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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_cfft_radix4_f32.c
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*
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* Description: Radix-4 Decimation in Frequency CFFT & CIFFT Floating point processing function
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*
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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 0.0.5 2010/04/26
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* incorporated review comments and updated with latest CMSIS layer
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*
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* Version 0.0.3 2010/03/10
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* Initial version
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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 CFFT_CIFFT Complex FFT Functions
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*
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* \par
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* Complex Fast Fourier Transform(CFFT) and Complex Inverse Fast Fourier Transform(CIFFT) is an efficient algorithm to compute Discrete Fourier Transform(DFT) and Inverse Discrete Fourier Transform(IDFT).
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* Computational complexity of CFFT reduces drastically when compared to DFT.
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* \par
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* This set of functions implements CFFT/CIFFT
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* for Q15, Q31, and floating-point data types. The functions operates on in-place buffer which uses same buffer for input and output.
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* Complex input is stored in input buffer in an interleaved fashion.
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*
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* \par
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* The functions operate on blocks of input and output data and each call to the function processes
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* <code>2*fftLen</code> samples through the transform. <code>pSrc</code> points to In-place arrays containing <code>2*fftLen</code> values.
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* \par
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* The <code>pSrc</code> points to the array of in-place buffer of size <code>2*fftLen</code> and inputs and outputs are stored in an interleaved fashion as shown below.
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* <pre> {real[0], imag[0], real[1], imag[1],..} </pre>
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*
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* \par Lengths supported by the transform:
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* \par
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* Internally, the function utilize a radix-4 decimation in frequency(DIF) algorithm
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* and the size of the FFT supported are of the lengths [16, 64, 256, 1024].
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*
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*
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* \par Algorithm:
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*
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* <b>Complex Fast Fourier Transform:</b>
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* \par
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* Input real and imaginary data:
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* <pre>
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* x(n) = xa + j * ya
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* x(n+N/4 ) = xb + j * yb
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* x(n+N/2 ) = xc + j * yc
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* x(n+3N 4) = xd + j * yd
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* </pre>
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* where N is length of FFT
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* \par
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* Output real and imaginary data:
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* <pre>
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* X(4r) = xa'+ j * ya'
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* X(4r+1) = xb'+ j * yb'
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* X(4r+2) = xc'+ j * yc'
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* X(4r+3) = xd'+ j * yd'
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* </pre>
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* \par
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* Twiddle factors for radix-4 FFT:
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* <pre>
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* Wn = co1 + j * (- si1)
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* W2n = co2 + j * (- si2)
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* W3n = co3 + j * (- si3)
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* </pre>
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*
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* \par
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* \image html CFFT.gif "Radix-4 Decimation-in Frequency Complex Fast Fourier Transform"
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*
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* \par
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* Output from Radix-4 CFFT Results in Digit reversal order. Interchange middle two branches of every butterfly results in Bit reversed output.
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* \par
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* <b> Butterfly CFFT equations:</b>
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* <pre>
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* xa' = xa + xb + xc + xd
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* ya' = ya + yb + yc + yd
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* xc' = (xa+yb-xc-yd)* co1 + (ya-xb-yc+xd)* (si1)
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* yc' = (ya-xb-yc+xd)* co1 - (xa+yb-xc-yd)* (si1)
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* xb' = (xa-xb+xc-xd)* co2 + (ya-yb+yc-yd)* (si2)
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* yb' = (ya-yb+yc-yd)* co2 - (xa-xb+xc-xd)* (si2)
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* xd' = (xa-yb-xc+yd)* co3 + (ya+xb-yc-xd)* (si3)
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* yd' = (ya+xb-yc-xd)* co3 - (xa-yb-xc+yd)* (si3)
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* </pre>
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*
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*
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* <b>Complex Inverse Fast Fourier Transform:</b>
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* \par
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* CIFFT uses same twiddle factor table as CFFT with modifications in the design equation as shown below.
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*
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* \par
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* <b> Modified Butterfly CIFFT equations:</b>
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* <pre>
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* xa' = xa + xb + xc + xd
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* ya' = ya + yb + yc + yd
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* xc' = (xa-yb-xc+yd)* co1 - (ya+xb-yc-xd)* (si1)
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* yc' = (ya+xb-yc-xd)* co1 + (xa-yb-xc+yd)* (si1)
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* xb' = (xa-xb+xc-xd)* co2 - (ya-yb+yc-yd)* (si2)
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* yb' = (ya-yb+yc-yd)* co2 + (xa-xb+xc-xd)* (si2)
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* xd' = (xa+yb-xc-yd)* co3 - (ya-xb-yc+xd)* (si3)
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* yd' = (ya-xb-yc+xd)* co3 + (xa+yb-xc-yd)* (si3)
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* </pre>
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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 and bit reversal tables 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 table and bit reversal table pointers
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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_cfft_radix4_instance_f32 S = {fftLen, ifftFlag, bitReverseFlag, pTwiddle, pBitRevTable, twidCoefModifier, bitRevFactor, onebyfftLen};
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*arm_cfft_radix4_instance_q31 S = {fftLen, ifftFlag, bitReverseFlag, pTwiddle, pBitRevTable, twidCoefModifier, bitRevFactor};
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*arm_cfft_radix4_instance_q15 S = {fftLen, ifftFlag, bitReverseFlag, pTwiddle, pBitRevTable, twidCoefModifier, bitRevFactor};
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* </pre>
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* \par
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* where <code>fftLen</code> length of CFFT/CIFFT; <code>ifftFlag</code> Flag for selection of CFFT or CIFFT(Set ifftFlag to calculate CIFFT otherwise calculates CFFT);
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* <code>bitReverseFlag</code> Flag for selection of output order(Set bitReverseFlag to output in normal order otherwise output in bit reversed order);
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* <code>pTwiddle</code>points to array of twiddle coefficients; <code>pBitRevTable</code> points to the array of bit reversal table.
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* <code>twidCoefModifier</code> modifier for twiddle factor table which supports all FFT lengths with same table;
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* <code>pBitRevTable</code> modifier for bit reversal table which supports all FFT lengths with same table.
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* <code>onebyfftLen</code> value of 1/fftLen to calculate CIFFT;
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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 CFFT/CIFFT 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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* @addtogroup CFFT_CIFFT
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* @{
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*/
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/**
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* @details
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* @brief Processing function for the floating-point CFFT/CIFFT.
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* @param[in] *S points to an instance of the floating-point CFFT/CIFFT structure.
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* @param[in, out] *pSrc points to the complex data buffer of size <code>2*fftLen</code>. Processing occurs in-place.
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* @return none.
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*/
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void arm_cfft_radix4_f32(
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const arm_cfft_radix4_instance_f32 * S,
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float32_t * pSrc)
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{
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if(S->ifftFlag == 1u)
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{
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/* Complex IFFT radix-4 */
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arm_radix4_butterfly_inverse_f32(pSrc, S->fftLen, S->pTwiddle,
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S->twidCoefModifier, S->onebyfftLen);
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}
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else
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{
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/* Complex FFT radix-4 */
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arm_radix4_butterfly_f32(pSrc, S->fftLen, S->pTwiddle,
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S->twidCoefModifier);
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}
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if(S->bitReverseFlag == 1u)
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{
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/* Bit Reversal */
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arm_bitreversal_f32(pSrc, S->fftLen, S->bitRevFactor, S->pBitRevTable);
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}
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}
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/**
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* @} end of CFFT_CIFFT group
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*/
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/* ----------------------------------------------------------------------
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** Internal helper function used by the FFTs
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** ------------------------------------------------------------------- */
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/*
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* @brief Core function for the floating-point CFFT butterfly process.
