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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_rfft_f32.c
-*
-* Description: RFFT & RIFFT Floating point process function
-*
-* 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 groupTransforms
- */
-
-/**
- * @defgroup RFFT_RIFFT Real FFT Functions
- *
- * \par
- * Complex FFT/IFFT typically assumes complex input and output. However many applications use real valued data in time domain.
- * Real FFT/IFFT efficiently process real valued sequences with the advantage of requirement of low memory and with less complexity.
- *
- * \par
- * This set of functions implements Real Fast Fourier Transforms(RFFT) and Real Inverse Fast Fourier Transform(RIFFT)
- * for Q15, Q31, and floating-point data types.
- *
- *
- * \par Algorithm:
- *
- * <b>Real Fast Fourier Transform:</b>
- * \par
- * Real FFT of N-point is calculated using CFFT of N/2-point and Split RFFT process as shown below figure.
- * \par
- * \image html RFFT.gif "Real Fast Fourier Transform"
- * \par
- * The RFFT functions operate on blocks of input and output data and each call to the function processes
- * <code>fftLenR</code> samples through the transform. <code>pSrc</code> points to input array containing <code>fftLenR</code> values.
- * <code>pDst</code> points to output array containing <code>2*fftLenR</code> values. \n
- * Input for real FFT is in the order of
- * <pre>{real[0], real[1], real[2], real[3], ..}</pre>
- * Output for real FFT is complex and are in the order of
- * <pre>{real(0), imag(0), real(1), imag(1), ...}</pre>
- *
- * <b>Real Inverse Fast Fourier Transform:</b>
- * \par
- * Real IFFT of N-point is calculated using Split RIFFT process and CFFT of N/2-point as shown below figure.
- * \par
- * \image html RIFFT.gif "Real Inverse Fast Fourier Transform"
- * \par
- * The RIFFT functions operate on blocks of input and output data and each call to the function processes
- * <code>2*fftLenR</code> samples through the transform. <code>pSrc</code> points to input array containing <code>2*fftLenR</code> values.
- * <code>pDst</code> points to output array containing <code>fftLenR</code> values. \n
- * Input for real IFFT is complex and are in the order of
- * <pre>{real(0), imag(0), real(1), imag(1), ...}</pre>
- * Output for real IFFT is real and in the order of
- * <pre>{real[0], real[1], real[2], real[3], ..}</pre>
- *
- * \par Lengths supported by the transform:
- * \par
- * Real FFT/IFFT supports the lengths [128, 512, 2048], as it internally uses CFFT/CIFFT.
- *
- * \par Instance Structure
- * A separate instance structure must be defined for each Instance but the twiddle factors can be reused.
- * There are separate instance structure declarations for each of the 3 supported data types.
- *
- * \par Initialization Functions
- * There is also an associated initialization function for each data type.
- * The initialization function performs the following operations:
- * - Sets the values of the internal structure fields.
- * - Initializes twiddle factor tables.
- * - Initializes CFFT data structure fields.
- * \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.
- * Manually initialize the instance structure as follows:
- * <pre>
- *arm_rfft_instance_f32 S = {fftLenReal, fftLenBy2, ifftFlagR, bitReverseFlagR, twidCoefRModifier, pTwiddleAReal, pTwiddleBReal, pCfft};
- *arm_rfft_instance_q31 S = {fftLenReal, fftLenBy2, ifftFlagR, bitReverseFlagR, twidCoefRModifier, pTwiddleAReal, pTwiddleBReal, pCfft};
- *arm_rfft_instance_q15 S = {fftLenReal, fftLenBy2, ifftFlagR, bitReverseFlagR, twidCoefRModifier, pTwiddleAReal, pTwiddleBReal, pCfft};
- * </pre>
- * where <code>fftLenReal</code> length of RFFT/RIFFT; <code>fftLenBy2</code> length of CFFT/CIFFT.
- * <code>ifftFlagR</code> Flag for selection of RFFT or RIFFT(Set ifftFlagR to calculate RIFFT otherwise calculates RFFT);
- * <code>bitReverseFlagR</code> Flag for selection of output order(Set bitReverseFlagR to output in normal order otherwise output in bit reversed order);
- * <code>twidCoefRModifier</code> modifier for twiddle factor table which supports 128, 512, 2048 RFFT lengths with same table;
- * <code>pTwiddleAReal</code>points to A array of twiddle coefficients; <code>pTwiddleBReal</code>points to B array of twiddle coefficients;
- * <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
- * static initialization of cfft structure.
- *
- * \par Fixed-Point Behavior
- * Care must be taken when using the fixed-point versions of the RFFT/RIFFT function.
- * Refer to the function specific documentation below for usage guidelines.
