621 lines
17 KiB
C
621 lines
17 KiB
C
/* ----------------------------------------------------------------------
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* Project: CMSIS DSP Library
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* Title: arm_cfft_f32.c
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* Description: Combined Radix Decimation in Frequency CFFT Floating point processing function
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*
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* $Date: 27. January 2017
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* $Revision: V.1.5.1
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*
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* Target Processor: Cortex-M cores
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* -------------------------------------------------------------------- */
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/*
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* Copyright (C) 2010-2017 ARM Limited or its affiliates. All rights reserved.
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*
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* SPDX-License-Identifier: Apache-2.0
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*
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* Licensed under the Apache License, Version 2.0 (the License); you may
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* not use this file except in compliance with the License.
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* You may obtain a copy of the License at
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*
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* www.apache.org/licenses/LICENSE-2.0
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*
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* Unless required by applicable law or agreed to in writing, software
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* distributed under the License is distributed on an AS IS BASIS, WITHOUT
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* WARRANTIES OR CONDITIONS OF ANY KIND, either express or implied.
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* See the License for the specific language governing permissions and
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* limitations under the License.
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*/
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#include "arm_math.h"
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#include "arm_common_tables.h"
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extern void arm_radix8_butterfly_f32(
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float32_t * pSrc,
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uint16_t fftLen,
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const float32_t * pCoef,
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uint16_t twidCoefModifier);
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extern void arm_bitreversal_32(
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uint32_t * pSrc,
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const uint16_t bitRevLen,
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const uint16_t * pBitRevTable);
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/**
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* @ingroup groupTransforms
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*/
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/**
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* @defgroup ComplexFFT Complex FFT Functions
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*
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* \par
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* The Fast Fourier Transform (FFT) is an efficient algorithm for computing the
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* Discrete Fourier Transform (DFT). The FFT can be orders of magnitude faster
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* than the DFT, especially for long lengths.
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* The algorithms described in this section
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* operate on complex data. A separate set of functions is devoted to handling
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* of real sequences.
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* \par
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* There are separate algorithms for handling floating-point, Q15, and Q31 data
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* types. The algorithms available for each data type are described next.
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* \par
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* The FFT functions operate in-place. That is, the array holding the input data
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* will also be used to hold the corresponding result. The input data is complex
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* and contains <code>2*fftLen</code> interleaved values as shown below.
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* <pre> {real[0], imag[0], real[1], imag[1],..} </pre>
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* The FFT result will be contained in the same array and the frequency domain
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* values will have the same interleaving.
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*
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* \par Floating-point
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* The floating-point complex FFT uses a mixed-radix algorithm. Multiple radix-8
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* stages are performed along with a single radix-2 or radix-4 stage, as needed.
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* The algorithm supports lengths of [16, 32, 64, ..., 4096] and each length uses
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* a different twiddle factor table.
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* \par
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* The function uses the standard FFT definition and output values may grow by a
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* factor of <code>fftLen</code> when computing the forward transform. The
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* inverse transform includes a scale of <code>1/fftLen</code> as part of the
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* calculation and this matches the textbook definition of the inverse FFT.
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* \par
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* Pre-initialized data structures containing twiddle factors and bit reversal
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* tables are provided and defined in <code>arm_const_structs.h</code>. Include
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* this header in your function and then pass one of the constant structures as
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* an argument to arm_cfft_f32. For example:
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* \par
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* <code>arm_cfft_f32(arm_cfft_sR_f32_len64, pSrc, 1, 1)</code>
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* \par
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* computes a 64-point inverse complex FFT including bit reversal.
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* The data structures are treated as constant data and not modified during the
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* calculation. The same data structure can be reused for multiple transforms
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* including mixing forward and inverse transforms.
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* \par
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* Earlier releases of the library provided separate radix-2 and radix-4
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* algorithms that operated on floating-point data. These functions are still
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* provided but are deprecated. The older functions are slower and less general
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* than the new functions.
