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/* ----------------------------------------------------------------------
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* Copyright (C) 2010 ARM Limited. All rights reserved.
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*
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* $Date: 15. July 2011
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* $Revision: V1.0.10
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*
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* Project: CMSIS DSP Library
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* Title: arm_biquad_cascade_df2T_f32.c
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*
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* Description: Processing function for the floating-point transposed
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* direct form II Biquad cascade filter.
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*
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* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
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*
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* Version 1.0.10 2011/7/15
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* Big Endian support added and Merged M0 and M3/M4 Source code.
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*
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* Version 1.0.3 2010/11/29
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* Re-organized the CMSIS folders and updated documentation.
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*
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* Version 1.0.2 2010/11/11
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* Documentation updated.
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*
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* Version 1.0.1 2010/10/05
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* Production release and review comments incorporated.
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*
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* Version 1.0.0 2010/09/20
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* Production release and review comments incorporated
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*
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* Version 0.0.7 2010/06/10
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* Misra-C changes done
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* -------------------------------------------------------------------- */
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#include "arm_math.h"
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/**
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* @ingroup groupFilters
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*/
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/**
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* @defgroup BiquadCascadeDF2T Biquad Cascade IIR Filters Using a Direct Form II Transposed Structure
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*
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* This set of functions implements arbitrary order recursive (IIR) filters using a transposed direct form II structure.
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* The filters are implemented as a cascade of second order Biquad sections.
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* These functions provide a slight memory savings as compared to the direct form I Biquad filter functions.
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* Only floating-point data is supported.
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*
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* This function operate on blocks of input and output data and each call to the function
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* processes <code>blockSize</code> samples through the filter.
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* <code>pSrc</code> points to the array of input data and
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* <code>pDst</code> points to the array of output data.
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* Both arrays contain <code>blockSize</code> values.
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*
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* \par Algorithm
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* Each Biquad stage implements a second order filter using the difference equation:
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* <pre>
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* y[n] = b0 * x[n] + d1
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* d1 = b1 * x[n] + a1 * y[n] + d2
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* d2 = b2 * x[n] + a2 * y[n]
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* </pre>
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* where d1 and d2 represent the two state values.
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*
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* \par
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* A Biquad filter using a transposed Direct Form II structure is shown below.
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* \image html BiquadDF2Transposed.gif "Single transposed Direct Form II Biquad"
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* Coefficients <code>b0, b1, and b2 </code> multiply the input signal <code>x[n]</code> and are referred to as the feedforward coefficients.
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* Coefficients <code>a1</code> and <code>a2</code> multiply the output signal <code>y[n]</code> and are referred to as the feedback coefficients.
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* Pay careful attention to the sign of the feedback coefficients.
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* Some design tools flip the sign of the feedback coefficients:
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* <pre>
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* y[n] = b0 * x[n] + d1;
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* d1 = b1 * x[n] - a1 * y[n] + d2;
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* d2 = b2 * x[n] - a2 * y[n];
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* </pre>
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* In this case the feedback coefficients <code>a1</code> and <code>a2</code> must be negated when used with the CMSIS DSP Library.
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*
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* \par
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* Higher order filters are realized as a cascade of second order sections.
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* <code>numStages</code> refers to the number of second order stages used.
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* For example, an 8th order filter would be realized with <code>numStages=4</code> second order stages.
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* A 9th order filter would be realized with <code>numStages=5</code> second order stages with the
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* coefficients for one of the stages configured as a first order filter (<code>b2=0</code> and <code>a2=0</code>).
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*
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* \par
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* <code>pState</code> points to the state variable array.
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* Each Biquad stage has 2 state variables <code>d1</code> and <code>d2</code>.
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* The state variables are arranged in the <code>pState</code> array as:
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* <pre>
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* {d11, d12, d21, d22, ...}
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* </pre>
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* where <code>d1x</code> refers to the state variables for the first Biquad and
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* <code>d2x</code> refers to the state variables for the second Biquad.
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* The state array has a total length of <code>2*numStages</code> values.
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* The state variables are updated after each block of data is processed; the coefficients are untouched.
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*
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* \par
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* The CMSIS library contains Biquad filters in both Direct Form I and transposed Direct Form II.
