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-/* ----------------------------------------------------------------------
-* Copyright (C) 2010 ARM Limited. All rights reserved.
-*
-* $Date: 15. February 2012
-* $Revision: V1.1.0
-*
-* 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 1.1.0 2012/02/15
-* Updated with more optimizations, bug fixes and minor API changes.
-*
-* 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; /* 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
-
- float32_t Xn1, Xn2; /* Input State variables */
- float32_t acc1; /* accumulator */
-
-
-
- /* 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)
- {
-
- /* y[n] = b0 * x[n] + d1 */
- /* d1 = b1 * x[n] + a1 * y[n] + d2 */
- /* d2 = b2 * x[n] + a2 * y[n] */
-
- /* Read the first input */
- Xn1 = *pIn++;
-
- /* y[n] = b0 * x[n] + d1 */
- acc0 = (b0 * Xn1) + d1;
-
- /* d1 = b1 * x[n] + d2 */
- d1 = (b1 * Xn1) + d2;
-
- /* d2 = b2 * x[n] */
- d2 = (b2 * Xn1);
-
- /* Read the second input */
- Xn2 = *pIn++;
-
- /* d1 = b1 * x[n] + a1 * y[n] */
- d1 = (a1 * acc0) + d1;
-
- /* Store the result in the accumulator in the destination buffer. */
- *pOut++ = acc0;
-
- d2 = (a2 * acc0) + d2;
-
- /* y[n] = b0 * x[n] + d1 */
- acc1 = (b0 * Xn2) + d1;
-
- /* Read the third input */
- Xn1 = *pIn++;
-
- d1 = (b1 * Xn2) + d2;
-
- d2 = (b2 * Xn2);
-
- /* Store the result in the accumulator in the destination buffer. */
- *pOut++ = acc1;
-
- d1 = (a1 * acc1) + d1;
-
- d2 = (a2 * acc1) + d2;
-
- /* y[n] = b0 * x[n] + d1 */
- acc0 = (b0 * Xn1) + d1;
-
- d1 = (b1 * Xn1) + d2;
-
- d2 = (b2 * Xn1);
-
- /* Read the fourth input */
- Xn2 = *pIn++;
-
- d1 = (a1 * acc0) + d1;
-
- /* Store the result in the accumulator in the destination buffer. */
- *pOut++ = acc0;
-
- d2 = (a2 * acc0) + d2;
-
- /* y[n] = b0 * x[n] + d1 */
- acc1 = (b0 * Xn2) + d1;
-
- d1 = (b1 * Xn2) + d2;
-
- d2 = (b2 * Xn2);
-
- /* Store the result in the accumulator in the destination buffer. */
- *pOut++ = acc1;
-
- d1 = (a1 * acc1) + d1;
-
- d2 = (a2 * acc1) + d2;
-
- /* 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
- */