arm_biquad_cascade_df1_f32.c
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r71 | /* ---------------------------------------------------------------------- | |||
* Copyright (C) 2010 ARM Limited. All rights reserved. | ||||
* | ||||
* $Date: 15. July 2011 | ||||
* $Revision: V1.0.10 | ||||
* | ||||
* Project: CMSIS DSP Library | ||||
* Title: arm_biquad_cascade_df1_f32.c | ||||
* | ||||
* Description: Processing function for the | ||||
* floating-point Biquad cascade DirectFormI(DF1) 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 0.0.5 2010/04/26 | ||||
* incorporated review comments and updated with latest CMSIS layer | ||||
* | ||||
* Version 0.0.3 2010/03/10 | ||||
* Initial version | ||||
* -------------------------------------------------------------------- */ | ||||
#include "arm_math.h" | ||||
/** | ||||
* @ingroup groupFilters | ||||
*/ | ||||
/** | ||||
* @defgroup BiquadCascadeDF1 Biquad Cascade IIR Filters Using Direct Form I Structure | ||||
* | ||||
* This set of functions implements arbitrary order recursive (IIR) filters. | ||||
* The filters are implemented as a cascade of second order Biquad sections. | ||||
* The functions support Q15, Q31 and floating-point data types. | ||||
* Fast version of Q15 and Q31 also supported on CortexM4 and Cortex-M3. | ||||
* | ||||
* The functions 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] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] | ||||
* </pre> | ||||
* A Direct Form I algorithm is used with 5 coefficients and 4 state variables per stage. | ||||
* \image html Biquad.gif "Single Biquad filter stage" | ||||
* 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 use the difference equation | ||||
* <pre> | ||||
* y[n] = b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] - a1 * y[n-1] - a2 * y[n-2] | ||||
* </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. | ||||
* \image html BiquadCascade.gif "8th order filter using a cascade of Biquad 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 | ||||
* The <code>pState</code> points to state variables array. | ||||
* Each Biquad stage has 4 state variables <code>x[n-1], x[n-2], y[n-1],</code> and <code>y[n-2]</code>. | ||||
* The state variables are arranged in the <code>pState</code> array as: | ||||
* <pre> | ||||
* {x[n-1], x[n-2], y[n-1], y[n-2]} | ||||
* </pre> | ||||
* | ||||
* \par | ||||
* The 4 state variables for stage 1 are first, then the 4 state variables for stage 2, and so on. | ||||
* The state array has a total length of <code>4*numStages</code> values. | ||||
* The state variables are updated after each block of data is processed, the coefficients are untouched. | ||||
* | ||||
* \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. | ||||
* There are separate instance structure declarations for each of the 3 supported data types. | ||||
* | ||||
* \par Init Functions | ||||
* There is also an associated initialization function for each data type. | ||||
* 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. | ||||
* The code below statically initializes each of the 3 different data type filter instance structures | ||||
* <pre> | ||||
* arm_biquad_casd_df1_inst_f32 S1 = {numStages, pState, pCoeffs}; | ||||
* arm_biquad_casd_df1_inst_q15 S2 = {numStages, pState, pCoeffs, postShift}; | ||||
* arm_biquad_casd_df1_inst_q31 S3 = {numStages, pState, pCoeffs, postShift}; | ||||
* </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; <code>postShift</code> shift to be applied. | ||||
* | ||||
* \par Fixed-Point Behavior | ||||
* Care must be taken when using the Q15 and Q31 versions of the Biquad Cascade filter functions. | ||||