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* The advantage of the Direct Form I structure is that it is numerically more robust for fixed-point data types.
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* That is why the Direct Form I structure supports Q15 and Q31 data types.
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* 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>.
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* Because of this, the CMSIS library only has a floating-point version of the Direct Form II Biquad.
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* 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.
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*
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* \par Instance Structure
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* The coefficients and state variables for a filter are stored together in an instance data structure.
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* A separate instance structure must be defined for each filter.
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* Coefficient arrays may be shared among several instances while state variable arrays cannot be shared.
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*
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* \par Init Functions
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* There is also an associated initialization function.
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* The initialization function performs following operations:
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* - Sets the values of the internal structure fields.
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* - Zeros out the values in the state buffer.
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*
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* \par
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* Use of the initialization function is optional.
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* However, if the initialization function is used, then the instance structure cannot be placed into a const data section.
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* To place an instance structure into a const data section, the instance structure must be manually initialized.
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* Set the values in the state buffer to zeros before static initialization.
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* For example, to statically initialize the instance structure use
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* <pre>
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* arm_biquad_cascade_df2T_instance_f32 S1 = {numStages, pState, pCoeffs};
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* </pre>
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* where <code>numStages</code> is the number of Biquad stages in the filter; <code>pState</code> is the address of the state buffer.
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* <code>pCoeffs</code> is the address of the coefficient buffer;
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*
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*/
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/**
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* @addtogroup BiquadCascadeDF2T
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* @{
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*/
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/**
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* @brief Processing function for the floating-point transposed direct form II Biquad cascade filter.
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* @param[in] *S points to an instance of the filter data structure.
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* @param[in] *pSrc points to the block of input data.
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* @param[out] *pDst points to the block of output data
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* @param[in] blockSize number of samples to process.
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* @return none.
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*/
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void arm_biquad_cascade_df2T_f32(
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const arm_biquad_cascade_df2T_instance_f32 * S,
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float32_t * pSrc,
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float32_t * pDst,
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uint32_t blockSize)
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{
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float32_t *pIn = pSrc; /* source pointer */
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float32_t *pOut = pDst; /* destination pointer */
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float32_t *pState = S->pState; /* State pointer */
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float32_t *pCoeffs = S->pCoeffs; /* coefficient pointer */
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float32_t acc0; /* Simulates the accumulator */
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float32_t b0, b1, b2, a1, a2; /* Filter coefficients */
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float32_t Xn; /* temporary input */
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float32_t d1, d2; /* state variables */
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uint32_t sample, stage = S->numStages; /* loop counters */
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#ifndef ARM_MATH_CM0
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/* Run the below code for Cortex-M4 and Cortex-M3 */
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do
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{
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/* Reading the coefficients */
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b0 = *pCoeffs++;
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b1 = *pCoeffs++;
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b2 = *pCoeffs++;
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a1 = *pCoeffs++;
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a2 = *pCoeffs++;
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/*Reading the state values */
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d1 = pState[0];
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d2 = pState[1];
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/* Apply loop unrolling and compute 4 output values simultaneously. */
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sample = blockSize >> 2u;
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/* First part of the processing with loop unrolling. Compute 4 outputs at a time.
