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/* ----------------------------------------------------------------------
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* Copyright (C) 2010 ARM Limited. All rights reserved.
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*
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* $Date: 15. July 2011
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* $Revision: V1.0.10
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*
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* Project: CMSIS DSP Library
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* Title: arm_rfft_f32.c
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*
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* Description: RFFT & RIFFT Floating point process function
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*
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* Target Processor: Cortex-M4/Cortex-M3/Cortex-M0
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*
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* Version 1.0.10 2011/7/15
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* Big Endian support added and Merged M0 and M3/M4 Source code.
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*
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* Version 1.0.3 2010/11/29
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* Re-organized the CMSIS folders and updated documentation.
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*
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* Version 1.0.2 2010/11/11
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* Documentation updated.
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*
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* Version 1.0.1 2010/10/05
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* Production release and review comments incorporated.
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*
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* Version 1.0.0 2010/09/20
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* Production release and review comments incorporated.
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*
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* Version 0.0.7 2010/06/10
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* Misra-C changes done
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* -------------------------------------------------------------------- */
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#include "arm_math.h"
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/**
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* @ingroup groupTransforms
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*/
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/**
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* @defgroup RFFT_RIFFT Real FFT Functions
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*
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* \par
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* Complex FFT/IFFT typically assumes complex input and output. However many applications use real valued data in time domain.
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* Real FFT/IFFT efficiently process real valued sequences with the advantage of requirement of low memory and with less complexity.
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*
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* \par
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* This set of functions implements Real Fast Fourier Transforms(RFFT) and Real Inverse Fast Fourier Transform(RIFFT)
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* for Q15, Q31, and floating-point data types.
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*
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*
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* \par Algorithm:
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*
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* <b>Real Fast Fourier Transform:</b>
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* \par
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* Real FFT of N-point is calculated using CFFT of N/2-point and Split RFFT process as shown below figure.
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* \par
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* \image html RFFT.gif "Real Fast Fourier Transform"
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* \par
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* The RFFT functions operate on blocks of input and output data and each call to the function processes
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* <code>fftLenR</code> samples through the transform. <code>pSrc</code> points to input array containing <code>fftLenR</code> values.
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* <code>pDst</code> points to output array containing <code>2*fftLenR</code> values. \n
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* Input for real FFT is in the order of
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* <pre>{real[0], real[1], real[2], real[3], ..}</pre>
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* Output for real FFT is complex and are in the order of
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* <pre>{real(0), imag(0), real(1), imag(1), ...}</pre>
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*
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* <b>Real Inverse Fast Fourier Transform:</b>
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* \par
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* Real IFFT of N-point is calculated using Split RIFFT process and CFFT of N/2-point as shown below figure.
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* \par
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* \image html RIFFT.gif "Real Inverse Fast Fourier Transform"
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* \par
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* The RIFFT functions operate on blocks of input and output data and each call to the function processes
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* <code>2*fftLenR</code> samples through the transform. <code>pSrc</code> points to input array containing <code>2*fftLenR</code> values.
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* <code>pDst</code> points to output array containing <code>fftLenR</code> values. \n
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* Input for real IFFT is complex and are in the order of
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* <pre>{real(0), imag(0), real(1), imag(1), ...}</pre>
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* Output for real IFFT is real and in the order of
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* <pre>{real[0], real[1], real[2], real[3], ..}</pre>
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*
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* \par Lengths supported by the transform:
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* \par
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* Real FFT/IFFT supports the lengths [128, 512, 2048], as it internally uses CFFT/CIFFT.
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*
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* \par Instance Structure
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* A separate instance structure must be defined for each Instance but the twiddle factors can be reused.
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* There are separate instance structure declarations for each of the 3 supported data types.
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*
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* \par Initialization Functions
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* There is also an associated initialization function for each data type.
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* The initialization function performs the following operations:
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* - Sets the values of the internal structure fields.
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* - Initializes twiddle factor tables.
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* - Initializes CFFT data structure fields.
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* \par
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* Use of the initialization function is optional.
