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Diffstat (limited to 'DSP_Lib/Source/TransformFunctions/arm_rfft_fast_f32.c')
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1 files changed, 353 insertions, 0 deletions
diff --git a/DSP_Lib/Source/TransformFunctions/arm_rfft_fast_f32.c b/DSP_Lib/Source/TransformFunctions/arm_rfft_fast_f32.c new file mode 100644 index 0000000..d4970b6 --- /dev/null +++ b/DSP_Lib/Source/TransformFunctions/arm_rfft_fast_f32.c @@ -0,0 +1,353 @@ +/* ---------------------------------------------------------------------- +* 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 +*/ |