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* @param[in, out] *pSrc points to the in-place buffer of floating-point data type.
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* @param[in] fftLen length of the FFT.
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* @param[in] *pCoef points to the twiddle coefficient buffer.
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* @param[in] twidCoefModifier 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_radix4_butterfly_f32(
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float32_t * pSrc,
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uint16_t fftLen,
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float32_t * pCoef,
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uint16_t twidCoefModifier)
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{
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float32_t co1, co2, co3, si1, si2, si3;
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float32_t t1, t2, r1, r2, s1, s2;
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uint32_t ia1, ia2, ia3;
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uint32_t i0, i1, i2, i3;
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uint32_t n1, n2, j, k;
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#ifndef ARM_MATH_CM0
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/* Run the below code for Cortex-M4 and Cortex-M3 */
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/* Initializations for the first stage */
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n2 = fftLen;
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n1 = n2;
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/* n2 = fftLen/4 */
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n2 >>= 2u;
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i0 = 0u;
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ia1 = 0u;
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j = n2;
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/* Calculation of first stage */
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do
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{
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/* index calculation for the input as, */
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/* pSrc[i0 + 0], pSrc[i0 + fftLen/4], pSrc[i0 + fftLen/2], pSrc[i0 + 3fftLen/4] */
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i1 = i0 + n2;
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i2 = i1 + n2;
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i3 = i2 + n2;
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/* Butterfly implementation */
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/* xa + xc */
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r1 = pSrc[(2u * i0)] + pSrc[(2u * i2)];
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/* xa - xc */
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r2 = pSrc[2u * i0] - pSrc[2u * i2];
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/* ya + yc */
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s1 = pSrc[(2u * i0) + 1u] + pSrc[(2u * i2) + 1u];
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/* ya - yc */
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s2 = pSrc[(2u * i0) + 1u] - pSrc[(2u * i2) + 1u];
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/* xb + xd */
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t1 = pSrc[2u * i1] + pSrc[2u * i3];
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/* xa' = xa + xb + xc + xd */
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pSrc[2u * i0] = r1 + t1;
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/* (xa + xc) - (xb + xd) */
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r1 = r1 - t1;
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/* yb + yd */
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t2 = pSrc[(2u * i1) + 1u] + pSrc[(2u * i3) + 1u];
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/* ya' = ya + yb + yc + yd */
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pSrc[(2u * i0) + 1u] = s1 + t2;
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/* (ya + yc) - (yb + yd) */
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s1 = s1 - t2;
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/* yb - yd */
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t1 = pSrc[(2u * i1) + 1u] - pSrc[(2u * i3) + 1u];
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/* xb - xd */
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t2 = pSrc[2u * i1] - pSrc[2u * i3];
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/* index calculation for the coefficients */
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ia2 = ia1 + ia1;
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co2 = pCoef[ia2 * 2u];
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si2 = pCoef[(ia2 * 2u) + 1u];
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/* xc' = (xa-xb+xc-xd)co2 + (ya-yb+yc-yd)(si2) */
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pSrc[2u * i1] = (r1 * co2) + (s1 * si2);
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/* yc' = (ya-yb+yc-yd)co2 - (xa-xb+xc-xd)(si2) */
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pSrc[(2u * i1) + 1u] = (s1 * co2) - (r1 * si2);
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/* (xa - xc) + (yb - yd) */
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r1 = r2 + t1;
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/* (xa - xc) - (yb - yd) */
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r2 = r2 - t1;
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/* (ya - yc) - (xb - xd) */
