| /* ---------------------------------------------------------------------- |
| * Copyright (C) 2010-2014 ARM Limited. All rights reserved. |
| * |
| * $Date: 19. March 2015 |
| * $Revision: V.1.4.5 |
| * |
| * Project: CMSIS DSP Library |
| * Title: arm_rfft_f32.c |
| * |
| * Description: RFFT & RIFFT Floating point process function |
| * |
| * Target Processor: Cortex-M4/Cortex-M3/Cortex-M0 |
| * |
| * Redistribution and use in source and binary forms, with or without |
| * modification, are permitted provided that the following conditions |
| * are met: |
| * - Redistributions of source code must retain the above copyright |
| * notice, this list of conditions and the following disclaimer. |
| * - Redistributions in binary form must reproduce the above copyright |
| * notice, this list of conditions and the following disclaimer in |
| * the documentation and/or other materials provided with the |
| * distribution. |
| * - Neither the name of ARM LIMITED nor the names of its contributors |
| * may be used to endorse or promote products derived from this |
| * software without specific prior written permission. |
| * |
| * THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS |
| * "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT |
| * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS |
| * FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE |
| * COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, |
| * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, |
| * BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; |
| * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER |
| * CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT |
| * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN |
| * ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE |
| * POSSIBILITY OF SUCH DAMAGE. |
| * -------------------------------------------------------------------- */ |
| |
| #include "arm_math.h" |
| |
| void stage_rfft_f32( |
| arm_rfft_fast_instance_f32 * S, |
| float32_t * p, float32_t * pOut) |
| { |
| uint32_t k; /* Loop Counter */ |
| float32_t twR, twI; /* RFFT Twiddle coefficients */ |
| float32_t * pCoeff = S->pTwiddleRFFT; /* Points to RFFT Twiddle factors */ |
| float32_t *pA = p; /* increasing pointer */ |
| float32_t *pB = p; /* decreasing pointer */ |
| float32_t xAR, xAI, xBR, xBI; /* temporary variables */ |
| float32_t t1a, t1b; /* temporary variables */ |
| float32_t p0, p1, p2, p3; /* temporary variables */ |
| |
| |
| k = (S->Sint).fftLen - 1; |
| |
| /* Pack first and last sample of the frequency domain together */ |
| |
| xBR = pB[0]; |
| xBI = pB[1]; |
| xAR = pA[0]; |
| xAI = pA[1]; |
| |
| twR = *pCoeff++ ; |
| twI = *pCoeff++ ; |
| |
| // U1 = XA(1) + XB(1); % It is real |
| t1a = xBR + xAR ; |
| |
| // U2 = XB(1) - XA(1); % It is imaginary |
| t1b = xBI + xAI ; |
| |
| // real(tw * (xB - xA)) = twR * (xBR - xAR) - twI * (xBI - xAI); |
| // imag(tw * (xB - xA)) = twI * (xBR - xAR) + twR * (xBI - xAI); |
| *pOut++ = 0.5f * ( t1a + t1b ); |
| *pOut++ = 0.5f * ( t1a - t1b ); |
| |
| // XA(1) = 1/2*( U1 - imag(U2) + i*( U1 +imag(U2) )); |
| pB = p + 2*k; |
| pA += 2; |
| |
| do |
| { |
| /* |
| function X = my_split_rfft(X, ifftFlag) |
| % X is a series of real numbers |
| L = length(X); |
| XC = X(1:2:end) +i*X(2:2:end); |
| XA = fft(XC); |
| XB = conj(XA([1 end:-1:2])); |
| TW = i*exp(-2*pi*i*[0:L/2-1]/L).'; |
| for l = 2:L/2 |
| XA(l) = 1/2 * (XA(l) + XB(l) + TW(l) * (XB(l) - XA(l))); |
| end |
| XA(1) = 1/2* (XA(1) + XB(1) + TW(1) * (XB(1) - XA(1))) + i*( 1/2*( XA(1) + XB(1) + i*( XA(1) - XB(1)))); |
| X = XA; |
| */ |
| |
| xBI = pB[1]; |
| xBR = pB[0]; |
| xAR = pA[0]; |
| xAI = pA[1]; |
| |
| twR = *pCoeff++; |
| twI = *pCoeff++; |
| |
| t1a = xBR - xAR ; |
| t1b = xBI + xAI ; |
| |
| // real(tw * (xB - xA)) = twR * (xBR - xAR) - twI * (xBI - xAI); |
| // imag(tw * (xB - xA)) = twI * (xBR - xAR) + twR * (xBI - xAI); |
| p0 = twR * t1a; |
