficients */
|
|
float32_t Xn1; /* temporary input */
|
|
float32_t d1, d2; /* state variables */
|
|
uint32_t sample, stage = S->numStages; /* loop counters */
|
|
|
|
#ifndef ARM_MATH_CM0_FAMILY_FAMILY
|
|
|
|
float32_t Xn2, Xn3, Xn4; /* Input State variables */
|
|
float32_t acc2, acc3, acc4; /* accumulator */
|
|
|
|
|
|
float32_t p0, p1, p2, p3, p4, A1;
|
|
|
|
/* Run the below code for Cortex-M4 and Cortex-M3 */
|
|
do
|
|
{
|
|
/* Reading the coefficients */
|
|
b0 = *pCoeffs++;
|
|
b1 = *pCoeffs++;
|
|
b2 = *pCoeffs++;
|
|
a1 = *pCoeffs++;
|
|
a2 = *pCoeffs++;
|
|
|
|
|
|
/*Reading the state values */
|
|
d1 = pState[0];
|
|
d2 = pState[1];
|
|
|
|
/* Apply loop unrolling and compute 4 output values simultaneously. */
|
|
sample = blockSize >> 2u;
|
|
|
|
/* 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. */
|
|
while(sample > 0u) {
|
|
|
|
/* y[n] = b0 * x[n] + d1 */
|
|
/* d1 = b1 * x[n] + a1 * y[n] + d2 */
|
|
/* d2 = b2 * x[n] + a2 * y[n] */
|
|
|
|
/* Read the four inputs */
|
|
Xn1 = pIn[0];
|
|
Xn2 = pIn[1];
|
|
Xn3 = pIn[2];
|
|
Xn4 = pIn[3];
|
|
pIn += 4;
|
|
|
|
p0 = b0 * Xn1;
|
|
p1 = b1 * Xn1;
|
|
acc1 = p0 + d1;
|
|
p0 = b0 * Xn2;
|
|
p3 = a1 * acc1;
|
|
p2 = b2 * Xn1;
|
|
A1 = p1 + p3;
|
|
p4 = a2 * acc1;
|
|
d1 = A1 + d2;
|
|
d2 = p2 + p4;
|
|
|
|
p1 = b1 * Xn2;
|
|
acc2 = p0 + d1;
|
|
p0 = b0 * Xn3;
|
|
p3 = a1 * acc2;
|
|
p2 = b2 * Xn2;
|
|
A1 = p1 + p3;
|
|
p4 = a2 * acc2;
|
|
d1 = A1 + d2;
|
|
d2 = p2 + p4;
|
|
|
|
p1 = b1 * Xn3;
|
|
acc3 = p0 + d1;
|
|
p0 = b0 * Xn4;
|
|
p3 = a1 * acc3;
|
|
p2 = b2 * Xn3;
|
|
A1 = p1 + p3;
|
|
p4 = a2 * acc3;
|
|
d1 = A1 + d2;
|
|
d2 = p2 + p4;
|
|
|
|
acc4 = p0 + d1;
|
|
p1 = b1 * Xn4;
|
|
p3 = a1 * acc4;
|
|
p2 = b2 * Xn4;
|
|
A1 = p1 + p3;
|
|
p4 = a2 * acc4;
|
|
d1 = A1 + d2;
|
|
d2 = p2 + p4;
|
|
|
|
pOut[0] = acc1;
|
|
pOut[1] = acc2;
|
|
pOut[2] = acc3;
|
|
pOut[3] = acc4;
|
|
pOut += 4;
|
|
|
|
sample--;
|
|
}
|
|
|
|
sample = blockSize & 0x3u;
|
|
while(sample > 0u) {
|
|
Xn1 = *pIn++;
|
|
|
|
p0 = b0 * Xn1;
|
|
p1 = b1 * Xn1;
|
|
acc1 = p0 + d1;
|
|
p3 = a1 * acc1;
|
|
p2 = b2 * Xn1;
|
|
A1 = p1 + p3;
|
|
p4 = a2 * acc1;
|
|
d1 = A1 + d2;
|
|
d2 = p2 + p4;
|
|
|
|
*pOut++ = acc1;
|
|
|
|
sample--;
|
|
}
|
|
|
|
/* Store the updated state variables back into the state array */
|
|
*pState++ = d1;
|
|
*pState++ = d2;
|
|
|
|
/* The current stage input is given as the output to the next stage */
|
|
pIn = pDst;
|
|
|
|
/*Reset the output working pointer */
|
|
pOut = pDst;
|
|
|
|
/* decrement the loop counter */
|
|
stage--;
|
|
|
|
} while(stage > 0u);
|
|
|
|
#else
|
|
|
|
/* Run the below code for Cortex-M0 */
|
|
|
|
do
|
|
{
|
|
/* Reading the coefficients */
|
|
b0 = *pCoeffs++;
|
|
b1 = *pCoeffs++;
|
|
b2 = *pCoeffs++;
|
|
a1 = *pCoeffs++;
|
|
a2 = *pCoeffs++;
|
|
|
|
/*Reading the state values */
|
|
d1 = pState[0];
|
|
d2 = pState[1];
|
|
|
|
|
|
sample = blockSize;
|
|
|
|
while(sample > 0u)
|
|
{
|
|
/* Read the input */
|
|
Xn1 = *pIn++;
|
|
|
|
/* y[n] = b0 * x[n] + d1 */
|
|
acc1 = (b0 * Xn1) + d1;
|
|
|
|
/* Store the result in the accumulator in the destination buffer. */
|
|
*pOut++ = acc1;
|
|
|
|
/* Every time after the output is computed state should be updated. */
|
|
/* d1 = b1 * x[n] + a1 * y[n] + d2 */
|
|
d1 = ((b1 * Xn1) + (a1 * acc1)) + d2;
|
|
|
|
/* d2 = b2 * x[n] + a2 * y[n] */
|
|
d2 = (b2 * Xn1) + (a2 * acc1);
|
|
|
|
/* decrement the loop counter */
|
|
sample--;
|
|
}
|
|
|
|
/* Store the updated state variables back into the state array */
|
|
*pState++ = d1;
|
|
*pState++ = d2;
|
|
|
|
/* The current stage input is given as the output to the next stage */
|
|
pIn = pDst;
|
|
|
|
/*Reset the output working pointer */
|
|
pOut = pDst;
|
|
|
|
/* decrement the loop counter */
|
|
stage--;
|
|
|
|
} while(stage > 0u);
|
|
|
|
#endif /* #ifndef ARM_MATH_CM0_FAMILY */
|
|
|
|
}
|
|
LOW_OPTIMIZATION_EXIT
|
|
|
|
/**
|
|
* @} end of BiquadCascadeDF2T group
|
|
*/
|