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s1 = s2 - t2;
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/* (ya - yc) + (xb - xd) */
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s2 = s2 + t2;
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co1 = pCoef[ia1 * 2u];
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si1 = pCoef[(ia1 * 2u) + 1u];
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/* xb' = (xa+yb-xc-yd)co1 + (ya-xb-yc+xd)(si1) */
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pSrc[2u * i2] = (r1 * co1) + (s1 * si1);
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/* yb' = (ya-xb-yc+xd)co1 - (xa+yb-xc-yd)(si1) */
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pSrc[(2u * i2) + 1u] = (s1 * co1) - (r1 * si1);
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/* index calculation for the coefficients */
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ia3 = ia2 + ia1;
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co3 = pCoef[ia3 * 2u];
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si3 = pCoef[(ia3 * 2u) + 1u];
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/* xd' = (xa-yb-xc+yd)co3 + (ya+xb-yc-xd)(si3) */
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pSrc[2u * i3] = (r2 * co3) + (s2 * si3);
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/* yd' = (ya+xb-yc-xd)co3 - (xa-yb-xc+yd)(si3) */
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pSrc[(2u * i3) + 1u] = (s2 * co3) - (r2 * si3);
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/* Twiddle coefficients index modifier */
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ia1 = ia1 + twidCoefModifier;
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/* Updating input index */
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i0 = i0 + 1u;
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}
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while(--j);
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twidCoefModifier <<= 2u;
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/* Calculation of second stage to excluding last stage */
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for (k = fftLen / 4; k > 4u; k >>= 2u)
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{
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/* Initializations for the first stage */
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n1 = n2;
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n2 >>= 2u;
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ia1 = 0u;
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/* Calculation of first stage */
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for (j = 0u; j <= (n2 - 1u); j++)
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{
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/* index calculation for the coefficients */
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ia2 = ia1 + ia1;
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ia3 = ia2 + ia1;
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co1 = pCoef[ia1 * 2u];
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si1 = pCoef[(ia1 * 2u) + 1u];
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co2 = pCoef[ia2 * 2u];
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si2 = pCoef[(ia2 * 2u) + 1u];
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co3 = pCoef[ia3 * 2u];
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si3 = pCoef[(ia3 * 2u) + 1u];
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/* Twiddle coefficients index modifier */
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ia1 = ia1 + twidCoefModifier;
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for (i0 = j; i0 < fftLen; i0 += n1)
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{
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/* index calculation for the input as, */
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|
|
/* pSrc[i0 + 0], pSrc[i0 + fftLen/4], pSrc[i0 + fftLen/2], pSrc[i0 + 3fftLen/4] */
|
|
|
i1 = i0 + n2;
|
|
|
i2 = i1 + n2;
|
|
|
i3 = i2 + n2;
|
|
|
|
|
|
/* xa + xc */
|
|
|
r1 = pSrc[(2u * i0)] + pSrc[(2u * i2)];
|
|
|
|
|
|
/* xa - xc */
|
|
|
r2 = pSrc[(2u * i0)] - pSrc[(2u * i2)];
|
|
|
|
|
|
/* ya + yc */
|
|
|
s1 = pSrc[(2u * i0) + 1u] + pSrc[(2u * i2) + 1u];
|
|
|
|
|
|
/* ya - yc */
|
|
|
s2 = pSrc[(2u * i0) + 1u] - pSrc[(2u * i2) + 1u];
|
|
|
|
|
|
/* xb + xd */
|
|
|
t1 = pSrc[2u * i1] + pSrc[2u * i3];
|
|
|
|
|
|
/* xa' = xa + xb + xc + xd */
|
|
|
pSrc[2u * i0] = r1 + t1;
|
|
|
|
|
|
/* xa + xc -(xb + xd) */
|
|
|
r1 = r1 - t1;
|
|
|
|
|
|
/* yb + yd */
|
|
|
t2 = pSrc[(2u * i1) + 1u] + pSrc[(2u * i3) + 1u];
|
|
|
|
|
|
/* ya' = ya + yb + yc + yd */
|
|
|
pSrc[(2u * i0) + 1u] = s1 + t2;
|
|
|
|
|
|
/* (ya + yc) - (yb + yd) */
|
|
|
s1 = s1 - t2;
|
|
|
|
|
|
/* (yb - yd) */
|
|
|
t1 = pSrc[(2u * i1) + 1u] - pSrc[(2u * i3) + 1u];
|
|
|
|
|
|
/* (xb - xd) */
|
|
|
t2 = pSrc[2u * i1] - pSrc[2u * i3];
|
|
|
|
|
|
/* xc' = (xa-xb+xc-xd)co2 + (ya-yb+yc-yd)(si2) */
|
|
|
pSrc[2u * i1] = (r1 * co2) + (s1 * si2);
|
|
|
|
|
|
/* yc' = (ya-yb+yc-yd)co2 - (xa-xb+xc-xd)(si2) */
|
|
|
pSrc[(2u * i1) + 1u] = (s1 * co2) - (r1 * si2);
|
|
|
|
|
|
/* (xa - xc) + (yb - yd) */
|
|
|
r1 = r2 + t1;
|
|
|
|
|
|
/* (xa - xc) - (yb - yd) */
|
|
|
r2 = r2 - t1;
|
|
|
|
|
|
/* (ya - yc) - (xb - xd) */
|
|
|
s1 = s2 - t2;
|
|
|
|
|
|
/* (ya - yc) + (xb - xd) */
|
|
|
s2 = s2 + t2;
|
|
|
|
|
|
/* xb' = (xa+yb-xc-yd)co1 + (ya-xb-yc+xd)(si1) */
|
|
|
pSrc[2u * i2] = (r1 * co1) + (s1 * si1);
|
|
|
|
|
|
/* yb' = (ya-xb-yc+xd)co1 - (xa+yb-xc-yd)(si1) */
|
|
|
pSrc[(2u * i2) + 1u] = (s1 * co1) - (r1 * si1);
|
|
|
|
|
|
/* xd' = (xa-yb-xc+yd)co3 + (ya+xb-yc-xd)(si3) */