| p1 = twI * t1a; |
| p2 = twR * t1b; |
| p3 = twI * t1b; |
| |
| *pOut++ = 0.5f * (xAR + xBR + p0 + p3 ); //xAR |
| *pOut++ = 0.5f * (xAI - xBI + p1 - p2 ); //xAI |
| |
| pA += 2; |
| pB -= 2; |
| k--; |
| } while(k > 0u); |
| } |
| |
| /* Prepares data for inverse cfft */ |
| void merge_rfft_f32( |
| arm_rfft_fast_instance_f32 * S, |
| float32_t * p, float32_t * pOut) |
| { |
| uint32_t k; /* Loop Counter */ |
| float32_t twR, twI; /* RFFT Twiddle coefficients */ |
| float32_t *pCoeff = S->pTwiddleRFFT; /* Points to RFFT Twiddle factors */ |
| float32_t *pA = p; /* increasing pointer */ |
| float32_t *pB = p; /* decreasing pointer */ |
| float32_t xAR, xAI, xBR, xBI; /* temporary variables */ |
| float32_t t1a, t1b, r, s, t, u; /* temporary variables */ |
| |
| k = (S->Sint).fftLen - 1; |
| |
| xAR = pA[0]; |
| xAI = pA[1]; |
| |
| pCoeff += 2 ; |
| |
| *pOut++ = 0.5f * ( xAR + xAI ); |
| *pOut++ = 0.5f * ( xAR - xAI ); |
| |
| pB = p + 2*k ; |
| pA += 2 ; |
| |
| while(k > 0u) |
| { |
| /* G is half of the frequency complex spectrum */ |
| //for k = 2:N |
| // Xk(k) = 1/2 * (G(k) + conj(G(N-k+2)) + Tw(k)*( G(k) - conj(G(N-k+2)))); |
| xBI = pB[1] ; |
| xBR = pB[0] ; |
| xAR = pA[0]; |
| xAI = pA[1]; |
| |
| twR = *pCoeff++; |
| twI = *pCoeff++; |
| |
| t1a = xAR - xBR ; |
| t1b = xAI + xBI ; |
| |
| r = twR * t1a; |
| s = twI * t1b; |
| t = twI * t1a; |
| u = twR * t1b; |
| |
| // real(tw * (xA - xB)) = twR * (xAR - xBR) - twI * (xAI - xBI); |
| // imag(tw * (xA - xB)) = twI * (xAR - xBR) + twR * (xAI - xBI); |
| *pOut++ = 0.5f * (xAR + xBR - r - s ); //xAR |
| *pOut++ = 0.5f * (xAI - xBI + t - u ); //xAI |
| |
| pA += 2; |
| pB -= 2; |
| k--; |
| } |
| |
| } |
| |
| /** |
| * @ingroup groupTransforms |
| */ |
| |
| /** |
| * @defgroup Fast Real FFT Functions |
| * |
| * \par |
| * The CMSIS DSP library includes specialized algorithms for computing the |
| * FFT of real data sequences. The FFT is defined over complex data but |
| * in many applications the input is real. Real FFT algorithms take advantage |
| * of the symmetry properties of the FFT and have a speed advantage over complex |
| * algorithms of the same length. |
| * \par |
| * The Fast RFFT algorith relays on the mixed radix CFFT that save processor usage. |
| * \par |
| * The real length N forward FFT of a sequence is computed using the steps shown below. |
| * \par |
| * \image html RFFT.gif "Real Fast Fourier Transform" |
| * \par |
| * The real sequence is initially treated as if it were complex to perform a CFFT. |
| * Later, a processing stage reshapes the data to obtain half of the frequency spectrum |
| * in complex format. Except the first complex number that contains the two real numbers |
| * X[0] and X[N/2] all the data is complex. In other words, the first complex sample |
| * contains two real values packed. |
| * \par |
| * The input for the inverse RFFT should keep the same format as the output of the |
| * forward RFFT. A first processing stage pre-process the data to later perform an |
| * inverse CFFT. |
| * \par |
| * \image html RIFFT.gif "Real Inverse Fast Fourier Transform" |
| * \par |
| * The algorithms for floating-point, Q15, and Q31 data are slightly different |
| * and we describe each algorithm in turn. |
| * \par Floating-point |
| * The main functions are <code>arm_rfft_fast_f32()</code> |
| * and <code>arm_rfft_fast_init_f32()</code>. The older functions |
| * <code>arm_rfft_f32()</code> and <code>arm_rfft_init_f32()</code> have been |
| * deprecated but are still documented. |
| * \par |
| * The FFT of a real N-point sequence has even symmetry in the frequency |
| * domain. The second half of the data equals the conjugate of the first half |
| * flipped in frequency: |
| * <pre> |
| *X[0] - real data |
| *X[1] - complex data |
| *X[2] - complex data |
| *... |
| *X[fftLen/2-1] - complex data |
| *X[fftLen/2] - real data |
| *X[fftLen/2+1] - conjugate of X[fftLen/2-1] |
| *X[fftLen/2+2] - conjugate of X[fftLen/2-2] |