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* However, if the initialization function is used, then the instance structure cannot be placed into a const data section.
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* To place an instance structure into a const data section, the instance structure must be manually initialized.
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* Manually initialize the instance structure as follows:
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* <pre>
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*arm_rfft_instance_f32 S = {fftLenReal, fftLenBy2, ifftFlagR, bitReverseFlagR, twidCoefRModifier, pTwiddleAReal, pTwiddleBReal, pCfft};
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*arm_rfft_instance_q31 S = {fftLenReal, fftLenBy2, ifftFlagR, bitReverseFlagR, twidCoefRModifier, pTwiddleAReal, pTwiddleBReal, pCfft};
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*arm_rfft_instance_q15 S = {fftLenReal, fftLenBy2, ifftFlagR, bitReverseFlagR, twidCoefRModifier, pTwiddleAReal, pTwiddleBReal, pCfft};
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* </pre>
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* where <code>fftLenReal</code> length of RFFT/RIFFT; <code>fftLenBy2</code> length of CFFT/CIFFT.
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* <code>ifftFlagR</code> Flag for selection of RFFT or RIFFT(Set ifftFlagR to calculate RIFFT otherwise calculates RFFT);
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* <code>bitReverseFlagR</code> Flag for selection of output order(Set bitReverseFlagR to output in normal order otherwise output in bit reversed order);
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* <code>twidCoefRModifier</code> modifier for twiddle factor table which supports 128, 512, 2048 RFFT lengths with same table;
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* <code>pTwiddleAReal</code>points to A array of twiddle coefficients; <code>pTwiddleBReal</code>points to B array of twiddle coefficients;
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* <code>pCfft</code> points to the CFFT Instance structure. The CFFT structure also needs to be initialized, refer to arm_cfft_radix4_f32() for details regarding
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* static initialization of cfft structure.
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*
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* \par Fixed-Point Behavior
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* Care must be taken when using the fixed-point versions of the RFFT/RIFFT function.
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* Refer to the function specific documentation below for usage guidelines.
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*/
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/*--------------------------------------------------------------------
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* Internal functions prototypes
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*--------------------------------------------------------------------*/
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void arm_split_rfft_f32(
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float32_t * pSrc,
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uint32_t fftLen,
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float32_t * pATable,
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float32_t * pBTable,
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float32_t * pDst,
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uint32_t modifier);
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void arm_split_rifft_f32(
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float32_t * pSrc,
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uint32_t fftLen,
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float32_t * pATable,
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float32_t * pBTable,
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float32_t * pDst,
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uint32_t modifier);
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/**
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* @addtogroup RFFT_RIFFT
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* @{
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*/
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/**
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* @brief Processing function for the floating-point RFFT/RIFFT.
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* @param[in] *S points to an instance of the floating-point RFFT/RIFFT structure.
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* @param[in] *pSrc points to the input buffer.
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* @param[out] *pDst points to the output buffer.
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* @return none.
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*/
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void arm_rfft_f32(
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const arm_rfft_instance_f32 * S,
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float32_t * pSrc,
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float32_t * pDst)
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{
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const arm_cfft_radix4_instance_f32 *S_CFFT = S->pCfft;
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/* Calculation of Real IFFT of input */
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if(S->ifftFlagR == 1u)
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{
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/* Real IFFT core process */
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arm_split_rifft_f32(pSrc, S->fftLenBy2, S->pTwiddleAReal,
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S->pTwiddleBReal, pDst, S->twidCoefRModifier);
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/* Complex radix-4 IFFT process */
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arm_radix4_butterfly_inverse_f32(pDst, S_CFFT->fftLen,
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S_CFFT->pTwiddle,
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S_CFFT->twidCoefModifier,
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S_CFFT->onebyfftLen);
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/* Bit reversal process */
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if(S->bitReverseFlagR == 1u)
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{
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arm_bitreversal_f32(pDst, S_CFFT->fftLen,
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S_CFFT->bitRevFactor, S_CFFT->pBitRevTable);
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}
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}
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else
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{
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/* Calculation of RFFT of input */
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/* Complex radix-4 FFT process */
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arm_radix4_butterfly_f32(pSrc, S_CFFT->fftLen,
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S_CFFT->pTwiddle, S_CFFT->twidCoefModifier);
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/* Bit reversal process */
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if(S->bitReverseFlagR == 1u)
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{
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arm_bitreversal_f32(pSrc, S_CFFT->fftLen,
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S_CFFT->bitRevFactor, S_CFFT->pBitRevTable);
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}
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/* Real FFT core process */
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arm_split_rfft_f32(pSrc, S->fftLenBy2, S->pTwiddleAReal,
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S->pTwiddleBReal, pDst, S->twidCoefRModifier);
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}
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}
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/**
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* @} end of RFFT_RIFFT group
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*/
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/**
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* @brief Core Real FFT process
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* @param[in] *pSrc points to the input buffer.