|
|
|
pSrc[2u * i3] = (r2 * co3) + (s2 * si3);
|
|
|
|
|
|
/* yd' = (ya+xb-yc-xd)co3 - (xa-yb-xc+yd)(si3) */
|
|
|
pSrc[(2u * i3) + 1u] = (s2 * co3) - (r2 * si3);
|
|
|
}
|
|
|
}
|
|
|
twidCoefModifier <<= 2u;
|
|
|
}
|
|
|
|
|
|
/* Initializations of last stage */
|
|
|
n1 = n2;
|
|
|
n2 >>= 2u;
|
|
|
|
|
|
/* Calculations of last stage */
|
|
|
for (i0 = 0u; i0 <= (fftLen - n1); i0 += n1)
|
|
|
{
|
|
|
/* index calculation for the input as, */
|
|
|
/* pSrc[i0 + 0], pSrc[i0 + fftLen/4], pSrc[i0 + fftLen/2], pSrc[i0 + 3fftLen/4] */
|
|
|
i1 = i0 + n2;
|
|
|
i2 = i1 + n2;
|
|
|
i3 = i2 + n2;
|
|
|
|
|
|
/* Butterfly implementation */
|
|
|
|
|
|
/* xa + xb */
|
|
|
r1 = pSrc[2u * i0] + pSrc[2u * i2];
|
|
|
|
|
|
/* xa - xb */
|
|
|
r2 = pSrc[2u * i0] - pSrc[2u * i2];
|
|
|
|
|
|
/* ya + yc */
|
|
|
s1 = pSrc[(2u * i0) + 1u] + pSrc[(2u * i2) + 1u];
|
|
|
|
|
|
/* ya - yc */
|
|
|
s2 = pSrc[(2u * i0) + 1u] - pSrc[(2u * i2) + 1u];
|
|
|
|
|
|
/* xc + xd */
|
|
|
t1 = pSrc[2u * i1] + pSrc[2u * i3];
|
|
|
|
|
|
/* xa' = xa + xb + xc + xd */
|
|
|
pSrc[2u * i0] = r1 + t1;
|
|
|
|
|
|
/* (xa + xb) - (xc + xd) */
|
|
|
r1 = r1 - t1;
|
|
|
|
|
|
/* yb + yd */
|
|
|
t2 = pSrc[(2u * i1) + 1u] + pSrc[(2u * i3) + 1u];
|
|
|
|
|
|
/* ya' = ya + yb + yc + yd */
|
|
|
pSrc[(2u * i0) + 1u] = s1 + t2;
|
|
|
|
|
|
/* (ya + yc) - (yb + yd) */
|
|
|
s1 = s1 - t2;
|
|
|
|
|
|
/* (yb-yd) */
|
|
|
t1 = pSrc[(2u * i1) + 1u] - pSrc[(2u * i3) + 1u];
|
|
|
|
|
|
/* (xb-xd) */
|
|
|
t2 = pSrc[2u * i1] - pSrc[2u * i3];
|
|
|
|
|
|
/* xc' = (xa-xb+xc-xd)co2 + (ya-yb+yc-yd)(si2) */
|
|
|
pSrc[2u * i1] = r1;
|
|
|
|
|
|
/* yc' = (ya-yb+yc-yd)co2 - (xa-xb+xc-xd)(si2) */
|
|
|
pSrc[(2u * i1) + 1u] = s1;
|
|
|
|
|
|
/* (xa+yb-xc-yd) */
|
|
|
r1 = r2 + t1;
|
|
|
|
|
|
/* (xa-yb-xc+yd) */
|
|
|
r2 = r2 - t1;
|
|
|
|
|
|
/* (ya-xb-yc+xd) */
|
|
|
s1 = s2 - t2;
|
|
|
|
|
|
/* (ya+xb-yc-xd) */
|
|
|
s2 = s2 + t2;
|
|
|
|
|
|
/* xb' = (xa+yb-xc-yd)co1 + (ya-xb-yc+xd)(si1) */
|
|
|
pSrc[2u * i2] = r1;
|
|
|
|
|
|
/* yb' = (ya-xb-yc+xd)co1 - (xa+yb-xc-yd)(si1) */
|
|
|
pSrc[(2u * i2) + 1u] = s1;
|
|
|
|
|
|
/* xd' = (xa-yb-xc+yd)co3 + (ya+xb-yc-xd)(si3) */
|
|
|
pSrc[2u * i3] = r2;
|
|
|
|
|
|
/* yd' = (ya+xb-yc-xd)co3 - (xa-yb-xc+yd)(si3) */
|
|
|
pSrc[(2u * i3) + 1u] = s2;
|
|
|
}
|
|
|
|
|
|
|
|
|
#else
|
|
|
|
|
|
/* Run the below code for Cortex-M0 */
|
|
|
|
|
|
/* Initializations for the fft calculation */
|
|
|
n2 = fftLen;
|
|
|
n1 = n2;
|
|
|
for (k = fftLen; k > 1u; k >>= 2u)
|
|
|
{
|
|
|
/* Initializations for the fft calculation */
|
|
|
n1 = n2;
|
|
|
n2 >>= 2u;
|
|
|
ia1 = 0u;
|
|
|
|
|
|
/* FFT Calculation */
|
|
|
for (j = 0u; j <= (n2 - 1u); j++)
|
|
|
{
|
|
|
/* index calculation for the coefficients */
|
|
|
ia2 = ia1 + ia1;
|
|
|
ia3 = ia2 + ia1;
|
|
|
co1 = pCoef[ia1 * 2u];
|
|
|
si1 = pCoef[(ia1 * 2u) + 1u];
|
|
|
co2 = pCoef[ia2 * 2u];
|
|
|
si2 = pCoef[(ia2 * 2u) + 1u];
|
|
|
co3 = pCoef[ia3 * 2u];
|
|
|
si3 = pCoef[(ia3 * 2u) + 1u];
|
|
|
|
|
|
/* Twiddle coefficients index modifier */
|
|
|
ia1 = ia1 + twidCoefModifier;
|
|
|
|
|
|
for (i0 = j; i0 < fftLen; i0 += n1)
|
|
|
{
|
|
|
/* index calculation for the input as, */
|
|
|
/* pSrc[i0 + 0], pSrc[i0 + fftLen/4], pSrc[i0 + fftLen/2], pSrc[i0 + 3fftLen/4] */
|
|
|
i1 = i0 + n2;
|
|
|
i2 = i1 + n2;
|
|
|
i3 = i2 + n2;
|
|
|
|
|
|
/* xa + xc */
|
|
|
r1 = pSrc[(2u * i0)] + pSrc[(2u * i2)];
|
|
|
|
|
|
/* xa - xc */
|
|
|
r2 = pSrc[(2u * i0)] - pSrc[(2u * i2)];
|
|
|
|
|
|
/* ya + yc */
|
|
|
s1 = pSrc[(2u * i0) + 1u] + pSrc[(2u * i2) + 1u];
|
|
|
|
|
|
/* ya - yc */
|
|
|
s2 = pSrc[(2u * i0) + 1u] - pSrc[(2u * i2) + 1u];
|
|
|
|
|
|
/* xb + xd */
|
|
|
t1 = pSrc[2u * i1] + pSrc[2u * i3];
|
|
|
|
|
|
/* xa' = xa + xb + xc + xd */
|
|
|
pSrc[2u * i0] = r1 + t1;
|
|
|
|
|
|
/* xa + xc -(xb + xd) */
|
|
|
r1 = r1 - t1;
|
|
|
|
|
|
/* yb + yd */
|
|
|
t2 = pSrc[(2u * i1) + 1u] + pSrc[(2u * i3) + 1u];
|
|
|
|
|
|
/* ya' = ya + yb + yc + yd */
|
|
|
pSrc[(2u * i0) + 1u] = s1 + t2;
|
|
|
|
|
|
/* (ya + yc) - (yb + yd) */
|
|
|
s1 = s1 - t2;
|
|
|
|
|
|
/* (yb - yd) */
|
|
|
t1 = pSrc[(2u * i1) + 1u] - pSrc[(2u * i3) + 1u];
|
|
|
|
|
|
/* (xb - xd) */
|
|
|
t2 = pSrc[2u * i1] - pSrc[2u * i3];
|
|
|
|
|
|
/* xc' = (xa-xb+xc-xd)co2 + (ya-yb+yc-yd)(si2) */
|
|
|
pSrc[2u * i1] = (r1 * co2) + (s1 * si2);
|
|
|
|
|
|
/* yc' = (ya-yb+yc-yd)co2 - (xa-xb+xc-xd)(si2) */
|
|
|
pSrc[(2u * i1) + 1u] = (s1 * co2) - (r1 * si2);
|
|
|
|
|
|
/* (xa - xc) + (yb - yd) */
|
|
|
r1 = r2 + t1;
|
|
|
|
|
|
/* (xa - xc) - (yb - yd) */
|
|
|
r2 = r2 - t1;
|
|
|
|
|
|
/* (ya - yc) - (xb - xd) */
|
|
|
s1 = s2 - t2;
|
|
|
|
|
|
/* (ya - yc) + (xb - xd) */
|
|
|
s2 = s2 + t2;
|
|
|
|
|
|
/* xb' = (xa+yb-xc-yd)co1 + (ya-xb-yc+xd)(si1) */
|
|
|
pSrc[2u * i2] = (r1 * co1) + (s1 * si1);
|
|
|
|
|
|
/* yb' = (ya-xb-yc+xd)co1 - (xa+yb-xc-yd)(si1) */
|
|
|
pSrc[(2u * i2) + 1u] = (s1 * co1) - (r1 * si1);
|
|
|
|
|
|
/* xd' = (xa-yb-xc+yd)co3 + (ya+xb-yc-xd)(si3) */
|
|
|
pSrc[2u * i3] = (r2 * co3) + (s2 * si3);
|
|
|
|
|
|
/* yd' = (ya+xb-yc-xd)co3 - (xa-yb-xc+yd)(si3) */
|
|
|
pSrc[(2u * i3) + 1u] = (s2 * co3) - (r2 * si3);
|
|
|
}
|
|
|
}
|
|
|
twidCoefModifier <<= 2u;
|
|
|
}
|
|
|
|
|
|
#endif /* #ifndef ARM_MATH_CM0 */
|
|
|
|
|
|
}
|
|
|
|
|
|
/*
|
|
|
* @brief Core function for the floating-point CIFFT butterfly process.
|
|
|
* @param[in, out] *pSrc points to the in-place buffer of floating-point data type.
|
|
|
* @param[in] fftLen length of the FFT.
|
|
|
* @param[in] *pCoef points to twiddle coefficient buffer.
|
|
|
* @param[in] twidCoefModifier twiddle coefficient modifier that supports different size FFTs with the same twiddle factor table.
|
|
|
* @param[in] onebyfftLen value of 1/fftLen.
|
|
|
* @return none.
