/* ----------------------------------------------------------------------
* Copyright (C) 2010-2012 ARM Limited. All rights reserved.
*
* $Date: 17. January 2013
* $Revision: V1.4.0
*
* Project: CMSIS DSP Library
* Title: arm_convolution_example_f32.c
*
* Description: Example code demonstrating Convolution of two input signals using fft.
*
* Target Processor: Cortex-M4/Cortex-M3
*
* Redistribution and use in source and binary forms, with or without
* modification, are permitted provided that the following conditions
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* notice, this list of conditions and the following disclaimer.
* - Redistributions in binary form must reproduce the above copyright
* notice, this list of conditions and the following disclaimer in
* the documentation and/or other materials provided with the
* distribution.
* - Neither the name of ARM LIMITED nor the names of its contributors
* may be used to endorse or promote products derived from this
* software without specific prior written permission.
*
* THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS
* "AS IS" AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT
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* -------------------------------------------------------------------- */
/**
* @ingroup groupExamples
*/
/**
* @defgroup ConvolutionExample Convolution Example
*
* \par Description:
* \par
* Demonstrates the convolution theorem with the use of the Complex FFT, Complex-by-Complex
* Multiplication, and Support Functions.
*
* \par Algorithm:
* \par
* The convolution theorem states that convolution in the time domain corresponds to
* multiplication in the frequency domain. Therefore, the Fourier transform of the convoution of
* two signals is equal to the product of their individual Fourier transforms.
* The Fourier transform of a signal can be evaluated efficiently using the Fast Fourier Transform (FFT).
* \par
* Two input signals, <code>a[n]</code> and <code>b[n]</code>, with lengths \c n1 and \c n2 respectively,
* are zero padded so that their lengths become \c N, which is greater than or equal to <code>(n1+n2-1)</code>
* and is a power of 4 as FFT implementation is radix-4.
* The convolution of <code>a[n]</code> and <code>b[n]</code> is obtained by taking the FFT of the input
* signals, multiplying the Fourier transforms of the two signals, and taking the inverse FFT of
* the multiplied result.
* \par
* This is denoted by the following equations:
* <pre> A[k] = FFT(a[n],N)
* B[k] = FFT(b[n],N)
* conv(a[n], b[n]) = IFFT(A[k] * B[k], N)</pre>
* where <code>A[k]</code> and <code>B[k]</code> are the N-point FFTs of the signals <code>a[n]</code>
* and <code>b[n]</code> respectively.
* The length of the convolved signal is <code>(n1+n2-1)</code>.
*
* \par Block Diagram:
* \par
* \image html Convolution.gif
*
* \par Variables Description:
* \par
* \li \c testInputA_f32 points to the first input sequence
* \li \c srcALen length of the first input sequence
* \li \c testInputB_f32 points to the second input sequence
* \li \c srcBLen length of the second input sequence
* \li \c outLen length of convolution output sequence, <code>(srcALen + srcBLen - 1)</code>
* \li \c AxB points to the output array where the product of individual FFTs of inputs is stored.
