/* ----------------------------------------------------------------------
|
* Project: CMSIS DSP Library
|
* Title: arm_rfft_f32.c
|
* Description: RFFT & RIFFT Floating point process function
|
*
|
* $Date: 27. January 2017
|
* $Revision: V.1.5.1
|
*
|
* Target Processor: Cortex-M cores
|
* -------------------------------------------------------------------- */
|
/*
|
* Copyright (C) 2010-2017 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(
|
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 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 arm_rfft_fast_f32() and arm_rfft_fast_init_f32().
|
* The older functions arm_rfft_f32() and 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 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
|
*/
|