- */
-
-/*--------------------------------------------------------------------
- * Internal functions prototypes
- *--------------------------------------------------------------------*/
-
-void arm_split_rfft_f32(
- float32_t * pSrc,
- uint32_t fftLen,
- float32_t * pATable,
- float32_t * pBTable,
- float32_t * pDst,
- uint32_t modifier);
-void arm_split_rifft_f32(
- float32_t * pSrc,
- uint32_t fftLen,
- float32_t * pATable,
- float32_t * pBTable,
- float32_t * pDst,
- uint32_t modifier);
-
-/**
- * @addtogroup RFFT_RIFFT
- * @{
- */
-
-/**
- * @brief Processing function for the floating-point RFFT/RIFFT.
- * @param[in] *S points to an instance of the floating-point RFFT/RIFFT structure.
- * @param[in] *pSrc points to the input buffer.
- * @param[out] *pDst points to the output buffer.
- * @return none.
- */
-
-void arm_rfft_f32(
- const arm_rfft_instance_f32 * S,
- float32_t * pSrc,
- float32_t * pDst)
-{
- const arm_cfft_radix4_instance_f32 *S_CFFT = S->pCfft;
-
-
- /* Calculation of Real IFFT of input */
- if(S->ifftFlagR == 1u)
- {
- /* Real IFFT core process */
- arm_split_rifft_f32(pSrc, S->fftLenBy2, S->pTwiddleAReal,
- S->pTwiddleBReal, pDst, S->twidCoefRModifier);
-
-
- /* Complex radix-4 IFFT process */
- arm_radix4_butterfly_inverse_f32(pDst, S_CFFT->fftLen,
- S_CFFT->pTwiddle,
- S_CFFT->twidCoefModifier,
- S_CFFT->onebyfftLen);
-
- /* Bit reversal process */
- if(S->bitReverseFlagR == 1u)
- {
- arm_bitreversal_f32(pDst, S_CFFT->fftLen,
- S_CFFT->bitRevFactor, S_CFFT->pBitRevTable);
- }
- }
- else
- {
-
- /* Calculation of RFFT of input */
-
- /* Complex radix-4 FFT process */
- arm_radix4_butterfly_f32(pSrc, S_CFFT->fftLen,
- S_CFFT->pTwiddle, S_CFFT->twidCoefModifier);
-
- /* Bit reversal process */
- if(S->bitReverseFlagR == 1u)
- {
- arm_bitreversal_f32(pSrc, S_CFFT->fftLen,
- S_CFFT->bitRevFactor, S_CFFT->pBitRevTable);
- }
-
-
- /* Real FFT core process */
- arm_split_rfft_f32(pSrc, S->fftLenBy2, S->pTwiddleAReal,
- S->pTwiddleBReal, pDst, S->twidCoefRModifier);
- }
-
-}
-
-/**
- * @} end of RFFT_RIFFT group
- */
-
-/**
- * @brief Core Real FFT process
- * @param[in] *pSrc points to the input buffer.
- * @param[in] fftLen length of FFT.
- * @param[in] *pATable points to the twiddle Coef A buffer.
- * @param[in] *pBTable points to the twiddle Coef B buffer.
- * @param[out] *pDst points to the output buffer.
- * @param[in] modifier twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table.
- * @return none.
- */
-
-void arm_split_rfft_f32(
- float32_t * pSrc,
- uint32_t fftLen,
- float32_t * pATable,
- float32_t * pBTable,
- float32_t * pDst,
- uint32_t modifier)
-{
- uint32_t i; /* Loop Counter */
- float32_t outR, outI; /* Temporary variables for output */
- float32_t *pCoefA, *pCoefB; /* Temporary pointers for twiddle factors */
- float32_t CoefA1, CoefA2, CoefB1; /* Temporary variables for twiddle coefficients */
- float32_t *pDst1 = &pDst[2], *pDst2 = &pDst[(4u * fftLen) - 1u]; /* temp pointers for output buffer */
- float32_t *pSrc1 = &pSrc[2], *pSrc2 = &pSrc[(2u * fftLen) - 1u]; /* temp pointers for input buffer */
-
- /* Init coefficient pointers */
- pCoefA = &pATable[modifier * 2u];
- pCoefB = &pBTable[modifier * 2u];
-
- i = fftLen - 1u;
-
- while(i > 0u)
- {
- /*
- outR = (pSrc[2 * i] * pATable[2 * i] - pSrc[2 * i + 1] * pATable[2 * i + 1]
- + pSrc[2 * n - 2 * i] * pBTable[2 * i] +
