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/* ----------------------------------------------------------------------
* 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.
*/
#include "arm_compiler_specific.h"
#include "dsp/transform_functions.h"
static void stage_rfft_f64(
const arm_rfft_fast_instance_f64 * S,
const 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 */
const float64_t *pA = p; /* increasing pointer */
const 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 */
static void merge_rfft_f64(
const arm_rfft_fast_instance_f64 * S,
const 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 */
const float64_t *pA = p; /* increasing pointer */
const 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 RealFFT
*/
/**
@defgroup RealFFTF64 Real FFT F64 Functions
*/
/**
@addtogroup RealFFTF64
@{
*/
/**
@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
@par Size of buffers according to the target architecture and datatype:
They are described on the page \ref transformbuffers "transform buffers".
*/
ARM_DSP_ATTRIBUTE 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 RealFFTF64 group
*/
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