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/* ----------------------------------------------------------------------
* 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
*/
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