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* \par
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* An example of initialization of the constants for the arm_cfft_f32 function follows:
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* \code
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* const static arm_cfft_instance_f32 *S;
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* ...
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* switch (length) {
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* case 16:
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* S = &arm_cfft_sR_f32_len16;
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* break;
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* case 32:
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* S = &arm_cfft_sR_f32_len32;
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* break;
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* case 64:
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* S = &arm_cfft_sR_f32_len64;
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* break;
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* case 128:
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* S = &arm_cfft_sR_f32_len128;
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* break;
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* case 256:
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* S = &arm_cfft_sR_f32_len256;
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* break;
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* case 512:
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* S = &arm_cfft_sR_f32_len512;
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* break;
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* case 1024:
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* S = &arm_cfft_sR_f32_len1024;
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* break;
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* case 2048:
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* S = &arm_cfft_sR_f32_len2048;
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* break;
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* case 4096:
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* S = &arm_cfft_sR_f32_len4096;
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* break;
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* }
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* \endcode
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* \par Q15 and Q31
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* The floating-point complex FFT uses a mixed-radix algorithm. Multiple radix-4
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* stages are performed along with a single radix-2 stage, as needed.
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* The algorithm supports lengths of [16, 32, 64, ..., 4096] and each length uses
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* a different twiddle factor table.
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* \par
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* The function uses the standard FFT definition and output values may grow by a
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* factor of <code>fftLen</code> when computing the forward transform. The
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* inverse transform includes a scale of <code>1/fftLen</code> as part of the
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* calculation and this matches the textbook definition of the inverse FFT.
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* \par
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* Pre-initialized data structures containing twiddle factors and bit reversal
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* tables are provided and defined in <code>arm_const_structs.h</code>. Include
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* this header in your function and then pass one of the constant structures as
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* an argument to arm_cfft_q31. For example:
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* \par
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* <code>arm_cfft_q31(arm_cfft_sR_q31_len64, pSrc, 1, 1)</code>
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* \par
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* computes a 64-point inverse complex FFT including bit reversal.
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* The data structures are treated as constant data and not modified during the
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* calculation. The same data structure can be reused for multiple transforms
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* including mixing forward and inverse transforms.
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* \par
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* Earlier releases of the library provided separate radix-2 and radix-4
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* algorithms that operated on floating-point data. These functions are still
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* provided but are deprecated. The older functions are slower and less general
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* than the new functions.
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* \par
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* An example of initialization of the constants for the arm_cfft_q31 function follows:
