/* ----------------------------------------------------------------------
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* Copyright (C) 2010-2012 ARM Limited. All rights reserved.
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*
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* $Date: 17. January 2013
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* $Revision: V1.4.0
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*
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* Project: CMSIS DSP Library
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* Title: arm_convolution_example_f32.c
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*
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* Description: Example code demonstrating Convolution of two input signals using fft.
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*
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* Target Processor: Cortex-M4/Cortex-M3
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*
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* Redistribution and use in source and binary forms, with or without
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* modification, are permitted provided that the following conditions
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* are met:
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* - Redistributions of source code must retain the above copyright
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* notice, this list of conditions and the following disclaimer.
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* - Redistributions in binary form must reproduce the above copyright
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* notice, this list of conditions and the following disclaimer in
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* the documentation and/or other materials provided with the
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* distribution.
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* - Neither the name of ARM LIMITED nor the names of its contributors
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* may be used to endorse or promote products derived from this
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* software without specific prior written permission.
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*
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* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
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* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
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* LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS
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* FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE
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* COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT,
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* INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING,
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* BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES;
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* LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER
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* CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT
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* LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN
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* ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE
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* POSSIBILITY OF SUCH DAMAGE.
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* -------------------------------------------------------------------- */
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/**
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* @ingroup groupExamples
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*/
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/**
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* @defgroup ConvolutionExample Convolution Example
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*
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* \par Description:
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* \par
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* Demonstrates the convolution theorem with the use of the Complex FFT, Complex-by-Complex
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* Multiplication, and Support Functions.
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*
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* \par Algorithm:
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* \par
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* The convolution theorem states that convolution in the time domain corresponds to
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* multiplication in the frequency domain. Therefore, the Fourier transform of the convoution of
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* two signals is equal to the product of their individual Fourier transforms.
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* The Fourier transform of a signal can be evaluated efficiently using the Fast Fourier Transform (FFT).
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* \par
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* Two input signals, <code>a[n]</code> and <code>b[n]</code>, with lengths \c n1 and \c n2 respectively,
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* are zero padded so that their lengths become \c N, which is greater than or equal to <code>(n1+n2-1)</code>
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* and is a power of 4 as FFT implementation is radix-4.
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* The convolution of <code>a[n]</code> and <code>b[n]</code> is obtained by taking the FFT of the input
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* signals, multiplying the Fourier transforms of the two signals, and taking the inverse FFT of
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* the multiplied result.
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* \par
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* This is denoted by the following equations:
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* <pre> A[k] = FFT(a[n],N)
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* B[k] = FFT(b[n],N)
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* conv(a[n], b[n]) = IFFT(A[k] * B[k], N)</pre>
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* where <code>A[k]</code> and <code>B[k]</code> are the N-point FFTs of the signals <code>a[n]</code>
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* and <code>b[n]</code> respectively.
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* The length of the convolved signal is <code>(n1+n2-1)</code>.
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*
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* \par Block Diagram:
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* \par
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* \image html Convolution.gif
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*
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* \par Variables Description:
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* \par
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* \li \c testInputA_f32 points to the first input sequence
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* \li \c srcALen length of the first input sequence
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* \li \c testInputB_f32 points to the second input sequence
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* \li \c srcBLen length of the second input sequence
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* \li \c outLen length of convolution output sequence, <code>(srcALen + srcBLen - 1)</code>
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* \li \c AxB points to the output array where the product of individual FFTs of inputs is stored.
