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Diffstat (limited to 'fw/cdc-dials/Drivers/CMSIS/DSP/Source/TransformFunctions/arm_rfft_fast_f32.c')
| -rw-r--r-- | fw/cdc-dials/Drivers/CMSIS/DSP/Source/TransformFunctions/arm_rfft_fast_f32.c | 317 |
1 files changed, 317 insertions, 0 deletions
diff --git a/fw/cdc-dials/Drivers/CMSIS/DSP/Source/TransformFunctions/arm_rfft_fast_f32.c b/fw/cdc-dials/Drivers/CMSIS/DSP/Source/TransformFunctions/arm_rfft_fast_f32.c new file mode 100644 index 0000000..08e06e0 --- /dev/null +++ b/fw/cdc-dials/Drivers/CMSIS/DSP/Source/TransformFunctions/arm_rfft_fast_f32.c @@ -0,0 +1,317 @@ +/* ----------------------------------------------------------------------
+ * 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
+*/
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