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* \code
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* const static arm_cfft_instance_q31 *S;
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* ...
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* switch (length) {
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* case 16:
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* S = &arm_cfft_sR_q31_len16;
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* break;
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* case 32:
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* S = &arm_cfft_sR_q31_len32;
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* break;
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* case 64:
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* S = &arm_cfft_sR_q31_len64;
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* break;
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* case 128:
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* S = &arm_cfft_sR_q31_len128;
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* break;
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* case 256:
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* S = &arm_cfft_sR_q31_len256;
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* break;
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* case 512:
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* S = &arm_cfft_sR_q31_len512;
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* break;
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* case 1024:
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* S = &arm_cfft_sR_q31_len1024;
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* break;
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* case 2048:
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* S = &arm_cfft_sR_q31_len2048;
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* break;
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* case 4096:
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* S = &arm_cfft_sR_q31_len4096;
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* break;
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* }
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* \endcode
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*
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*/
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void arm_cfft_radix8by2_f32( arm_cfft_instance_f32 * S, float32_t * p1)
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{
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uint32_t L = S->fftLen;
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float32_t * pCol1, * pCol2, * pMid1, * pMid2;
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float32_t * p2 = p1 + L;
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const float32_t * tw = (float32_t *) S->pTwiddle;
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float32_t t1[4], t2[4], t3[4], t4[4], twR, twI;
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float32_t m0, m1, m2, m3;
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uint32_t l;
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pCol1 = p1;
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pCol2 = p2;
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// Define new length
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L >>= 1;
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// Initialize mid pointers
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pMid1 = p1 + L;
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pMid2 = p2 + L;
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// do two dot Fourier transform
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for ( l = L >> 2; l > 0; l-- )
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{
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t1[0] = p1[0];
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t1[1] = p1[1];
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t1[2] = p1[2];
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t1[3] = p1[3];
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t2[0] = p2[0];
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t2[1] = p2[1];
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t2[2] = p2[2];
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t2[3] = p2[3];
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t3[0] = pMid1[0];
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t3[1] = pMid1[1];
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t3[2] = pMid1[2];
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t3[3] = pMid1[3];
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t4[0] = pMid2[0];
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t4[1] = pMid2[1];
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t4[2] = pMid2[2];
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t4[3] = pMid2[3];
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*p1++ = t1[0] + t2[0];
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*p1++ = t1[1] + t2[1];
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*p1++ = t1[2] + t2[2];
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*p1++ = t1[3] + t2[3]; // col 1
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t2[0] = t1[0] - t2[0];
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t2[1] = t1[1] - t2[1];
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t2[2] = t1[2] - t2[2];