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*
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* \par CMSIS DSP Software Library Functions Used:
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* \par
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* - arm_fill_f32()
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* - arm_copy_f32()
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* - arm_cfft_radix4_init_f32()
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* - arm_cfft_radix4_f32()
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* - arm_cmplx_mult_cmplx_f32()
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*
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* <b> Refer </b>
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* \link arm_convolution_example_f32.c \endlink
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*
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*/
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/** \example arm_convolution_example_f32.c
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*/
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#include "arm_math.h"
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#include "math_helper.h"
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/* ----------------------------------------------------------------------
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* Defines each of the tests performed
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* ------------------------------------------------------------------- */
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#define MAX_BLOCKSIZE 128
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#define DELTA (0.000001f)
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#define SNR_THRESHOLD 90
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/* ----------------------------------------------------------------------
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* Declare I/O buffers
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* ------------------------------------------------------------------- */
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float32_t Ak[MAX_BLOCKSIZE]; /* Input A */
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float32_t Bk[MAX_BLOCKSIZE]; /* Input B */
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float32_t AxB[MAX_BLOCKSIZE * 2]; /* Output */
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/* ----------------------------------------------------------------------
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* Test input data for Floating point Convolution example for 32-blockSize
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* Generated by the MATLAB randn() function
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* ------------------------------------------------------------------- */
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float32_t testInputA_f32[64] =
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{
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-0.808920, 1.357369, 1.180861, -0.504544, 1.762637, -0.703285,
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1.696966, 0.620571, -0.151093, -0.100235, -0.872382, -0.403579,
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-0.860749, -0.382648, -1.052338, 0.128113, -0.646269, 1.093377,
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-2.209198, 0.471706, 0.408901, 1.266242, 0.598252, 1.176827,
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-0.203421, 0.213596, -0.851964, -0.466958, 0.021841, -0.698938,
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-0.604107, 0.461778, -0.318219, 0.942520, 0.577585, 0.417619,
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0.614665, 0.563679, -1.295073, -0.764437, 0.952194, -0.859222,
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-0.618554, -2.268542, -1.210592, 1.655853, -2.627219, -0.994249,
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-1.374704, 0.343799, 0.025619, 1.227481, -0.708031, 0.069355,
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-1.845228, -1.570886, 1.010668, -1.802084, 1.630088, 1.286090,
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-0.161050, -0.940794, 0.367961, 0.291907
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};
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float32_t testInputB_f32[64] =
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{
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0.933724, 0.046881, 1.316470, 0.438345, 0.332682, 2.094885,
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0.512081, 0.035546, 0.050894, -2.320371, 0.168711, -1.830493,
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-0.444834, -1.003242, -0.531494, -1.365600, -0.155420, -0.757692,
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-0.431880, -0.380021, 0.096243, -0.695835, 0.558850, -1.648962,
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0.020369, -0.363630, 0.887146, 0.845503, -0.252864, -0.330397,
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1.269131, -1.109295, -1.027876, 0.135940, 0.116721, -0.293399,
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-1.349799, 0.166078, -0.802201, 0.369367, -0.964568, -2.266011,
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0.465178, 0.651222, -0.325426, 0.320245, -0.784178, -0.579456,
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0.093374, 0.604778, -0.048225, 0.376297, -0.394412, 0.578182,
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-1.218141, -1.387326, 0.692462, -0.631297, 0.153137, -0.638952,
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0.635474, -0.970468, 1.334057, -0.111370
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};
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const float testRefOutput_f32[127] =
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{
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-0.818943, 1.229484, -0.533664, 1.016604, 0.341875, -1.963656,
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5.171476, 3.478033, 7.616361, 6.648384, 0.479069, 1.792012,
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-1.295591, -7.447818, 0.315830, -10.657445, -2.483469, -6.524236,
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-7.380591, -3.739005, -8.388957, 0.184147, -1.554888, 3.786508,
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-1.684421, 5.400610, -1.578126, 7.403361, 8.315999, 2.080267,
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11.077776, 2.749673, 7.138962, 2.748762, 0.660363, 0.981552,
