arm_biquad_cascade_df2T_f32.c
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r41 | /* ---------------------------------------------------------------------- | ||
* Copyright (C) 2010 ARM Limited. All rights reserved. | ||||
* | ||||
* $Date: 15. July 2011 | ||||
* $Revision: V1.0.10 | ||||
* | ||||
* 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 | ||||
* | ||||
* Version 1.0.10 2011/7/15 | ||||
* Big Endian support added and Merged M0 and M3/M4 Source code. | ||||
* | ||||
* Version 1.0.3 2010/11/29 | ||||
* Re-organized the CMSIS folders and updated documentation. | ||||
* | ||||
* Version 1.0.2 2010/11/11 | ||||
* Documentation updated. | ||||
* | ||||
* Version 1.0.1 2010/10/05 | ||||
* Production release and review comments incorporated. | ||||
* | ||||
* Version 1.0.0 2010/09/20 | ||||
* Production release and review comments incorporated | ||||
* | ||||
* Version 0.0.7 2010/06/10 | ||||
* Misra-C changes done | ||||
* -------------------------------------------------------------------- */ | ||||
#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. | ||||
* | ||||
* \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. | ||||
*/ | ||||
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 acc0; /* Simulates the accumulator */ | ||||
float32_t b0, b1, b2, a1, a2; /* Filter coefficients */ | ||||
float32_t Xn; /* temporary input */ | ||||
float32_t d1, d2; /* state variables */ | ||||
uint32_t sample, stage = S->numStages; /* loop counters */ | ||||
#ifndef ARM_MATH_CM0 | ||||
/* 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) | ||||
{ | ||||
/* Read the first input */ | ||||
Xn = *pIn++; | ||||
/* y[n] = b0 * x[n] + d1 */ | ||||
acc0 = (b0 * Xn) + d1; | ||||
/* Store the result in the accumulator in the destination buffer. */ | ||||
*pOut++ = acc0; | ||||
/* Every time after the output is computed state should be updated. */ | ||||
/* d1 = b1 * x[n] + a1 * y[n] + d2 */ | ||||
d1 = ((b1 * Xn) + (a1 * acc0)) + d2; | ||||
/* d2 = b2 * x[n] + a2 * y[n] */ | ||||
d2 = (b2 * Xn) + (a2 * acc0); | ||||
/* Read the second input */ | ||||
Xn = *pIn++; | ||||
/* y[n] = b0 * x[n] + d1 */ | ||||
acc0 = (b0 * Xn) + d1; | ||||
/* Store the result in the accumulator in the destination buffer. */ | ||||
*pOut++ = acc0; | ||||
/* Every time after the output is computed state should be updated. */ | ||||
/* d1 = b1 * x[n] + a1 * y[n] + d2 */ | ||||
d1 = ((b1 * Xn) + (a1 * acc0)) + d2; | ||||
/* d2 = b2 * x[n] + a2 * y[n] */ | ||||
d2 = (b2 * Xn) + (a2 * acc0); | ||||
/* Read the third input */ | ||||
Xn = *pIn++; | ||||
/* y[n] = b0 * x[n] + d1 */ | ||||
acc0 = (b0 * Xn) + d1; | ||||
/* Store the result in the accumulator in the destination buffer. */ | ||||
*pOut++ = acc0; | ||||
/* Every time after the output is computed state should be updated. */ | ||||
/* d1 = b1 * x[n] + a1 * y[n] + d2 */ | ||||
d1 = ((b1 * Xn) + (a1 * acc0)) + d2; | ||||
/* d2 = b2 * x[n] + a2 * y[n] */ | ||||
d2 = (b2 * Xn) + (a2 * acc0); | ||||
/* Read the fourth input */ | ||||
Xn = *pIn++; | ||||
/* y[n] = b0 * x[n] + d1 */ | ||||
acc0 = (b0 * Xn) + d1; | ||||
/* Store the result in the accumulator in the destination buffer. */ | ||||
*pOut++ = acc0; | ||||
/* Every time after the output is computed state should be updated. */ | ||||
/* d1 = b1 * x[n] + a1 * y[n] + d2 */ | ||||
d1 = (b1 * Xn) + (a1 * acc0) + d2; | ||||
/* d2 = b2 * x[n] + a2 * y[n] */ | ||||
d2 = (b2 * Xn) + (a2 * acc0); | ||||
/* decrement the loop counter */ | ||||
sample--; | ||||
} | ||||
/* If the blockSize 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 */ | ||||
Xn = *pIn++; | ||||
/* y[n] = b0 * x[n] + d1 */ | ||||
acc0 = (b0 * Xn) + d1; | ||||
/* Store the result in the accumulator in the destination buffer. */ | ||||
*pOut++ = acc0; | ||||
/* Every time after the output is computed state should be updated. */ | ||||
/* d1 = b1 * x[n] + a1 * y[n] + d2 */ | ||||
d1 = ((b1 * Xn) + (a1 * acc0)) + d2; | ||||
/* d2 = b2 * x[n] + a2 * y[n] */ | ||||
d2 = (b2 * Xn) + (a2 * acc0); | ||||
/* 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); | ||||
#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 */ | ||||
Xn = *pIn++; | ||||
/* y[n] = b0 * x[n] + d1 */ | ||||
acc0 = (b0 * Xn) + d1; | ||||
/* Store the result in the accumulator in the destination buffer. */ | ||||
*pOut++ = acc0; | ||||
/* Every time after the output is computed state should be updated. */ | ||||
/* d1 = b1 * x[n] + a1 * y[n] + d2 */ | ||||
d1 = ((b1 * Xn) + (a1 * acc0)) + d2; | ||||
/* d2 = b2 * x[n] + a2 * y[n] */ | ||||
d2 = (b2 * Xn) + (a2 * acc0); | ||||
/* 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 */ | ||||
} | ||||
/** | ||||
* @} end of BiquadCascadeDF2T group | ||||
*/ | ||||