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** a second loop below computes the remaining 1 to 3 samples. */
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while(sample > 0u)
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{
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/* Read the first input */
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Xn = *pIn++;
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/* y[n] = b0 * x[n] + d1 */
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acc0 = (b0 * Xn) + d1;
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/* Store the result in the accumulator in the destination buffer. */
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*pOut++ = acc0;
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/* Every time after the output is computed state should be updated. */
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/* d1 = b1 * x[n] + a1 * y[n] + d2 */
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d1 = ((b1 * Xn) + (a1 * acc0)) + d2;
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/* d2 = b2 * x[n] + a2 * y[n] */
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d2 = (b2 * Xn) + (a2 * acc0);
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/* Read the second input */
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Xn = *pIn++;
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/* y[n] = b0 * x[n] + d1 */
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acc0 = (b0 * Xn) + d1;
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/* Store the result in the accumulator in the destination buffer. */
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*pOut++ = acc0;
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/* Every time after the output is computed state should be updated. */
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/* d1 = b1 * x[n] + a1 * y[n] + d2 */
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d1 = ((b1 * Xn) + (a1 * acc0)) + d2;
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/* d2 = b2 * x[n] + a2 * y[n] */
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d2 = (b2 * Xn) + (a2 * acc0);
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/* Read the third input */
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Xn = *pIn++;
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/* y[n] = b0 * x[n] + d1 */
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acc0 = (b0 * Xn) + d1;
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/* Store the result in the accumulator in the destination buffer. */
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*pOut++ = acc0;
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/* Every time after the output is computed state should be updated. */
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/* d1 = b1 * x[n] + a1 * y[n] + d2 */
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d1 = ((b1 * Xn) + (a1 * acc0)) + d2;
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/* d2 = b2 * x[n] + a2 * y[n] */
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d2 = (b2 * Xn) + (a2 * acc0);
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/* Read the fourth input */
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Xn = *pIn++;
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/* y[n] = b0 * x[n] + d1 */
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acc0 = (b0 * Xn) + d1;
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/* Store the result in the accumulator in the destination buffer. */
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*pOut++ = acc0;
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/* Every time after the output is computed state should be updated. */
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/* d1 = b1 * x[n] + a1 * y[n] + d2 */
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d1 = (b1 * Xn) + (a1 * acc0) + d2;
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/* d2 = b2 * x[n] + a2 * y[n] */
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d2 = (b2 * Xn) + (a2 * acc0);
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/* decrement the loop counter */
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sample--;
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}
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/* If the blockSize is not a multiple of 4, compute any remaining output samples here.
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** No loop unrolling is used. */
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sample = blockSize & 0x3u;
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while(sample > 0u)
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{
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/* Read the input */
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Xn = *pIn++;
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/* y[n] = b0 * x[n] + d1 */
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acc0 = (b0 * Xn) + d1;
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/* Store the result in the accumulator in the destination buffer. */
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*pOut++ = acc0;
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/* Every time after the output is computed state should be updated. */
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/* d1 = b1 * x[n] + a1 * y[n] + d2 */
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d1 = ((b1 * Xn) + (a1 * acc0)) + d2;
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/* d2 = b2 * x[n] + a2 * y[n] */
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d2 = (b2 * Xn) + (a2 * acc0);
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/* decrement the loop counter */
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sample--;
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}
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/* Store the updated state variables back into the state array */
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*pState++ = d1;
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*pState++ = d2;
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/* The current stage input is given as the output to the next stage */
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pIn = pDst;
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/*Reset the output working pointer */
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pOut = pDst;
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/* decrement the loop counter */
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stage--;
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} while(stage > 0u);
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#else
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/* Run the below code for Cortex-M0 */
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do
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{
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/* Reading the coefficients */
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b0 = *pCoeffs++;
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b1 = *pCoeffs++;
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b2 = *pCoeffs++;
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a1 = *pCoeffs++;
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a2 = *pCoeffs++;
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/*Reading the state values */
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d1 = pState[0];
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d2 = pState[1];
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sample = blockSize;
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while(sample > 0u)
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{
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/* Read the input */
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Xn = *pIn++;
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/* y[n] = b0 * x[n] + d1 */
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acc0 = (b0 * Xn) + d1;
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/* Store the result in the accumulator in the destination buffer. */
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*pOut++ = acc0;
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/* Every time after the output is computed state should be updated. */
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/* d1 = b1 * x[n] + a1 * y[n] + d2 */
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d1 = ((b1 * Xn) + (a1 * acc0)) + d2;
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/* d2 = b2 * x[n] + a2 * y[n] */
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d2 = (b2 * Xn) + (a2 * acc0);
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/* decrement the loop counter */
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sample--;
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}
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/* Store the updated state variables back into the state array */
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*pState++ = d1;
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*pState++ = d2;
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/* The current stage input is given as the output to the next stage */
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pIn = pDst;
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/*Reset the output working pointer */
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pOut = pDst;
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/* decrement the loop counter */
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stage--;
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} while(stage > 0u);
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#endif /* #ifndef ARM_MATH_CM0 */
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}
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/**
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* @} end of BiquadCascadeDF2T group
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*/
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