- pSrc[2 * n - 2 * i + 1] * pBTable[2 * i + 1]);
- */
-
- /* outI = (pIn[2 * i + 1] * pATable[2 * i] + pIn[2 * i] * pATable[2 * i + 1] +
- pIn[2 * n - 2 * i] * pBTable[2 * i + 1] -
- pIn[2 * n - 2 * i + 1] * pBTable[2 * i]); */
-
- /* read pATable[2 * i] */
- CoefA1 = *pCoefA++;
- /* pATable[2 * i + 1] */
- CoefA2 = *pCoefA;
-
- /* pSrc[2 * i] * pATable[2 * i] */
- outR = *pSrc1 * CoefA1;
- /* pSrc[2 * i] * CoefA2 */
- outI = *pSrc1++ * CoefA2;
-
- /* (pSrc[2 * i + 1] + pSrc[2 * fftLen - 2 * i + 1]) * CoefA2 */
- outR -= (*pSrc1 + *pSrc2) * CoefA2;
- /* pSrc[2 * i + 1] * CoefA1 */
- outI += *pSrc1++ * CoefA1;
-
- CoefB1 = *pCoefB;
-
- /* pSrc[2 * fftLen - 2 * i + 1] * CoefB1 */
- outI -= *pSrc2-- * CoefB1;
- /* pSrc[2 * fftLen - 2 * i] * CoefA2 */
- outI -= *pSrc2 * CoefA2;
-
- /* pSrc[2 * fftLen - 2 * i] * CoefB1 */
- outR += *pSrc2-- * CoefB1;
-
- /* write output */
- *pDst1++ = outR;
- *pDst1++ = outI;
-
- /* write complex conjugate output */
- *pDst2-- = -outI;
- *pDst2-- = outR;
-
- /* update coefficient pointer */
- pCoefB = pCoefB + (modifier * 2u);
- pCoefA = pCoefA + ((modifier * 2u) - 1u);
-
- i--;
-
- }
-
- pDst[2u * fftLen] = pSrc[0] - pSrc[1];
- pDst[(2u * fftLen) + 1u] = 0.0f;
-
- pDst[0] = pSrc[0] + pSrc[1];
- pDst[1] = 0.0f;
-
-}
-
-
-/**
- * @brief Core Real IFFT process
- * @param[in] *pSrc points to the input buffer.
- * @param[in] fftLen length of FFT.
- * @param[in] *pATable points to the twiddle Coef A buffer.
- * @param[in] *pBTable points to the twiddle Coef B buffer.
- * @param[out] *pDst points to the output buffer.
- * @param[in] modifier twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table.
- * @return none.
- */
-
-void arm_split_rifft_f32(
- float32_t * pSrc,
- uint32_t fftLen,
- float32_t * pATable,
- float32_t * pBTable,
- float32_t * pDst,
- uint32_t modifier)
-{
- float32_t outR, outI; /* Temporary variables for output */
- float32_t *pCoefA, *pCoefB; /* Temporary pointers for twiddle factors */
- float32_t CoefA1, CoefA2, CoefB1; /* Temporary variables for twiddle coefficients */
- float32_t *pSrc1 = &pSrc[0], *pSrc2 = &pSrc[(2u * fftLen) + 1u];
-
- pCoefA = &pATable[0];
- pCoefB = &pBTable[0];
-
- while(fftLen > 0u)
- {
- /*
- outR = (pIn[2 * i] * pATable[2 * i] + pIn[2 * i + 1] * pATable[2 * i + 1] +
- pIn[2 * n - 2 * i] * pBTable[2 * i] -
- pIn[2 * n - 2 * i + 1] * pBTable[2 * i + 1]);
-
- outI = (pIn[2 * i + 1] * pATable[2 * i] - pIn[2 * i] * pATable[2 * i + 1] -
- pIn[2 * n - 2 * i] * pBTable[2 * i + 1] -
- pIn[2 * n - 2 * i + 1] * pBTable[2 * i]);
-
- */
-
- CoefA1 = *pCoefA++;
- CoefA2 = *pCoefA;
-
- /* outR = (pSrc[2 * i] * CoefA1 */
- outR = *pSrc1 * CoefA1;
-
- /* - pSrc[2 * i] * CoefA2 */
- outI = -(*pSrc1++) * CoefA2;
-
- /* (pSrc[2 * i + 1] + pSrc[2 * fftLen - 2 * i + 1]) * CoefA2 */
- outR += (*pSrc1 + *pSrc2) * CoefA2;
-
- /* pSrc[2 * i + 1] * CoefA1 */
- outI += (*pSrc1++) * CoefA1;
-
- CoefB1 = *pCoefB;
-
- /* - pSrc[2 * fftLen - 2 * i + 1] * CoefB1 */
- outI -= *pSrc2-- * CoefB1;
-
- /* pSrc[2 * fftLen - 2 * i] * CoefB1 */
- outR += *pSrc2 * CoefB1;
-
- /* pSrc[2 * fftLen - 2 * i] * CoefA2 */
- outI += *pSrc2-- * CoefA2;
-
- /* write output */
- *pDst++ = outR;
- *pDst++ = outI;
-
- /* update coefficient pointer */
- pCoefB = pCoefB + (modifier * 2u);
- pCoefA = pCoefA + ((modifier * 2u) - 1u);
-
- /* Decrement loop count */
- fftLen--;
- }
-
-}