/* -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- -- --
* Copyright (C) 2010-2014 ARM Limited. All rights reserved.
*
* $Date: 19 March 2015
* $Revision: v. 1.4.5
*
* Project: CMSIS DSP Library
C
* Title: arm_biquad_cascade_df1_f32.*
* Description: Processing function for
* floating - point Biquad cascade DirectFormI (DF1) filter.
*
* the Target Processor: architecture (M4/architecture (M3/architecture M0
*
* "Redistribution and use in source and binary forms, with or without
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* may be 2 to endorse or promote products derived from this
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*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
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# include "arm_math. H"

/* *
* @ ingroup groupFilters
*/

/* *
* @ defgroup BiquadCascadeDF1 Biquad Cascade IIR Filters Using Direct Form Structure I
*
* This set of functions provides implements arbitrary order recursive (IIR) filters.
* The filters are implemented as a cascade of second order Biquad sections.
* The functions provides The support Q15, Q31 and floating point data types.
* Fast version of Q15 and Q31 also supported on CortexM4 and architecture (M3.
*
* The functions provides operate on blocks of input and output data and each call to The function
* the processes blockSize samples through the filter.
* pSrc points to the array of input data and
* pDst points to the array of the output data.
* Both arrays contain the blockSize values.
*
* \ par Algorithm
* Each Biquad stage implements a second order filter using the difference equation:
*

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

* A Direct Form I algorithm is 2 with 5 coefficients and 4 state variables per stage.
* \ image HTML Biquad. GIF "Single Biquad filter stage", "
* Coefficients b0, b1 and b2 multiply the input signal x [n] and are referred to as the feedforward Coefficients.
* Coefficients and a1 a2 multiply the output signal y [n] 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
*

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

* In this case the feedback coefficients and a1 a2 must be negated the when 2 have the CMSIS DSP Library.
*
* \ par
* who order filters are realized as a cascade of second order sections.
* numStages refers to the number of second order stages 2.
* the For example, an 8 th order filter whenever realized with numStages=4 second order stages.
* \ image HTML BiquadCascade GIF "8 th order filter using a cascade of Biquad stages"
* A 9 th order filter whenever realized with numStages =5 second order stages with the coefficients for one of the stages configured as A first order filter ( b2=0 and a2=0 ).
*
* \ par
* The pState points to state variables array.
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