|
|
|
*/
|
|
|
|
|
|
void arm_radix4_butterfly_inverse_f32(
|
|
|
float32_t * pSrc,
|
|
|
uint16_t fftLen,
|
|
|
float32_t * pCoef,
|
|
|
uint16_t twidCoefModifier,
|
|
|
float32_t onebyfftLen)
|
|
|
{
|
|
|
float32_t co1, co2, co3, si1, si2, si3;
|
|
|
float32_t t1, t2, r1, r2, s1, s2;
|
|
|
uint32_t ia1, ia2, ia3;
|
|
|
uint32_t i0, i1, i2, i3;
|
|
|
uint32_t n1, n2, j, k;
|
|
|
|
|
|
#ifndef ARM_MATH_CM0
|
|
|
|
|
|
/* Run the below code for Cortex-M4 and Cortex-M3 */
|
|
|
|
|
|
/* Initializations for the first stage */
|
|
|
n2 = fftLen;
|
|
|
n1 = n2;
|
|
|
|
|
|
/* n2 = fftLen/4 */
|
|
|
n2 >>= 2u;
|
|
|
i0 = 0u;
|
|
|
ia1 = 0u;
|
|
|
|
|
|
j = n2;
|
|
|
|
|
|
/* Calculation of first stage */
|
|
|
do
|
|
|
{
|
|
|
/* index calculation for the input as, */
|
|
|
/* pSrc[i0 + 0], pSrc[i0 + fftLen/4], pSrc[i0 + fftLen/2], pSrc[i0 + 3fftLen/4] */
|
|
|
i1 = i0 + n2;
|
|
|
i2 = i1 + n2;
|
|
|
i3 = i2 + n2;
|
|
|
|
|
|
/* Butterfly implementation */
|
|
|
/* xa + xc */
|
|
|
r1 = pSrc[(2u * i0)] + pSrc[(2u * i2)];
|
|
|
|
|
|
/* xa - xc */
|
|
|
r2 = pSrc[2u * i0] - pSrc[2u * i2];
|
|
|
|
|
|
/* ya + yc */
|
|
|
s1 = pSrc[(2u * i0) + 1u] + pSrc[(2u * i2) + 1u];
|
|
|
|
|
|
/* ya - yc */
|
|
|
s2 = pSrc[(2u * i0) + 1u] - pSrc[(2u * i2) + 1u];
|
|
|
|
|
|
/* xb + xd */
|
|
|
t1 = pSrc[2u * i1] + pSrc[2u * i3];
|
|
|
|
|
|
/* xa' = xa + xb + xc + xd */
|
|
|
pSrc[2u * i0] = r1 + t1;
|
|
|
|
|
|
/* (xa + xc) - (xb + xd) */
|
|
|
r1 = r1 - t1;
|
|
|
|
|
|
/* yb + yd */
|
|
|
t2 = pSrc[(2u * i1) + 1u] + pSrc[(2u * i3) + 1u];
|
|
|
|
|
|
/* ya' = ya + yb + yc + yd */
|
|
|
pSrc[(2u * i0) + 1u] = s1 + t2;
|
|
|
|
|
|
/* (ya + yc) - (yb + yd) */
|
|
|
s1 = s1 - t2;
|
|
|
|
|
|
/* yb - yd */
|
|
|
t1 = pSrc[(2u * i1) + 1u] - pSrc[(2u * i3) + 1u];
|
|
|
|
|
|
/* xb - xd */
|
|
|
t2 = pSrc[2u * i1] - pSrc[2u * i3];
|
|
|
|
|
|
/* index calculation for the coefficients */
|
|
|
ia2 = ia1 + ia1;
|
|
|
co2 = pCoef[ia2 * 2u];
|
|
|
si2 = pCoef[(ia2 * 2u) + 1u];
|
|
|
|
|
|
/* xc' = (xa-xb+xc-xd)co2 - (ya-yb+yc-yd)(si2) */
|
|
|
pSrc[2u * i1] = (r1 * co2) - (s1 * si2);
|
|
|
|
|
|
/* yc' = (ya-yb+yc-yd)co2 + (xa-xb+xc-xd)(si2) */
|
|
|
pSrc[(2u * i1) + 1u] = (s1 * co2) + (r1 * si2);
|
|
|
|
|
|
/* (xa - xc) - (yb - yd) */
|
|
|
r1 = r2 - t1;
|
|
|
|
|
|
/* (xa - xc) + (yb - yd) */
|
|
|
r2 = r2 + t1;
|
|
|
|
|
|
/* (ya - yc) + (xb - xd) */
|
|
|
s1 = s2 + t2;
|
|
|
|
|
|
/* (ya - yc) - (xb - xd) */
|
|
|
s2 = s2 - t2;
|
|
|
|
|
|
co1 = pCoef[ia1 * 2u];
|
|
|
si1 = pCoef[(ia1 * 2u) + 1u];
|
|
|
|
|
|
/* xb' = (xa+yb-xc-yd)co1 - (ya-xb-yc+xd)(si1) */
|
|
|
pSrc[2u * i2] = (r1 * co1) - (s1 * si1);
|
|
|
|
|
|
/* yb' = (ya-xb-yc+xd)co1 + (xa+yb-xc-yd)(si1) */
|
|
|
pSrc[(2u * i2) + 1u] = (s1 * co1) + (r1 * si1);
|
|
|
|
|
|
/* index calculation for the coefficients */
|
|
|
ia3 = ia2 + ia1;
|
|
|
co3 = pCoef[ia3 * 2u];
|
|
|
si3 = pCoef[(ia3 * 2u) + 1u];
|
|
|
|
|
|
/* xd' = (xa-yb-xc+yd)co3 - (ya+xb-yc-xd)(si3) */
|
|
|
pSrc[2u * i3] = (r2 * co3) - (s2 * si3);
|
|
|
|
|
|
/* yd' = (ya+xb-yc-xd)co3 + (xa-yb-xc+yd)(si3) */
|
|
|
pSrc[(2u * i3) + 1u] = (s2 * co3) + (r2 * si3);
|
|
|
|
|
|
/* Twiddle coefficients index modifier */
|
|
|
ia1 = ia1 + twidCoefModifier;
|
|
|
|
|
|
/* Updating input index */
|
|
|
i0 = i0 + 1u;
|
|
|
|
|
|
}
|
|
|
while(--j);
|
|
|
|
|
|
twidCoefModifier <<= 2u;
|
|
|
|
|
|
/* Calculation of second stage to excluding last stage */
|
|
|
for (k = fftLen / 4; k > 4u; k >>= 2u)
|
|
|
{
|
|
|
/* Initializations for the first stage */
|
|
|
n1 = n2;
|
|
|
n2 >>= 2u;
|
|
|
ia1 = 0u;
|
|
|
|
|
|
/* Calculation of first stage */
|
|
|
for (j = 0u; j <= (n2 - 1u); j++)
|
|
|
{
|
|
|
/* index calculation for the coefficients */
|
|
|
ia2 = ia1 + ia1;
|
|
|
ia3 = ia2 + ia1;
|
|
|
co1 = pCoef[ia1 * 2u];
|
|
|
si1 = pCoef[(ia1 * 2u) + 1u];
|
|
|
co2 = pCoef[ia2 * 2u];
|
|
|
si2 = pCoef[(ia2 * 2u) + 1u];
|
|
|
co3 = pCoef[ia3 * 2u];
|
|
|
si3 = pCoef[(ia3 * 2u) + 1u];
|
|