* Following issues must be considered: | ||||
* - Scaling of coefficients | ||||
* - Filter gain | ||||
* - Overflow and saturation | ||||
* | ||||
* \par | ||||
* <b>Scaling of coefficients: </b> | ||||
* Filter coefficients are represented as fractional values and | ||||
* coefficients are restricted to lie in the range <code>[-1 +1)</code>. | ||||
* The fixed-point functions have an additional scaling parameter <code>postShift</code> | ||||
* which allow the filter coefficients to exceed the range <code>[+1 -1)</code>. | ||||
* At the output of the filter's accumulator is a shift register which shifts the result by <code>postShift</code> bits. | ||||
* \image html BiquadPostshift.gif "Fixed-point Biquad with shift by postShift bits after accumulator" | ||||
* This essentially scales the filter coefficients by <code>2^postShift</code>. | ||||
* For example, to realize the coefficients | ||||
* <pre> | ||||
* {1.5, -0.8, 1.2, 1.6, -0.9} | ||||
* </pre> | ||||
* set the pCoeffs array to: | ||||
* <pre> | ||||
* {0.75, -0.4, 0.6, 0.8, -0.45} | ||||
* </pre> | ||||
* and set <code>postShift=1</code> | ||||
* | ||||
* \par | ||||
* <b>Filter gain: </b> | ||||
* The frequency response of a Biquad filter is a function of its coefficients. | ||||
* It is possible for the gain through the filter to exceed 1.0 meaning that the filter increases the amplitude of certain frequencies. | ||||
* 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. | ||||
* 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. | ||||
* | ||||
* \par | ||||
* <b>Overflow and saturation: </b> | ||||
* For Q15 and Q31 versions, it is described separately as part of the function specific documentation below. | ||||
*/ | ||||
/** | ||||
* @addtogroup BiquadCascadeDF1 | ||||
* @{ | ||||
*/ | ||||
/** | ||||
* @param[in] *S points to an instance of the floating-point Biquad cascade 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 per call. | ||||
* @return none. | ||||
* | ||||
*/ | ||||
void arm_biquad_cascade_df1_f32( | ||||
const arm_biquad_casd_df1_inst_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; /* pState pointer */ | ||||
float32_t *pCoeffs = S->pCoeffs; /* coefficient pointer */ | ||||
float32_t acc; /* Simulates the accumulator */ | ||||
float32_t b0, b1, b2, a1, a2; /* Filter coefficients */ | ||||
float32_t Xn1, Xn2, Yn1, Yn2; /* Filter pState variables */ | ||||
float32_t Xn; /* temporary input */ | ||||
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 pState values */ | ||||
Xn1 = pState[0]; | ||||
Xn2 = pState[1]; | ||||
Yn1 = pState[2]; | ||||
Yn2 = pState[3]; | ||||
/* Apply loop unrolling and compute 4 output values simultaneously. */ | ||||
/* The variable acc hold output values that are being computed: | ||||
* | ||||
* acc = b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] | ||||
* acc = b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] | ||||
* acc = b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] | ||||
* acc = b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] | ||||
*/ | ||||
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++; | ||||
/* acc = b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] */ | ||||
Yn2 = (b0 * Xn) + (b1 * Xn1) + (b2 * Xn2) + (a1 * Yn1) + (a2 * Yn2); | ||||
/* Store the result in the accumulator in the destination buffer. */ | ||||
*pOut++ = Yn2; | ||||
/* Every time after the output is computed state should be updated. */ | ||||
/* The states should be updated as: */ | ||||
/* Xn2 = Xn1 */ | ||||
/* Xn1 = Xn */ | ||||
/* Yn2 = Yn1 */ | ||||
