| /* ---------------------------------------------------------------------- | |
| * Project: CMSIS DSP Library | |
| * Title: arm_rfft_fast_f64.c | |
| * Description: RFFT & RIFFT Double precision Floating point process function | |
| * | |
| * $Date: 23 April 2021 | |
| * $Revision: V1.9.0 | |
| * | |
| * Target Processor: Cortex-M and Cortex-A cores | |
| * -------------------------------------------------------------------- */ | |
| /* | |
| * Copyright (C) 2010-2021 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. | |
| */ | |
| void stage_rfft_f64( | |
| const arm_rfft_fast_instance_f64 * S, | |
| float64_t * p, | |
| float64_t * pOut) | |
| { | |
| uint32_t k; /* Loop Counter */ | |
| float64_t twR, twI; /* RFFT Twiddle coefficients */ | |
| const float64_t * pCoeff = S->pTwiddleRFFT; /* Points to RFFT Twiddle factors */ | |
| float64_t *pA = p; /* increasing pointer */ | |
| float64_t *pB = p; /* decreasing pointer */ | |
| float64_t xAR, xAI, xBR, xBI; /* temporary variables */ | |
| float64_t t1a, t1b; /* temporary variables */ | |
| float64_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++ = 0.5 * ( t1a + t1b ); | |
| *pOut++ = 0.5 * ( 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++ = 0.5 * (xAR + xBR + p0 + p3 ); //xAR | |
| *pOut++ = 0.5 * (xAI - xBI + p1 - p2 ); //xAI | |
| pA += 2; | |
| pB -= 2; | |
| k--; | |
| } while (k > 0U); | |
| } | |
| /* Prepares data for inverse cfft */ | |
| void merge_rfft_f64( | |
| const arm_rfft_fast_instance_f64 * S, | |
| float64_t * p, | |
| float64_t * pOut) | |
| { | |
| uint32_t k; /* Loop Counter */ | |
| float64_t twR, twI; /* RFFT Twiddle coefficients */ | |
| const float64_t *pCoeff = S->pTwiddleRFFT; /* Points to RFFT Twiddle factors */ | |
| float64_t *pA = p; /* increasing pointer */ | |
| float64_t *pB = p; /* decreasing pointer */ | |
| float64_t xAR, xAI, xBR, xBI; /* temporary variables */ | |
| float64_t t1a, t1b, r, s, t, u; /* temporary variables */ | |
| k = (S->Sint).fftLen - 1; | |
| xAR = pA[0]; | |
| xAI = pA[1]; | |
| pCoeff += 2 ; | |
| *pOut++ = 0.5 * ( xAR + xAI ); | |
| *pOut++ = 0.5 * ( 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++ = 0.5 * (xAR + xBR - r - s ); //xAR | |
| *pOut++ = 0.5 * (xAI - xBI + t - u ); //xAI | |
| pA += 2; | |
| pB -= 2; | |
| k--; | |
| } | |
| } | |
| /** | |
| @ingroup groupTransforms | |
| */ | |
| /** | |
| @addtogroup RealFFT | |
| @{ | |
| */ | |
| /** | |
| @brief Processing function for the Double Precision floating-point real FFT. | |
| @param[in] S points to an arm_rfft_fast_instance_f64 structure | |
| @param[in] p points to input buffer (Source buffer is modified by this function.) | |
| @param[in] pOut points to output buffer | |
| @param[in] ifftFlag | |
| - value = 0: RFFT | |
| - value = 1: RIFFT | |
| @return none | |
| */ | |
| void arm_rfft_fast_f64( | |
| arm_rfft_fast_instance_f64 * S, | |
| float64_t * p, | |
| float64_t * pOut, | |
| uint8_t ifftFlag) | |
| { | |
| arm_cfft_instance_f64 * Sint = &(S->Sint); | |
| Sint->fftLen = S->fftLenRFFT / 2; | |
| /* Calculation of Real FFT */ | |
| if (ifftFlag) | |
| { | |
| /* Real FFT compression */ | |
| merge_rfft_f64(S, p, pOut); | |
| /* Complex radix-4 IFFT process */ | |
| arm_cfft_f64( Sint, pOut, ifftFlag, 1); | |
| } | |
| else | |
| { | |
| /* Calculation of RFFT of input */ | |
| arm_cfft_f64( Sint, p, ifftFlag, 1); | |
| /* Real FFT extraction */ | |
| stage_rfft_f64(S, p, pOut); | |
| } | |
| } | |
| /** | |
| * @} end of RealFFT group | |
| */ | |