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t2[3] = t1[3] - t2[3]; // for col 2
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*pMid1++ = t3[0] + t4[0];
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*pMid1++ = t3[1] + t4[1];
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*pMid1++ = t3[2] + t4[2];
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*pMid1++ = t3[3] + t4[3]; // col 1
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t4[0] = t4[0] - t3[0];
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t4[1] = t4[1] - t3[1];
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t4[2] = t4[2] - t3[2];
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t4[3] = t4[3] - t3[3]; // for col 2
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twR = *tw++;
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twI = *tw++;
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// multiply by twiddle factors
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m0 = t2[0] * twR;
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m1 = t2[1] * twI;
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m2 = t2[1] * twR;
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m3 = t2[0] * twI;
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// R = R * Tr - I * Ti
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*p2++ = m0 + m1;
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// I = I * Tr + R * Ti
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*p2++ = m2 - m3;
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// use vertical symmetry
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// 0.9988 - 0.0491i <==> -0.0491 - 0.9988i
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m0 = t4[0] * twI;
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m1 = t4[1] * twR;
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m2 = t4[1] * twI;
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m3 = t4[0] * twR;
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*pMid2++ = m0 - m1;
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*pMid2++ = m2 + m3;
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twR = *tw++;
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twI = *tw++;
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m0 = t2[2] * twR;
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m1 = t2[3] * twI;
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m2 = t2[3] * twR;
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m3 = t2[2] * twI;
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*p2++ = m0 + m1;
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*p2++ = m2 - m3;
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m0 = t4[2] * twI;
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m1 = t4[3] * twR;
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m2 = t4[3] * twI;
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m3 = t4[2] * twR;
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*pMid2++ = m0 - m1;
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*pMid2++ = m2 + m3;
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}
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// first col
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arm_radix8_butterfly_f32( pCol1, L, (float32_t *) S->pTwiddle, 2U);
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// second col
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arm_radix8_butterfly_f32( pCol2, L, (float32_t *) S->pTwiddle, 2U);
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}
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void arm_cfft_radix8by4_f32( arm_cfft_instance_f32 * S, float32_t * p1)
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{
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uint32_t L = S->fftLen >> 1;
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float32_t * pCol1, *pCol2, *pCol3, *pCol4, *pEnd1, *pEnd2, *pEnd3, *pEnd4;
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const float32_t *tw2, *tw3, *tw4;
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float32_t * p2 = p1 + L;
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float32_t * p3 = p2 + L;
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float32_t * p4 = p3 + L;
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float32_t t2[4], t3[4], t4[4], twR, twI;
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float32_t p1ap3_0, p1sp3_0, p1ap3_1, p1sp3_1;
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float32_t m0, m1, m2, m3;
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uint32_t l, twMod2, twMod3, twMod4;
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pCol1 = p1; // points to real values by default
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pCol2 = p2;
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pCol3 = p3;
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pCol4 = p4;
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pEnd1 = p2 - 1; // points to imaginary values by default
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pEnd2 = p3 - 1;
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pEnd3 = p4 - 1;
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pEnd4 = pEnd3 + L;
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tw2 = tw3 = tw4 = (float32_t *) S->pTwiddle;
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L >>= 1;
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// do four dot Fourier transform
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twMod2 = 2;
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twMod3 = 4;