|
|
|
|
/* Twiddle coefficients index modifier */
|
|
|
ia1 = ia1 + twidCoefModifier;
|
|
|
|
|
|
for (i0 = j; i0 < fftLen; i0 += n1)
|
|
|
{
|
|
|
/* index calculation for the input as, */
|
|
|
/* pSrc[i0 + 0], pSrc[i0 + fftLen/4], pSrc[i0 + fftLen/2], pSrc[i0 + 3fftLen/4] */
|
|
|
i1 = i0 + n2;
|
|
|
i2 = i1 + n2;
|
|
|
i3 = i2 + n2;
|
|
|
|
|
|
/* xa + xc */
|
|
|
r1 = pSrc[(2u * i0)] + pSrc[(2u * i2)];
|
|
|
|
|
|
/* xa - xc */
|
|
|
r2 = pSrc[(2u * i0)] - pSrc[(2u * i2)];
|
|
|
|
|
|
/* ya + yc */
|
|
|
s1 = pSrc[(2u * i0) + 1u] + pSrc[(2u * i2) + 1u];
|
|
|
|
|
|
/* ya - yc */
|
|
|
s2 = pSrc[(2u * i0) + 1u] - pSrc[(2u * i2) + 1u];
|
|
|
|
|
|
/* xb + xd */
|
|
|
t1 = pSrc[2u * i1] + pSrc[2u * i3];
|
|
|
|
|
|
/* xa' = xa + xb + xc + xd */
|
|
|
pSrc[2u * i0] = r1 + t1;
|
|
|
|
|
|
/* xa + xc -(xb + xd) */
|
|
|
r1 = r1 - t1;
|
|
|
|
|
|
/* yb + yd */
|
|
|
t2 = pSrc[(2u * i1) + 1u] + pSrc[(2u * i3) + 1u];
|
|
|
|
|
|
/* ya' = ya + yb + yc + yd */
|
|
|
pSrc[(2u * i0) + 1u] = s1 + t2;
|
|
|
|
|
|
/* (ya + yc) - (yb + yd) */
|
|
|
s1 = s1 - t2;
|
|
|
|
|
|
/* (yb - yd) */
|
|
|
t1 = pSrc[(2u * i1) + 1u] - pSrc[(2u * i3) + 1u];
|
|
|
|
|
|
/* (xb - xd) */
|
|
|
t2 = pSrc[2u * i1] - pSrc[2u * i3];
|
|
|
|
|
|
/* xc' = (xa-xb+xc-xd)co2 - (ya-yb+yc-yd)(si2) */
|
|
|
pSrc[2u * i1] = (r1 * co2) - (s1 * si2);
|
|
|
|
|
|
/* yc' = (ya-yb+yc-yd)co2 + (xa-xb+xc-xd)(si2) */
|
|
|
pSrc[(2u * i1) + 1u] = (s1 * co2) + (r1 * si2);
|
|
|
|
|
|
/* (xa - xc) - (yb - yd) */
|
|
|
r1 = r2 - t1;
|
|
|
|
|
|
/* (xa - xc) + (yb - yd) */
|
|
|
r2 = r2 + t1;
|
|
|
|
|
|
/* (ya - yc) + (xb - xd) */
|
|
|
s1 = s2 + t2;
|
|
|
|
|
|
/* (ya - yc) - (xb - xd) */
|
|
|
s2 = s2 - t2;
|
|
|
|
|
|
/* xb' = (xa+yb-xc-yd)co1 - (ya-xb-yc+xd)(si1) */
|
|
|
pSrc[2u * i2] = (r1 * co1) - (s1 * si1);
|
|
|
|
|
|
/* yb' = (ya-xb-yc+xd)co1 + (xa+yb-xc-yd)(si1) */
|
|
|
pSrc[(2u * i2) + 1u] = (s1 * co1) + (r1 * si1);
|
|
|
|
|
|
/* xd' = (xa-yb-xc+yd)co3 - (ya+xb-yc-xd)(si3) */
|
|
|
pSrc[2u * i3] = (r2 * co3) - (s2 * si3);
|
|
|
|
|
|
/* yd' = (ya+xb-yc-xd)co3 + (xa-yb-xc+yd)(si3) */
|
|
|
pSrc[(2u * i3) + 1u] = (s2 * co3) + (r2 * si3);
|
|
|
}
|
|
|
}
|
|
|
twidCoefModifier <<= 2u;
|
|
|
}
|
|
|
|
|
|
/* Initializations of last stage */
|
|
|
n1 = n2;
|
|
|
n2 >>= 2u;
|
|
|
|
|
|
/* Calculations of last stage */
|
|
|
for (i0 = 0u; i0 <= (fftLen - n1); i0 += n1)
|
|
|
{
|
|
|
/* index calculation for the input as, */
|
|
|
/* pSrc[i0 + 0], pSrc[i0 + fftLen/4], pSrc[i0 + fftLen/2], pSrc[i0 + 3fftLen/4] */
|
|
|
i1 = i0 + n2;
|
|
|
i2 = i1 + n2;
|
|
|
i3 = i2 + n2;
|
|
|
|
|
|
/* Butterfly implementation */
|
|
|
/* xa + xc */
|
|
|
r1 = pSrc[2u * i0] + pSrc[2u * i2];
|
|
|
|
|
|
/* xa - xc */
|
|
|
r2 = pSrc[2u * i0] - pSrc[2u * i2];
|
|
|
|
|
|
/* ya + yc */
|
|
|
s1 = pSrc[(2u * i0) + 1u] + pSrc[(2u * i2) + 1u];
|
|
|
|
|
|
/* ya - yc */
|
|
|
s2 = pSrc[(2u * i0) + 1u] - pSrc[(2u * i2) + 1u];
|
|
|
|
|
|
/* xc + xd */
|
|
|
t1 = pSrc[2u * i1] + pSrc[2u * i3];
|
|
|
|
|
|
/* xa' = xa + xb + xc + xd */
|
|
|
pSrc[2u * i0] = (r1 + t1) * onebyfftLen;
|
|
|
|
|
|
/* (xa + xb) - (xc + xd) */
|
|
|
r1 = r1 - t1;
|
|
|
|
|
|
/* yb + yd */
|
|
|
t2 = pSrc[(2u * i1) + 1u] + pSrc[(2u * i3) + 1u];
|
|
|
|
|
|
/* ya' = ya + yb + yc + yd */
|
|
|
pSrc[(2u * i0) + 1u] = (s1 + t2) * onebyfftLen;
|
|
|
|
|
|
/* (ya + yc) - (yb + yd) */
|
|
|
s1 = s1 - t2;
|
|
|
|
|
|
/* (yb-yd) */
|
|
|
t1 = pSrc[(2u * i1) + 1u] - pSrc[(2u * i3) + 1u];
|
|
|
|
|
|
/* (xb-xd) */
|
|
|
t2 = pSrc[2u * i1] - pSrc[2u * i3];
|
|
|
|
|
|
/* xc' = (xa-xb+xc-xd)co2 - (ya-yb+yc-yd)(si2) */
|
|
|
pSrc[2u * i1] = r1 * onebyfftLen;
|
|
|
|
|
|
/* yc' = (ya-yb+yc-yd)co2 + (xa-xb+xc-xd)(si2) */
|
|
|
pSrc[(2u * i1) + 1u] = s1 * onebyfftLen;
|
|
|
|
|
|
|
|
|
/* (xa - xc) - (yb-yd) */
|
|
|
r1 = r2 - t1;
|
|
|
|
|
|
/* (xa - xc) + (yb-yd) */
|
|
|
r2 = r2 + t1;
|
|
|
|
|
|
/* (ya - yc) + (xb-xd) */
|
|
|
s1 = s2 + t2;
|
|
|
|
|
|
/* (ya - yc) - (xb-xd) */
