| /* ---------------------------------------------------------------------- |
| * Project: CMSIS DSP Library |
| * Title: arm_rfft_f32.c |
| * Description: RFFT & RIFFT Floating point process function |
| * |
| * $Date: 18. March 2019 |
| * $Revision: V1.6.0 |
| * |
| * Target Processor: Cortex-M cores |
| * -------------------------------------------------------------------- */ |
| /* |
| * Copyright (C) 2010-2019 ARM Limited or its affiliates. All rights reserved. |
| * |
| * SPDX-License-Identifier: Apache-2.0 |
| * |
| * Licensed under the Apache License, Version 2.0 (the License); you may |
| * not use this file except in compliance with the License. |
| * You may obtain a copy of the License at |
| * |
| * www.apache.org/licenses/LICENSE-2.0 |
| * |
| * Unless required by applicable law or agreed to in writing, software |
| * distributed under the License is distributed on an AS IS BASIS, WITHOUT |
| * WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied. |
| * See the License for the specific language governing permissions and |
| * limitations under the License. |
| */ |
| |
| #include "arm_math.h" |
| |
| void stage_rfft_f32( |
| const arm_rfft_fast_instance_f32 * S, |
| float32_t * p, |
| float32_t * pOut) |
| { |
| uint32_t k; /* Loop Counter */ |
| float32_t twR, twI; /* RFFT Twiddle coefficients */ |
| const 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( |
| const arm_rfft_fast_instance_f32 * S, |
| float32_t * p, |
| float32_t * pOut) |
| { |
| uint32_t k; /* Loop Counter */ |
| float32_t twR, twI; /* RFFT Twiddle coefficients */ |
| const 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 RealFFT 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 \ref arm_rfft_fast_f32() and \ref arm_rfft_fast_init_f32(). |
| The older functions \ref arm_rfft_f32() and \ref arm_rfft_init_f32() 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. |
| Looking at the data, we see that we can uniquely represent the FFT using only N/2 complex numbers. |
| These are packed into the output array in alternating real and imaginary components: |
| @par |
| X = { real[0], imag[0], real[1], imag[1], real[2], imag[2] ... |
| real[(N/2)-1], imag[(N/2)-1 } |
| @par |
| It happens that the first complex number (real[0], imag[0]) is actually |
| all real. real[0] represents the DC offset, and imag[0] should be 0. |
| (real[1], imag[1]) is the fundamental frequency, (real[2], imag[2]) is |
| the first harmonic and so on. |
| @par |
| 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 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 input buffer |
| @param[in] pOut points to output buffer |
| @param[in] ifftFlag |
| - value = 0: RFFT |
| - value = 1: RIFFT |
| @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 |
| */ |