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twMod4 = 6;
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// TOP
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p1ap3_0 = p1[0] + p3[0];
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p1sp3_0 = p1[0] - p3[0];
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p1ap3_1 = p1[1] + p3[1];
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p1sp3_1 = p1[1] - p3[1];
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// col 2
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t2[0] = p1sp3_0 + p2[1] - p4[1];
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t2[1] = p1sp3_1 - p2[0] + p4[0];
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// col 3
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t3[0] = p1ap3_0 - p2[0] - p4[0];
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t3[1] = p1ap3_1 - p2[1] - p4[1];
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// col 4
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t4[0] = p1sp3_0 - p2[1] + p4[1];
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t4[1] = p1sp3_1 + p2[0] - p4[0];
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// col 1
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*p1++ = p1ap3_0 + p2[0] + p4[0];
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*p1++ = p1ap3_1 + p2[1] + p4[1];
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// Twiddle factors are ones
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*p2++ = t2[0];
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*p2++ = t2[1];
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*p3++ = t3[0];
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*p3++ = t3[1];
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*p4++ = t4[0];
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*p4++ = t4[1];
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tw2 += twMod2;
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tw3 += twMod3;
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tw4 += twMod4;
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for (l = (L - 2) >> 1; l > 0; l-- )
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{
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// TOP
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p1ap3_0 = p1[0] + p3[0];
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p1sp3_0 = p1[0] - p3[0];
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p1ap3_1 = p1[1] + p3[1];
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p1sp3_1 = p1[1] - p3[1];
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// col 2
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t2[0] = p1sp3_0 + p2[1] - p4[1];
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t2[1] = p1sp3_1 - p2[0] + p4[0];
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// col 3
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t3[0] = p1ap3_0 - p2[0] - p4[0];
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t3[1] = p1ap3_1 - p2[1] - p4[1];
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// col 4
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t4[0] = p1sp3_0 - p2[1] + p4[1];
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t4[1] = p1sp3_1 + p2[0] - p4[0];
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// col 1 - top
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*p1++ = p1ap3_0 + p2[0] + p4[0];
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*p1++ = p1ap3_1 + p2[1] + p4[1];
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// BOTTOM
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p1ap3_1 = pEnd1[-1] + pEnd3[-1];
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p1sp3_1 = pEnd1[-1] - pEnd3[-1];
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p1ap3_0 = pEnd1[0] + pEnd3[0];
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p1sp3_0 = pEnd1[0] - pEnd3[0];
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// col 2
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t2[2] = pEnd2[0] - pEnd4[0] + p1sp3_1;
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t2[3] = pEnd1[0] - pEnd3[0] - pEnd2[-1] + pEnd4[-1];
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// col 3
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t3[2] = p1ap3_1 - pEnd2[-1] - pEnd4[-1];
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t3[3] = p1ap3_0 - pEnd2[0] - pEnd4[0];
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// col 4
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t4[2] = pEnd2[0] - pEnd4[0] - p1sp3_1;
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t4[3] = pEnd4[-1] - pEnd2[-1] - p1sp3_0;
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// col 1 - Bottom
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*pEnd1-- = p1ap3_0 + pEnd2[0] + pEnd4[0];
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*pEnd1-- = p1ap3_1 + pEnd2[-1] + pEnd4[-1];
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// COL 2
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// read twiddle factors
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twR = *tw2++;
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twI = *tw2++;
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// multiply by twiddle factors
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// let Z1 = a + i(b), Z2 = c + i(d)
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// => Z1 * Z2 = (a*c - b*d) + i(b*c + a*d)
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// Top
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m0 = t2[0] * twR;