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* @param[in] fftLen length of FFT.
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* @param[in] *pATable points to the twiddle Coef A buffer.
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* @param[in] *pBTable points to the twiddle Coef B buffer.
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* @param[out] *pDst points to the output buffer.
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* @param[in] modifier twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table.
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* @return none.
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*/
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void arm_split_rfft_f32(
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float32_t * pSrc,
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uint32_t fftLen,
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float32_t * pATable,
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float32_t * pBTable,
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float32_t * pDst,
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uint32_t modifier)
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{
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uint32_t i; /* Loop Counter */
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float32_t outR, outI; /* Temporary variables for output */
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float32_t *pCoefA, *pCoefB; /* Temporary pointers for twiddle factors */
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float32_t CoefA1, CoefA2, CoefB1; /* Temporary variables for twiddle coefficients */
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float32_t *pDst1 = &pDst[2], *pDst2 = &pDst[(4u * fftLen) - 1u]; /* temp pointers for output buffer */
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float32_t *pSrc1 = &pSrc[2], *pSrc2 = &pSrc[(2u * fftLen) - 1u]; /* temp pointers for input buffer */
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pSrc[2u * fftLen] = pSrc[0];
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pSrc[(2u * fftLen) + 1u] = pSrc[1];
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/* Init coefficient pointers */
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pCoefA = &pATable[modifier * 2u];
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pCoefB = &pBTable[modifier * 2u];
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i = fftLen - 1u;
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while(i > 0u)
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{
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/*
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outR = (pSrc[2 * i] * pATable[2 * i] - pSrc[2 * i + 1] * pATable[2 * i + 1]
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+ pSrc[2 * n - 2 * i] * pBTable[2 * i] +
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pSrc[2 * n - 2 * i + 1] * pBTable[2 * i + 1]);
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*/
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/* outI = (pIn[2 * i + 1] * pATable[2 * i] + pIn[2 * i] * pATable[2 * i + 1] +
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pIn[2 * n - 2 * i] * pBTable[2 * i + 1] -
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pIn[2 * n - 2 * i + 1] * pBTable[2 * i]); */
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/* read pATable[2 * i] */
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CoefA1 = *pCoefA++;
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/* pATable[2 * i + 1] */
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CoefA2 = *pCoefA;
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/* pSrc[2 * i] * pATable[2 * i] */
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outR = *pSrc1 * CoefA1;
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/* pSrc[2 * i] * CoefA2 */
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outI = *pSrc1++ * CoefA2;
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/* (pSrc[2 * i + 1] + pSrc[2 * fftLen - 2 * i + 1]) * CoefA2 */
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outR -= (*pSrc1 + *pSrc2) * CoefA2;
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/* pSrc[2 * i + 1] * CoefA1 */
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outI += *pSrc1++ * CoefA1;
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CoefB1 = *pCoefB;
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/* pSrc[2 * fftLen - 2 * i + 1] * CoefB1 */
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outI -= *pSrc2-- * CoefB1;
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/* pSrc[2 * fftLen - 2 * i] * CoefA2 */
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outI -= *pSrc2 * CoefA2;
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/* pSrc[2 * fftLen - 2 * i] * CoefB1 */
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outR += *pSrc2-- * CoefB1;
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/* write output */
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*pDst1++ = outR;
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*pDst1++ = outI;
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/* write complex conjugate output */
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*pDst2-- = -outI;
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*pDst2-- = outR;
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/* update coefficient pointer */
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pCoefB = pCoefB + (modifier * 2u);
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pCoefA = pCoefA + ((modifier * 2u) - 1u);
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i--;
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}
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pDst[2u * fftLen] = pSrc[0] - pSrc[1];
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pDst[(2u * fftLen) + 1u] = 0.0f;
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pDst[0] = pSrc[0] + pSrc[1];
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pDst[1] = 0.0f;
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}
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/**
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* @brief Core Real IFFT process
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* @param[in] *pSrc points to the input buffer.