/* Yn1 = acc */ | ||||
/* Read the second input */ | ||||
Xn2 = *pIn++; | ||||
/* acc = b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] */ | ||||
Yn1 = (b0 * Xn2) + (b1 * Xn) + (b2 * Xn1) + (a1 * Yn2) + (a2 * Yn1); | ||||
/* Store the result in the accumulator in the destination buffer. */ | ||||
*pOut++ = Yn1; | ||||
/* Every time after the output is computed state should be updated. */ | ||||
/* The states should be updated as: */ | ||||
/* Xn2 = Xn1 */ | ||||
/* Xn1 = Xn */ | ||||
/* Yn2 = Yn1 */ | ||||
/* Yn1 = acc */ | ||||
/* Read the third input */ | ||||
Xn1 = *pIn++; | ||||
/* acc = b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] */ | ||||
Yn2 = (b0 * Xn1) + (b1 * Xn2) + (b2 * Xn) + (a1 * Yn1) + (a2 * Yn2); | ||||
/* Store the result in the accumulator in the destination buffer. */ | ||||
*pOut++ = Yn2; | ||||
/* Every time after the output is computed state should be updated. */ | ||||
/* The states should be updated as: */ | ||||
/* Xn2 = Xn1 */ | ||||
/* Xn1 = Xn */ | ||||
/* Yn2 = Yn1 */ | ||||
/* Yn1 = acc */ | ||||
/* Read the forth input */ | ||||
Xn = *pIn++; | ||||
/* acc = b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] */ | ||||
Yn1 = (b0 * Xn) + (b1 * Xn1) + (b2 * Xn2) + (a1 * Yn2) + (a2 * Yn1); | ||||
/* Store the result in the accumulator in the destination buffer. */ | ||||
*pOut++ = Yn1; | ||||
/* Every time after the output is computed state should be updated. */ | ||||
/* The states should be updated as: */ | ||||
/* Xn2 = Xn1 */ | ||||
/* Xn1 = Xn */ | ||||
/* Yn2 = Yn1 */ | ||||
/* Yn1 = acc */ | ||||
Xn2 = Xn1; | ||||
Xn1 = Xn; | ||||
/* 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++; | ||||
/* acc = b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] */ | ||||
acc = (b0 * Xn) + (b1 * Xn1) + (b2 * Xn2) + (a1 * Yn1) + (a2 * Yn2); | ||||
/* Store the result in the accumulator in the destination buffer. */ | ||||
*pOut++ = acc; | ||||
/* Every time after the output is computed state should be updated. */ | ||||
/* The states should be updated as: */ | ||||
/* Xn2 = Xn1 */ | ||||
/* Xn1 = Xn */ | ||||
/* Yn2 = Yn1 */ | ||||
/* Yn1 = acc */ | ||||
Xn2 = Xn1; | ||||
Xn1 = Xn; | ||||
Yn2 = Yn1; | ||||
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 */ | ||||
pIn = pDst; | ||||
/* Reset the output 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 pState values */ | ||||
Xn1 = pState[0]; | ||||
Xn2 = pState[1]; | ||||
Yn1 = pState[2]; | ||||
Yn2 = pState[3]; | ||||
/* The variables acc holds the output value that is computed: | ||||
* acc = b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] | ||||
*/ | ||||
sample = blockSize; | ||||
while(sample > 0u) | ||||
{ | ||||
/* Read the input */ | ||||
Xn = *pIn++; | ||||
/* acc = b0 * x[n] + b1 * x[n-1] + b2 * x[n-2] + a1 * y[n-1] + a2 * y[n-2] */ | ||||
acc = (b0 * Xn) + (b1 * Xn1) + (b2 * Xn2) + (a1 * Yn1) + (a2 * Yn2); | ||||
/* Store the result in the accumulator in the destination buffer. */ | ||||
*pOut++ = acc; | ||||
/* Every time after the output is computed state should be updated. */ | ||||
/* The states should be updated as: */ | ||||
/* Xn2 = Xn1 */ | ||||
/* Xn1 = Xn */ | ||||
/* Yn2 = Yn1 */ | ||||
/* Yn1 = acc */ | ||||
Xn2 = Xn1; | ||||
Xn1 = Xn; | ||||
Yn2 = Yn1; | ||||
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 */ | ||||
pIn = pDst; | ||||
/* Reset the output pointer */ | ||||
pOut = pDst; | ||||
/* decrement the loop counter */ | ||||
stage--; | ||||
} while(stage > 0u); | ||||
#endif /* #ifndef ARM_MATH_CM0 */ | ||||
} | ||||
/** | ||||
* @} end of BiquadCascadeDF1 group | ||||
*/ | ||||