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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_df1_f32.c
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*
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* Description: Processing function for the
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* floating-point Biquad cascade DirectFormI(DF1) 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 0.0.5 2010/04/26
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* incorporated review comments and updated with latest CMSIS layer
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*
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* Version 0.0.3 2010/03/10
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* Initial version
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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 BiquadCascadeDF1 Biquad Cascade IIR Filters Using Direct Form I Structure
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*
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* This set of functions implements arbitrary order recursive (IIR) filters.
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* The filters are implemented as a cascade of second order Biquad sections.
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* The functions support Q15, Q31 and floating-point data types.
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* Fast version of Q15 and Q31 also supported on CortexM4 and Cortex-M3.
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*
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* The functions 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] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2]
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* </pre>
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* A Direct Form I algorithm is used with 5 coefficients and 4 state variables per stage.
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* \image html Biquad.gif "Single Biquad filter stage"
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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 use the difference equation
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* <pre>
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* y[n] = b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] - a1 * y[n-1] - a2 * y[n-2]
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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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* \image html BiquadCascade.gif "8th order filter using a cascade of Biquad stages"
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* 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>).
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*
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* \par
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* The <code>pState</code> points to state variables array.
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* Each Biquad stage has 4 state variables <code>x[n-1], x[n-2], y[n-1],</code> and <code>y[n-2]</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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* {x[n-1], x[n-2], y[n-1], y[n-2]}
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* </pre>
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*
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* \par
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* The 4 state variables for stage 1 are first, then the 4 state variables for stage 2, and so on.
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* The state array has a total length of <code>4*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 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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* There are separate instance structure declarations for each of the 3 supported data types.
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*
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* \par Init Functions
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* There is also an associated initialization function for each data type.
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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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* The code below statically initializes each of the 3 different data type filter instance structures
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* <pre>
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* arm_biquad_casd_df1_inst_f32 S1 = {numStages, pState, pCoeffs};
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* arm_biquad_casd_df1_inst_q15 S2 = {numStages, pState, pCoeffs, postShift};
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* arm_biquad_casd_df1_inst_q31 S3 = {numStages, pState, pCoeffs, postShift};
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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; <code>postShift</code> shift to be applied.
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*
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* \par Fixed-Point Behavior
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* Care must be taken when using the Q15 and Q31 versions of the Biquad Cascade filter functions.
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* Following issues must be considered:
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* - Scaling of coefficients
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* - Filter gain
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* - Overflow and saturation
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*
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* \par
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* <b>Scaling of coefficients: </b>
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* Filter coefficients are represented as fractional values and
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* coefficients are restricted to lie in the range <code>[-1 +1)</code>.
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* The fixed-point functions have an additional scaling parameter <code>postShift</code>
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* which allow the filter coefficients to exceed the range <code>[+1 -1)</code>.
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* At the output of the filter's accumulator is a shift register which shifts the result by <code>postShift</code> bits.
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* \image html BiquadPostshift.gif "Fixed-point Biquad with shift by postShift bits after accumulator"
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* This essentially scales the filter coefficients by <code>2^postShift</code>.
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* For example, to realize the coefficients
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* <pre>
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* {1.5, -0.8, 1.2, 1.6, -0.9}
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* </pre>
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* set the pCoeffs array to:
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* <pre>
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* {0.75, -0.4, 0.6, 0.8, -0.45}
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* </pre>
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* and set <code>postShift=1</code>
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*
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* \par
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* <b>Filter gain: </b>
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* The frequency response of a Biquad filter is a function of its coefficients.
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* It is possible for the gain through the filter to exceed 1.0 meaning that the filter increases the amplitude of certain frequencies.
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* 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.
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* 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.
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*
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* \par
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* <b>Overflow and saturation: </b>
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* For Q15 and Q31 versions, it is described separately as part of the function specific documentation below.
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*/
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/**
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* @addtogroup BiquadCascadeDF1
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* @{
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*/
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/**
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* @param[in] *S points to an instance of the floating-point Biquad cascade 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 per call.
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* @return none.