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* @param[in] fftLen length of FFT.
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* @param[in] *pATable points to the twiddle Coef A buffer.
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* @param[in] *pBTable points to the twiddle Coef B buffer.
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* @param[out] *pDst points to the output buffer.
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* @param[in] modifier twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table.
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* @return none.
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*/
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void arm_split_rifft_f32(
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float32_t * pSrc,
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uint32_t fftLen,
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float32_t * pATable,
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float32_t * pBTable,
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float32_t * pDst,
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uint32_t modifier)
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{
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float32_t outR, outI; /* Temporary variables for output */
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float32_t *pCoefA, *pCoefB; /* Temporary pointers for twiddle factors */
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float32_t CoefA1, CoefA2, CoefB1; /* Temporary variables for twiddle coefficients */
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float32_t *pSrc1 = &pSrc[0], *pSrc2 = &pSrc[(2u * fftLen) + 1u];
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pCoefA = &pATable[0];
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pCoefB = &pBTable[0];
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while(fftLen > 0u)
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{
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/*
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outR = (pIn[2 * i] * pATable[2 * i] + pIn[2 * i + 1] * pATable[2 * i + 1] +
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pIn[2 * n - 2 * i] * pBTable[2 * i] -
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pIn[2 * n - 2 * i + 1] * pBTable[2 * i + 1]);
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outI = (pIn[2 * i + 1] * pATable[2 * i] - pIn[2 * i] * pATable[2 * i + 1] -
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pIn[2 * n - 2 * i] * pBTable[2 * i + 1] -
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pIn[2 * n - 2 * i + 1] * pBTable[2 * i]);
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*/
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CoefA1 = *pCoefA++;
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CoefA2 = *pCoefA;
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/* outR = (pSrc[2 * i] * CoefA1 */
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outR = *pSrc1 * CoefA1;
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/* - pSrc[2 * i] * CoefA2 */
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outI = -(*pSrc1++) * CoefA2;
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/* (pSrc[2 * i + 1] + pSrc[2 * fftLen - 2 * i + 1]) * CoefA2 */
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outR += (*pSrc1 + *pSrc2) * CoefA2;
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/* pSrc[2 * i + 1] * CoefA1 */
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outI += (*pSrc1++) * CoefA1;
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CoefB1 = *pCoefB;
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/* - pSrc[2 * fftLen - 2 * i + 1] * CoefB1 */
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outI -= *pSrc2-- * CoefB1;
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/* pSrc[2 * fftLen - 2 * i] * CoefB1 */
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outR += *pSrc2 * CoefB1;
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/* pSrc[2 * fftLen - 2 * i] * CoefA2 */
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outI += *pSrc2-- * CoefA2;
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/* write output */
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*pDst++ = outR;
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*pDst++ = outI;
|
|
|
|
|
|
/* update coefficient pointer */
|
|
|
pCoefB = pCoefB + (modifier * 2u);
|
|
|
pCoefA = pCoefA + ((modifier * 2u) - 1u);
|
|
|
|
|
|
/* Decrement loop count */
|
|
|
fftLen--;
|
|
|
}
|
|
|
|
|
|
}
|
|
|
|