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1.442275, 0.552721, -2.576892, 4.703989, 0.989156, 8.759344,
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-0.564825, -3.994680, 0.954710, -5.014144, 6.592329, 1.599488,
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-13.979146, -0.391891, -4.453369, -2.311242, -2.948764, 1.761415,
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-0.138322, 10.433007, -2.309103, 4.297153, 8.535523, 3.209462,
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8.695819, 5.569919, 2.514304, 5.582029, 2.060199, 0.642280,
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7.024616, 1.686615, -6.481756, 1.343084, -3.526451, 1.099073,
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-2.965764, -0.173723, -4.111484, 6.528384, -6.965658, 1.726291,
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1.535172, 11.023435, 2.338401, -4.690188, 1.298210, 3.943885,
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8.407885, 5.168365, 0.684131, 1.559181, 1.859998, 2.852417,
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8.574070, -6.369078, 6.023458, 11.837963, -6.027632, 4.469678,
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-6.799093, -2.674048, 6.250367, -6.809971, -3.459360, 9.112410,
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-2.711621, -1.336678, 1.564249, -1.564297, -1.296760, 8.904013,
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-3.230109, 6.878013, -7.819823, 3.369909, -1.657410, -2.007358,
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-4.112825, 1.370685, -3.420525, -6.276605, 3.244873, -3.352638,
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1.545372, 0.902211, 0.197489, -1.408732, 0.523390, 0.348440, 0
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};
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/* ----------------------------------------------------------------------
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* Declare Global variables
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* ------------------------------------------------------------------- */
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uint32_t srcALen = 64; /* Length of Input A */
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uint32_t srcBLen = 64; /* Length of Input B */
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uint32_t outLen; /* Length of convolution output */
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float32_t snr; /* output SNR */
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int32_t main(void)
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{
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arm_status status; /* Status of the example */
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arm_cfft_radix4_instance_f32 cfft_instance; /* CFFT Structure instance */
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/* CFFT Structure instance pointer */
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arm_cfft_radix4_instance_f32 *cfft_instance_ptr =
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(arm_cfft_radix4_instance_f32*) &cfft_instance;
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/* output length of convolution */
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outLen = srcALen + srcBLen - 1;
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/* Initialise the fft input buffers with all zeros */
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arm_fill_f32(0.0, Ak, MAX_BLOCKSIZE);
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arm_fill_f32(0.0, Bk, MAX_BLOCKSIZE);
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/* Copy the input values to the fft input buffers */
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arm_copy_f32(testInputA_f32, Ak, MAX_BLOCKSIZE/2);
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arm_copy_f32(testInputB_f32, Bk, MAX_BLOCKSIZE/2);
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/* Initialize the CFFT function to compute 64 point fft */
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status = arm_cfft_radix4_init_f32(cfft_instance_ptr, 64, 0, 1);
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/* Transform input a[n] from time domain to frequency domain A[k] */
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arm_cfft_radix4_f32(cfft_instance_ptr, Ak);
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/* Transform input b[n] from time domain to frequency domain B[k] */
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arm_cfft_radix4_f32(cfft_instance_ptr, Bk);
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/* Complex Multiplication of the two input buffers in frequency domain */
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arm_cmplx_mult_cmplx_f32(Ak, Bk, AxB, MAX_BLOCKSIZE/2);
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/* Initialize the CIFFT function to compute 64 point ifft */
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status = arm_cfft_radix4_init_f32(cfft_instance_ptr, 64, 1, 1);
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/* Transform the multiplication output from frequency domain to time domain,
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that gives the convolved output */
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arm_cfft_radix4_f32(cfft_instance_ptr, AxB);
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/* SNR Calculation */
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snr = arm_snr_f32((float32_t *)testRefOutput_f32, AxB, srcALen + srcBLen - 1);
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/* Compare the SNR with threshold to test whether the
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computed output is matched with the reference output values. */
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if ( snr > SNR_THRESHOLD)
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{
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status = ARM_MATH_SUCCESS;
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}
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if ( status != ARM_MATH_SUCCESS)
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{
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while (1);
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}
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while (1); /* main function does not return */
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}
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/** \endlink */
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