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*
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*/
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void arm_biquad_cascade_df1_f32(
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const arm_biquad_casd_df1_inst_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; /* pState pointer */
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float32_t *pCoeffs = S->pCoeffs; /* coefficient pointer */
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float32_t acc; /* Simulates the accumulator */
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float32_t b0, b1, b2, a1, a2; /* Filter coefficients */
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float32_t Xn1, Xn2, Yn1, Yn2; /* Filter pState variables */
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float32_t Xn; /* temporary input */
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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 pState values */
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Xn1 = pState[0];
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Xn2 = pState[1];
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Yn1 = pState[2];
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Yn2 = pState[3];
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/* Apply loop unrolling and compute 4 output values simultaneously. */
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/* The variable acc hold output values that are being computed:
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*
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* acc = b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2]
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* acc = b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2]
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* acc = b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2]
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* acc = b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2]
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*/
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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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/* acc = b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] */
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Yn2 = (b0 * Xn) + (b1 * Xn1) + (b2 * Xn2) + (a1 * Yn1) + (a2 * Yn2);
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/* Store the result in the accumulator in the destination buffer. */
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*pOut++ = Yn2;
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/* Every time after the output is computed state should be updated. */
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/* The states should be updated as: */
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/* Xn2 = Xn1 */
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/* Xn1 = Xn */
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/* Yn2 = Yn1 */
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/* Yn1 = acc */
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/* Read the second input */
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Xn2 = *pIn++;
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/* acc = b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] */
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Yn1 = (b0 * Xn2) + (b1 * Xn) + (b2 * Xn1) + (a1 * Yn2) + (a2 * Yn1);
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/* Store the result in the accumulator in the destination buffer. */
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*pOut++ = Yn1;
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/* Every time after the output is computed state should be updated. */
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/* The states should be updated as: */
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/* Xn2 = Xn1 */
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/* Xn1 = Xn */
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/* Yn2 = Yn1 */
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/* Yn1 = acc */
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/* Read the third input */
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Xn1 = *pIn++;
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/* acc = b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] */
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Yn2 = (b0 * Xn1) + (b1 * Xn2) + (b2 * Xn) + (a1 * Yn1) + (a2 * Yn2);
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/* Store the result in the accumulator in the destination buffer. */
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*pOut++ = Yn2;
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/* Every time after the output is computed state should be updated. */
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/* The states should be updated as: */
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/* Xn2 = Xn1 */
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/* Xn1 = Xn */
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/* Yn2 = Yn1 */
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/* Yn1 = acc */
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/* Read the forth input */
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Xn = *pIn++;
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/* acc = b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] */
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Yn1 = (b0 * Xn) + (b1 * Xn1) + (b2 * Xn2) + (a1 * Yn2) + (a2 * Yn1);
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/* Store the result in the accumulator in the destination buffer. */
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*pOut++ = Yn1;
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/* Every time after the output is computed state should be updated. */
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/* The states should be updated as: */
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/* Xn2 = Xn1 */
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/* Xn1 = Xn */
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/* Yn2 = Yn1 */
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/* Yn1 = acc */
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Xn2 = Xn1;
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Xn1 = Xn;
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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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/* acc = b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] */
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acc = (b0 * Xn) + (b1 * Xn1) + (b2 * Xn2) + (a1 * Yn1) + (a2 * Yn2);
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/* Store the result in the accumulator in the destination buffer. */
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*pOut++ = acc;
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/* Every time after the output is computed state should be updated. */
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/* The states should be updated as: */
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/* Xn2 = Xn1 */
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/* Xn1 = Xn */
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/* Yn2 = Yn1 */
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/* Yn1 = acc */
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Xn2 = Xn1;
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Xn1 = Xn;
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Yn2 = Yn1;
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Yn1 = acc;
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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 pState array */
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*pState++ = Xn1;
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*pState++ = Xn2;
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*pState++ = Yn1;
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*pState++ = Yn2;
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/* The first stage goes from the input buffer to the output buffer. */
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/* Subsequent numStages occur in-place in the output buffer */
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pIn = pDst;
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/* Reset the output 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 pState values */
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Xn1 = pState[0];
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Xn2 = pState[1];
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Yn1 = pState[2];
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Yn2 = pState[3];
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/* The variables acc holds the output value that is computed:
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* acc = b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2]
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*/
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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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/* acc = b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] */
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acc = (b0 * Xn) + (b1 * Xn1) + (b2 * Xn2) + (a1 * Yn1) + (a2 * Yn2);
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|
|
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/* Store the result in the accumulator in the destination buffer. */
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|
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*pOut++ = acc;
|
|
|
|
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|
/* Every time after the output is computed state should be updated. */
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|
|
/* The states should be updated as: */
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|
/* Xn2 = Xn1 */
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/* Xn1 = Xn */
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/* Yn2 = Yn1 */
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|
/* Yn1 = acc */
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|
Xn2 = Xn1;
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Xn1 = Xn;
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|
Yn2 = Yn1;
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Yn1 = acc;
|
|
|
|
|
|
/* decrement the 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 */
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|
|
pIn = pDst;
|
|
|
|
|
|
/* Reset the output pointer */
|
|
|
pOut = pDst;
|
|
|
|
|
|
/* decrement the loop counter */
|
|
|
stage--;
|
|
|
|
|
|
} while(stage > 0u);
|
|
|
|
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|
#endif /* #ifndef ARM_MATH_CM0 */
|
|
|
|
|
|
}
|
|
|
|
|
|
|
|
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/**
|
|
|
* @} end of BiquadCascadeDF1 group
|
|
|
*/
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|
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|