|
|
|
s2 = s2 - t2;
|
|
|
|
|
|
/* xb' = (xa+yb-xc-yd)co1 - (ya-xb-yc+xd)(si1) */
|
|
|
pSrc[2u * i2] = r1 * onebyfftLen;
|
|
|
|
|
|
/* yb' = (ya-xb-yc+xd)co1 + (xa+yb-xc-yd)(si1) */
|
|
|
pSrc[(2u * i2) + 1u] = s1 * onebyfftLen;
|
|
|
|
|
|
/* xd' = (xa-yb-xc+yd)co3 - (ya+xb-yc-xd)(si3) */
|
|
|
pSrc[2u * i3] = r2 * onebyfftLen;
|
|
|
|
|
|
/* yd' = (ya+xb-yc-xd)co3 + (xa-yb-xc+yd)(si3) */
|
|
|
pSrc[(2u * i3) + 1u] = s2 * onebyfftLen;
|
|
|
}
|
|
|
|
|
|
|
|
|
#else
|
|
|
|
|
|
/* Run the below code for Cortex-M0 */
|
|
|
|
|
|
/* Initializations for the first stage */
|
|
|
n2 = fftLen;
|
|
|
n1 = n2;
|
|
|
|
|
|
/* Calculation of first stage */
|
|
|
for (k = fftLen; k > 4u; k >>= 2u)
|
|
|
{
|
|
|
/* Initializations for the first stage */
|
|
|
n1 = n2;
|
|
|
n2 >>= 2u;
|
|
|
ia1 = 0u;
|
|
|
|
|
|
/* Calculation of first stage */
|
|
|
for (j = 0u; j <= (n2 - 1u); j++)
|
|
|
{
|
|
|
/* index calculation for the coefficients */
|
|
|
ia2 = ia1 + ia1;
|
|
|
ia3 = ia2 + ia1;
|
|
|
co1 = pCoef[ia1 * 2u];
|
|
|
si1 = pCoef[(ia1 * 2u) + 1u];
|
|
|
co2 = pCoef[ia2 * 2u];
|
|
|
si2 = pCoef[(ia2 * 2u) + 1u];
|
|
|
co3 = pCoef[ia3 * 2u];
|
|
|
si3 = pCoef[(ia3 * 2u) + 1u];
|
|
|
|
|
|
/* Twiddle coefficients index modifier */
|
|
|
ia1 = ia1 + twidCoefModifier;
|
|
|
|
|
|
for (i0 = j; i0 < fftLen; i0 += n1)
|
|
|
{
|
|
|
/* index calculation for the input as, */
|
|
|
/* pSrc[i0 + 0], pSrc[i0 + fftLen/4], pSrc[i0 + fftLen/2], pSrc[i0 + 3fftLen/4] */
|
|
|
i1 = i0 + n2;
|
|
|
i2 = i1 + n2;
|
|
|
i3 = i2 + n2;
|
|
|
|
|
|
/* xa + xc */
|
|
|
r1 = pSrc[(2u * i0)] + pSrc[(2u * i2)];
|
|
|
|
|
|
/* xa - xc */
|
|
|
r2 = pSrc[(2u * i0)] - pSrc[(2u * i2)];
|
|
|
|
|
|
/* ya + yc */
|
|
|
s1 = pSrc[(2u * i0) + 1u] + pSrc[(2u * i2) + 1u];
|
|
|
|
|
|
/* ya - yc */
|
|
|
s2 = pSrc[(2u * i0) + 1u] - pSrc[(2u * i2) + 1u];
|
|
|
|
|
|
/* xb + xd */
|
|
|
t1 = pSrc[2u * i1] + pSrc[2u * i3];
|
|
|
|
|
|
/* xa' = xa + xb + xc + xd */
|
|
|
pSrc[2u * i0] = r1 + t1;
|
|
|
|
|
|
/* xa + xc -(xb + xd) */
|
|
|
r1 = r1 - t1;
|
|
|
|
|
|
/* yb + yd */
|
|
|
t2 = pSrc[(2u * i1) + 1u] + pSrc[(2u * i3) + 1u];
|
|
|
|
|
|
/* ya' = ya + yb + yc + yd */
|
|
|
pSrc[(2u * i0) + 1u] = s1 + t2;
|
|
|
|
|
|
/* (ya + yc) - (yb + yd) */
|
|
|
s1 = s1 - t2;
|
|
|
|
|
|
/* (yb - yd) */
|
|
|
t1 = pSrc[(2u * i1) + 1u] - pSrc[(2u * i3) + 1u];
|
|
|
|
|
|
/* (xb - xd) */
|
|
|
t2 = pSrc[2u * i1] - pSrc[2u * i3];
|
|
|
|
|
|
/* xc' = (xa-xb+xc-xd)co2 - (ya-yb+yc-yd)(si2) */
|
|
|
pSrc[2u * i1] = (r1 * co2) - (s1 * si2);
|
|
|
|
|
|
/* yc' = (ya-yb+yc-yd)co2 + (xa-xb+xc-xd)(si2) */
|
|
|
pSrc[(2u * i1) + 1u] = (s1 * co2) + (r1 * si2);
|
|
|
|
|
|
/* (xa - xc) - (yb - yd) */
|
|
|
r1 = r2 - t1;
|
|
|
|
|
|
/* (xa - xc) + (yb - yd) */
|
|
|
r2 = r2 + t1;
|
|
|
|
|
|
/* (ya - yc) + (xb - xd) */
|
|
|
s1 = s2 + t2;
|
|
|
|
|
|
/* (ya - yc) - (xb - xd) */
|
|
|
s2 = s2 - t2;
|
|
|
|
|
|
/* xb' = (xa+yb-xc-yd)co1 - (ya-xb-yc+xd)(si1) */
|
|
|
pSrc[2u * i2] = (r1 * co1) - (s1 * si1);
|
|
|
|
|
|
/* yb' = (ya-xb-yc+xd)co1 + (xa+yb-xc-yd)(si1) */
|
|
|
pSrc[(2u * i2) + 1u] = (s1 * co1) + (r1 * si1);
|
|
|
|
|
|
/* xd' = (xa-yb-xc+yd)co3 - (ya+xb-yc-xd)(si3) */
|
|
|
pSrc[2u * i3] = (r2 * co3) - (s2 * si3);
|
|
|
|
|
|
/* yd' = (ya+xb-yc-xd)co3 + (xa-yb-xc+yd)(si3) */
|
|
|
pSrc[(2u * i3) + 1u] = (s2 * co3) + (r2 * si3);
|
|
|
}
|
|
|
}
|
|
|
twidCoefModifier <<= 2u;
|
|
|
}
|
|
|
/* Initializations of last stage */
|
|
|
n1 = n2;
|
|
|
n2 >>= 2u;
|
|
|
|
|
|
/* Calculations of last stage */
|
|
|
for (i0 = 0u; i0 <= (fftLen - n1); i0 += n1)
|
|
|
{
|
|
|
/* index calculation for the input as, */
|
|
|
/* pSrc[i0 + 0], pSrc[i0 + fftLen/4], pSrc[i0 + fftLen/2], pSrc[i0 + 3fftLen/4] */
|
|
|
i1 = i0 + n2;
|
|
|
i2 = i1 + n2;
|
|
|
i3 = i2 + n2;
|
|
|
|
|
|
/* Butterfly implementation */
|
|
|
/* xa + xc */
|
|
|
r1 = pSrc[2u * i0] + pSrc[2u * i2];
|
|
|
|
|
|
/* xa - xc */
|
|
|
r2 = pSrc[2u * i0] - pSrc[2u * i2];
|
|