| *... |
| *X[fftLen-1] - conjugate of X[1] |
| * </pre> |
| * Looking at the data, we see that we can uniquely represent the FFT using only |
| * <pre> |
| *N/2+1 samples: |
| *X[0] - real data |
| *X[1] - complex data |
| *X[2] - complex data |
| *... |
| *X[fftLen/2-1] - complex data |
| *X[fftLen/2] - real data |
| * </pre> |
| * Looking more closely we see that the first and last samples are real valued. |
| * They can be packed together and we can thus represent the FFT of an N-point |
| * real sequence by N/2 complex values: |
| * <pre> |
| *X[0],X[N/2] - packed real data: X[0] + jX[N/2] |
| *X[1] - complex data |
| *X[2] - complex data |
| *... |
| *X[fftLen/2-1] - complex data |
| * </pre> |
| * The real FFT functions pack the frequency domain data in this fashion. The |
| * forward transform outputs the data in this form and the inverse transform |
| * expects input data in this form. The function always performs the needed |
| * bitreversal so that the input and output data is always in normal order. The |
| * functions support lengths of [32, 64, 128, ..., 4096] samples. |
| * \par |
| * The forward and inverse real FFT functions apply the standard FFT scaling; no |
| * scaling on the forward transform and 1/fftLen scaling on the inverse |
| * transform. |
| * \par Q15 and Q31 |
| * The real algorithms are defined in a similar manner and utilize N/2 complex |
| * transforms behind the scenes. |
| * \par |
| * The complex transforms used internally include scaling to prevent fixed-point |
| * overflows. The overall scaling equals 1/(fftLen/2). |
| * \par |
| * A separate instance structure must be defined for each transform used but |
| * twiddle factor and bit reversal tables can be reused. |
| * \par |
| * 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 table and bit reversal table pointers. |
| * - Initializes the internal complex FFT data structure. |
| * \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 should be manually |
| * initialized as follows: |
| * <pre> |
| *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> is the length of the real transform; |
| * <code>fftLenBy2</code> length of the internal complex transform. |
| * <code>ifftFlagR</code> Selects forward (=0) or inverse (=1) transform. |
| * <code>bitReverseFlagR</code> Selects bit reversed output (=0) or normal order |
| * output (=1). |
| * <code>twidCoefRModifier</code> stride modifier for the twiddle factor table. |
| * The value is based on the FFT length; |
| * <code>pTwiddleAReal</code>points to the A array of twiddle coefficients; |
| * <code>pTwiddleBReal</code>points to the B array of twiddle coefficients; |
| * <code>pCfft</code> points to the CFFT Instance structure. The CFFT structure |
| * must also be initialized. Refer to arm_cfft_radix4_f32() for details regarding |
| * static initialization of the complex FFT instance structure. |
| */ |
| |
| /** |
| * @addtogroup RealFFT |
| * @{ |
| */ |
| |
| /** |
| * @brief Processing function for the floating-point real FFT. |
| * @param[in] *S points to an arm_rfft_fast_instance_f32 structure. |
| * @param[in] *p points to the input buffer. |
| * @param[in] *pOut points to the output buffer. |
| * @param[in] ifftFlag RFFT if flag is 0, RIFFT if flag is 1 |
| * @return none. |
| */ |
| |
| void arm_rfft_fast_f32( |
| arm_rfft_fast_instance_f32 * S, |
| float32_t * p, float32_t * pOut, |
| uint8_t ifftFlag) |
| { |
| arm_cfft_instance_f32 * Sint = &(S->Sint); |
| Sint->fftLen = S->fftLenRFFT / 2; |
| |
| /* Calculation of Real FFT */ |
| if(ifftFlag) |
| { |
| /* Real FFT compression */ |
| merge_rfft_f32(S, p, pOut); |
| |
| /* Complex radix-4 IFFT process */ |
| arm_cfft_f32( Sint, pOut, ifftFlag, 1); |
| } |
| else |
| { |
| /* Calculation of RFFT of input */ |
| arm_cfft_f32( Sint, p, ifftFlag, 1); |
| |
| /* Real FFT extraction */ |
| stage_rfft_f32(S, p, pOut); |
| } |
| } |
| |
| /** |
| * @} end of RealFFT group |
| */ |
