File content as of revision 2:da51fb522205:

/* ----------------------------------------------------------------------    
* 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--;
  }

}