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m1 = t2[1] * twI;
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m2 = t2[1] * twR;
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m3 = t2[0] * twI;
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*p2++ = m0 + m1;
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*p2++ = m2 - m3;
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// use vertical symmetry col 2
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// 0.9997 - 0.0245i <==> 0.0245 - 0.9997i
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// Bottom
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m0 = t2[3] * twI;
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m1 = t2[2] * twR;
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m2 = t2[2] * twI;
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m3 = t2[3] * twR;
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*pEnd2-- = m0 - m1;
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*pEnd2-- = m2 + m3;
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// COL 3
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twR = tw3[0];
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twI = tw3[1];
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tw3 += twMod3;
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// Top
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m0 = t3[0] * twR;
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m1 = t3[1] * twI;
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m2 = t3[1] * twR;
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m3 = t3[0] * twI;
|
|
|
|
*p3++ = m0 + m1;
|
|
*p3++ = m2 - m3;
|
|
// use vertical symmetry col 3
|
|
// 0.9988 - 0.0491i <==> -0.9988 - 0.0491i
|
|
// Bottom
|
|
m0 = -t3[3] * twR;
|
|
m1 = t3[2] * twI;
|
|
m2 = t3[2] * twR;
|
|
m3 = t3[3] * twI;
|
|
|
|
*pEnd3-- = m0 - m1;
|
|
*pEnd3-- = m3 - m2;
|
|
|
|
// COL 4
|
|
twR = tw4[0];
|
|
twI = tw4[1];
|
|
tw4 += twMod4;
|
|
// Top
|
|
m0 = t4[0] * twR;
|
|
m1 = t4[1] * twI;
|
|
m2 = t4[1] * twR;
|
|
m3 = t4[0] * twI;
|
|
|
|
*p4++ = m0 + m1;
|
|
*p4++ = m2 - m3;
|
|
// use vertical symmetry col 4
|
|
// 0.9973 - 0.0736i <==> -0.0736 + 0.9973i
|
|
// Bottom
|
|
m0 = t4[3] * twI;
|
|
m1 = t4[2] * twR;
|
|
m2 = t4[2] * twI;
|
|
m3 = t4[3] * twR;
|
|
|
|
*pEnd4-- = m0 - m1;
|
|
*pEnd4-- = m2 + m3;
|
|
}
|
|
|
|
//MIDDLE
|
|
// Twiddle factors are
|
|
// 1.0000 0.7071-0.7071i -1.0000i -0.7071-0.7071i
|
|
p1ap3_0 = p1[0] + p3[0];
|
|
p1sp3_0 = p1[0] - p3[0];
|
|
p1ap3_1 = p1[1] + p3[1];
|
|
p1sp3_1 = p1[1] - p3[1];
|
|
|
|
// col 2
|
|
t2[0] = p1sp3_0 + p2[1] - p4[1];
|
|
t2[1] = p1sp3_1 - p2[0] + p4[0];
|
|
// col 3
|
|
t3[0] = p1ap3_0 - p2[0] - p4[0];
|
|
t3[1] = p1ap3_1 - p2[1] - p4[1];
|
|
// col 4
|
|
t4[0] = p1sp3_0 - p2[1] + p4[1];
|
|
t4[1] = p1sp3_1 + p2[0] - p4[0];
|
|
// col 1 - Top
|
|
*p1++ = p1ap3_0 + p2[0] + p4[0];
|
|
*p1++ = p1ap3_1 + p2[1] + p4[1];
|
|
|
|
// COL 2
|
|
twR = tw2[0];
|
|
twI = tw2[1];
|
|
|
|
m0 = t2[0] * twR;
|
|
m1 = t2[1] * twI;
|
|
m2 = t2[1] * twR;
|
|
m3 = t2[0] * twI;
|
|
|
|
*p2++ = m0 + m1;
|
|
*p2++ = m2 - m3;
|
|
// COL 3
|
|
twR = tw3[0];
|
|
twI = tw3[1];
|
|
|
|
m0 = t3[0] * twR;
|
|
m1 = t3[1] * twI;
|
|
m2 = t3[1] * twR;
|
|
m3 = t3[0] * twI;
|
|
|
|
*p3++ = m0 + m1;
|
|
*p3++ = m2 - m3;
|
|
// COL 4
|
|
twR = tw4[0];
|
|
twI = tw4[1];
|
|
|
|
m0 = t4[0] * twR;
|
|
m1 = t4[1] * twI;
|
|
m2 = t4[1] * twR;
|
|
m3 = t4[0] * twI;
|
|
|
|
*p4++ = m0 + m1;
|
|
*p4++ = m2 - m3;
|
|
|
|
// first col
|
|
arm_radix8_butterfly_f32( pCol1, L, (float32_t *) S->pTwiddle, 4U);
|
|
// second col
|
|
arm_radix8_butterfly_f32( pCol2, L, (float32_t *) S->pTwiddle, 4U);
|
|
// third col
|
|
arm_radix8_butterfly_f32( pCol3, L, (float32_t *) S->pTwiddle, 4U);
|
|
// fourth col
|
|
arm_radix8_butterfly_f32( pCol4, L, (float32_t *) S->pTwiddle, 4U);
|
|
}
|
|
|
|
/**
|
|
* @addtogroup ComplexFFT
|
|
* @{
|
|
*/
|
|
|
|
/**
|
|
* @details
|
|
* @brief Processing function for the floating-point complex FFT.
|
|
* @param[in] *S points to an instance of the floating-point CFFT structure.
|
|
* @param[in, out] *p1 points to the complex data buffer of size <code>2*fftLen</code>. Processing occurs in-place.
|
|
* @param[in] ifftFlag flag that selects forward (ifftFlag=0) or inverse (ifftFlag=1) transform.
|
|
* @param[in] bitReverseFlag flag that enables (bitReverseFlag=1) or disables (bitReverseFlag=0) bit reversal of output.
|
|
* @return none.
|
|
*/
|
|
|
|
void arm_cfft_f32(
|
|
const arm_cfft_instance_f32 * S,
|
|
float32_t * p1,
|
|
uint8_t ifftFlag,
|
|
uint8_t bitReverseFlag)
|
|
{
|
|
uint32_t L = S->fftLen, l;
|
|
float32_t invL, * pSrc;
|
|
|
|
if (ifftFlag == 1U)
|
|
{
|
|
/* Conjugate input data */
|
|
pSrc = p1 + 1;
|
|
for(l=0; l<L; l++)
|
|
{
|
|
*pSrc = -*pSrc;
|
|
pSrc += 2;
|
|
}
|
|
}
|
|
|
|
switch (L)
|
|
{
|
|
case 16:
|
|
case 128:
|
|
case 1024:
|
|
arm_cfft_radix8by2_f32 ( (arm_cfft_instance_f32 *) S, p1);
|
|
break;
|
|
case 32:
|
|
case 256:
|
|
case 2048:
|
|
arm_cfft_radix8by4_f32 ( (arm_cfft_instance_f32 *) S, p1);
|
|
break;
|
|
case 64:
|
|
case 512:
|
|
case 4096:
|
|
arm_radix8_butterfly_f32( p1, L, (float32_t *) S->pTwiddle, 1);
|
|
break;
|
|
}
|
|
|
|
if ( bitReverseFlag )
|
|
arm_bitreversal_32((uint32_t*)p1,S->bitRevLength,S->pBitRevTable);
|
|
|
|
if (ifftFlag == 1U)
|
|
{
|
|
invL = 1.0f/(float32_t)L;
|
|
/* Conjugate and scale output data */
|
|
pSrc = p1;
|
|
for(l=0; l<L; l++)
|
|
{
|
|
*pSrc++ *= invL ;
|
|
*pSrc = -(*pSrc) * invL;
|
|
pSrc++;
|
|
}
|
|
}
|
|
}
|
|
|
|
/**
|
|
* @} end of ComplexFFT group
|
|
*/
|