From 86608c6770cf08c138a2bdab5855072f64be09ef Mon Sep 17 00:00:00 2001 From: joshua Date: Sat, 30 Dec 2023 23:54:31 -0500 Subject: initial commit --- .../Source/TransformFunctions/arm_rfft_fast_f32.c | 320 +++++++++++++++++++++ 1 file changed, 320 insertions(+) create mode 100644 Drivers/CMSIS/DSP/Source/TransformFunctions/arm_rfft_fast_f32.c (limited to 'Drivers/CMSIS/DSP/Source/TransformFunctions/arm_rfft_fast_f32.c') diff --git a/Drivers/CMSIS/DSP/Source/TransformFunctions/arm_rfft_fast_f32.c b/Drivers/CMSIS/DSP/Source/TransformFunctions/arm_rfft_fast_f32.c new file mode 100644 index 0000000..ebaa7d9 --- /dev/null +++ b/Drivers/CMSIS/DSP/Source/TransformFunctions/arm_rfft_fast_f32.c @@ -0,0 +1,320 @@ +/* ---------------------------------------------------------------------- + * 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: + 
+      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};
+
+ where fftLenReal is the length of the real transform; + fftLenBy2 length of the internal complex transform. + ifftFlagR Selects forward (=0) or inverse (=1) transform. + bitReverseFlagR Selects bit reversed output (=0) or normal order + output (=1). + twidCoefRModifier stride modifier for the twiddle factor table. + The value is based on the FFT length; + pTwiddleARealpoints to the A array of twiddle coefficients; + pTwiddleBRealpoints to the B array of twiddle coefficients; + pCfft 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 +*/ -- cgit v1.2.3