|
|
|
|
/* ya + yc */
|
|
|
s1 = pSrc[(2u * i0) + 1u] + pSrc[(2u * i2) + 1u];
|
|
|
|
|
|
/* ya - yc */
|
|
|
s2 = pSrc[(2u * i0) + 1u] - pSrc[(2u * i2) + 1u];
|
|
|
|
|
|
/* xc + xd */
|
|
|
t1 = pSrc[2u * i1] + pSrc[2u * i3];
|
|
|
|
|
|
/* xa' = xa + xb + xc + xd */
|
|
|
pSrc[2u * i0] = (r1 + t1) * onebyfftLen;
|
|
|
|
|
|
/* (xa + xb) - (xc + xd) */
|
|
|
r1 = r1 - t1;
|
|
|
|
|
|
/* yb + yd */
|
|
|
t2 = pSrc[(2u * i1) + 1u] + pSrc[(2u * i3) + 1u];
|
|
|
|
|
|
/* ya' = ya + yb + yc + yd */
|
|
|
pSrc[(2u * i0) + 1u] = (s1 + t2) * onebyfftLen;
|
|
|
|
|
|
/* (ya + yc) - (yb + yd) */
|
|
|
s1 = s1 - t2;
|
|
|
|
|
|
/* (yb-yd) */
|
|
|
t1 = pSrc[(2u * i1) + 1u] - pSrc[(2u * i3) + 1u];
|
|
|
|
|
|
/* (xb-xd) */
|
|
|
t2 = pSrc[2u * i1] - pSrc[2u * i3];
|
|
|
|
|
|
/* xc' = (xa-xb+xc-xd)co2 - (ya-yb+yc-yd)(si2) */
|
|
|
pSrc[2u * i1] = r1 * onebyfftLen;
|
|
|
|
|
|
/* yc' = (ya-yb+yc-yd)co2 + (xa-xb+xc-xd)(si2) */
|
|
|
pSrc[(2u * i1) + 1u] = s1 * onebyfftLen;
|
|
|
|
|
|
|
|
|
/* (xa - xc) - (yb-yd) */
|
|
|
r1 = r2 - t1;
|
|
|
|
|
|
/* (xa - xc) + (yb-yd) */
|
|
|
r2 = r2 + t1;
|
|
|
|
|
|
/* (ya - yc) + (xb-xd) */
|
|
|
s1 = s2 + t2;
|
|
|
|
|
|
/* (ya - yc) - (xb-xd) */
|
|
|
s2 = s2 - t2;
|
|
|
|
|
|
/* xb' = (xa+yb-xc-yd)co1 - (ya-xb-yc+xd)(si1) */
|
|
|
pSrc[2u * i2] = r1 * onebyfftLen;
|
|
|
|
|
|
/* yb' = (ya-xb-yc+xd)co1 + (xa+yb-xc-yd)(si1) */
|
|
|
pSrc[(2u * i2) + 1u] = s1 * onebyfftLen;
|
|
|
|
|
|
/* xd' = (xa-yb-xc+yd)co3 - (ya+xb-yc-xd)(si3) */
|
|
|
pSrc[2u * i3] = r2 * onebyfftLen;
|
|
|
|
|
|
/* yd' = (ya+xb-yc-xd)co3 + (xa-yb-xc+yd)(si3) */
|
|
|
pSrc[(2u * i3) + 1u] = s2 * onebyfftLen;
|
|
|
}
|
|
|
|
|
|
#endif /* #ifndef ARM_MATH_CM0 */
|
|
|
|
|
|
}
|
|
|
|
|
|
/*
|
|
|
* @brief In-place bit reversal function.
|
|
|
* @param[in, out] *pSrc points to the in-place buffer of floating-point data type.
|
|
|
* @param[in] fftSize length of the FFT.
|
|
|
* @param[in] bitRevFactor bit reversal modifier that supports different size FFTs with the same bit reversal table.
|
|
|
* @param[in] *pBitRevTab points to the bit reversal table.
|
|
|
* @return none.
|
|
|
*/
|
|
|
|
|
|
void arm_bitreversal_f32(
|
|
|
float32_t * pSrc,
|
|
|
uint16_t fftSize,
|
|
|
uint16_t bitRevFactor,
|
|
|
uint16_t * pBitRevTab)
|
|
|
{
|
|
|
uint16_t fftLenBy2, fftLenBy2p1;
|
|
|
uint16_t i, j;
|
|
|
float32_t in;
|
|
|
|
|
|
/* Initializations */
|
|
|
j = 0u;
|
|
|
fftLenBy2 = fftSize >> 1u;
|
|
|
fftLenBy2p1 = (fftSize >> 1u) + 1u;
|
|
|
|
|
|
/* Bit Reversal Implementation */
|
|
|
for (i = 0u; i <= (fftLenBy2 - 2u); i += 2u)
|
|
|
{
|
|
|
if(i < j)
|
|
|
{
|
|
|
/* pSrc[i] <-> pSrc[j]; */
|
|
|
in = pSrc[2u * i];
|
|
|
pSrc[2u * i] = pSrc[2u * j];
|
|
|
pSrc[2u * j] = in;
|
|
|
|
|
|
/* pSrc[i+1u] <-> pSrc[j+1u] */
|
|
|
in = pSrc[(2u * i) + 1u];
|
|
|
pSrc[(2u * i) + 1u] = pSrc[(2u * j) + 1u];
|
|
|
pSrc[(2u * j) + 1u] = in;
|
|
|
|
|
|
/* pSrc[i+fftLenBy2p1] <-> pSrc[j+fftLenBy2p1] */
|
|
|
in = pSrc[2u * (i + fftLenBy2p1)];
|
|
|
pSrc[2u * (i + fftLenBy2p1)] = pSrc[2u * (j + fftLenBy2p1)];
|
|
|
pSrc[2u * (j + fftLenBy2p1)] = in;
|
|
|
|
|
|
/* pSrc[i+fftLenBy2p1+1u] <-> pSrc[j+fftLenBy2p1+1u] */
|
|
|
in = pSrc[(2u * (i + fftLenBy2p1)) + 1u];
|
|
|
pSrc[(2u * (i + fftLenBy2p1)) + 1u] =
|
|
|
pSrc[(2u * (j + fftLenBy2p1)) + 1u];
|
|
|
pSrc[(2u * (j + fftLenBy2p1)) + 1u] = in;
|
|
|
|
|
|
}
|
|
|
|
|
|
/* pSrc[i+1u] <-> pSrc[j+1u] */
|
|
|
in = pSrc[2u * (i + 1u)];
|
|
|
pSrc[2u * (i + 1u)] = pSrc[2u * (j + fftLenBy2)];
|
|
|
pSrc[2u * (j + fftLenBy2)] = in;
|
|
|
|
|
|
/* pSrc[i+2u] <-> pSrc[j+2u] */
|
|
|
in = pSrc[(2u * (i + 1u)) + 1u];
|
|
|
pSrc[(2u * (i + 1u)) + 1u] = pSrc[(2u * (j + fftLenBy2)) + 1u];
|
|
|
pSrc[(2u * (j + fftLenBy2)) + 1u] = in;
|
|
|
|
|
|
/* Reading the index for the bit reversal */
|
|
|
j = *pBitRevTab;
|
|
|
|
|
|
/* Updating the bit reversal index depending on the fft length */
|
|
|
pBitRevTab += bitRevFactor;
|
|
|
}
|
|
|
}
|
|
|
|
