| /* ---------------------------------------------------------------------- |
| * Copyright (C) 2010 ARM Limited. All rights reserved. |
| * |
| * $Date: 15. July 2011 |
| * $Revision: V1.0.10 |
| * |
| * 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 1.0.10 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 */ |
| |
| |
| pSrc[2u * fftLen] = pSrc[0]; |
| pSrc[(2u * fftLen) + 1u] = pSrc[1]; |
| |
| /* 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--; |
| } |
| |
| } |