*
* \par CMSIS DSP Software Library Functions Used:
* \par
* - arm_fill_f32()
* - arm_copy_f32()
* - arm_cfft_radix4_init_f32()
* - arm_cfft_radix4_f32()
* - arm_cmplx_mult_cmplx_f32()
*
* <b> Refer </b>
* \link arm_convolution_example_f32.c \endlink
*
*/
/** \example arm_convolution_example_f32.c
*/
#include "arm_math.h"
#include "math_helper.h"
/* ----------------------------------------------------------------------
* Defines each of the tests performed
* ------------------------------------------------------------------- */
#define MAX_BLOCKSIZE 128
#define DELTA (0.000001f)
#define SNR_THRESHOLD 90
/* ----------------------------------------------------------------------
* Declare I/O buffers
* ------------------------------------------------------------------- */
float32_t Ak[MAX_BLOCKSIZE]; /* Input A */
float32_t Bk[MAX_BLOCKSIZE]; /* Input B */
float32_t AxB[MAX_BLOCKSIZE * 2]; /* Output */
/* ----------------------------------------------------------------------
* Test input data for Floating point Convolution example for 32-blockSize
* Generated by the MATLAB randn() function
* ------------------------------------------------------------------- */
float32_t testInputA_f32[64] =
{
-0.808920, 1.357369, 1.180861, -0.504544, 1.762637, -0.703285,
1.696966, 0.620571, -0.151093, -0.100235, -0.872382, -0.403579,
-0.860749, -0.382648, -1.052338, 0.128113, -0.646269, 1.093377,
-2.209198, 0.471706, 0.408901, 1.266242, 0.598252, 1.176827,
-0.203421, 0.213596, -0.851964, -0.466958, 0.021841, -0.698938,
-0.604107, 0.461778, -0.318219, 0.942520, 0.577585, 0.417619,
0.614665, 0.563679, -1.295073, -0.764437, 0.952194, -0.859222,
-0.618554, -2.268542, -1.210592, 1.655853, -2.627219, -0.994249,
-1.374704, 0.343799, 0.025619, 1.227481, -0.708031, 0.069355,
-1.845228, -1.570886, 1.010668, -1.802084, 1.630088, 1.286090,
-0.161050, -0.940794, 0.367961, 0.291907
};
float32_t testInputB_f32[64] =
{
0.933724, 0.046881, 1.316470, 0.438345, 0.332682, 2.094885,
0.512081, 0.035546, 0.050894, -2.320371, 0.168711, -1.830493,
-0.444834, -1.003242, -0.531494, -1.365600, -0.155420, -0.757692,
-0.431880, -0.380021, 0.096243, -0.695835, 0.558850, -1.648962,
0.020369, -0.363630, 0.887146, 0.845503, -0.252864, -0.330397,
1.269131, -1.109295, -1.027876, 0.135940, 0.116721, -0.293399,
-1.349799, 0.166078, -0.802201, 0.369367, -0.964568, -2.266011,
0.465178, 0.651222, -0.325426, 0.320245, -0.784178, -0.579456,
0.093374, 0.604778, -0.048225, 0.376297, -0.394412, 0.578182,
-1.218141, -1.387326, 0.692462, -0.631297, 0.153137, -0.638952,
0.635474, -0.970468, 1.334057, -0.111370
};
const float testRefOutput_f32[127] =
{
-0.818943, 1.229484, -0.533664, 1.016604, 0.341875, -1.963656,
5.171476, 3.478033, 7.616361, 6.648384, 0.479069, 1.792012,
-1.295591, -7.447818, 0.315830, -10.657445, -2.483469, -6.524236,
-7.380591, -3.739005, -8.388957, 0.184147, -1.554888, 3.786508,
-1.684421, 5.400610, -1.578126, 7.403361, 8.315999, 2.080267,
11.077776, 2.749673, 7.138962, 2.748762, 0.660363, 0.981552,
1.442275, 0.552721, -2.576892, 4.703989, 0.989156, 8.759344,
-0.564825, -3.994680, 0.954710, -5.014144, 6.592329, 1.599488,
-13.979146, -0.391891, -4.453369, -2.311242, -2.948764, 1.761415,
-0.138322, 10.433007, -2.309103, 4.297153, 8.535523, 3.209462,
8.695819, 5.569919, 2.514304, 5.582029, 2.060199, 0.642280,
7.024616, 1.686615, -6.481756, 1.343084, -3.526451, 1.099073,
-2.965764, -0.173723, -4.111484, 6.528384, -6.965658, 1.726291,
1.535172, 11.023435, 2.338401, -4.690188, 1.298210, 3.943885,
8.407885, 5.168365, 0.684131, 1.559181, 1.859998, 2.852417,
8.574070, -6.369078, 6.023458, 11.837963, -6.027632, 4.469678,
-6.799093, -2.674048, 6.250367, -6.809971, -3.459360, 9.112410,
-2.711621, -1.336678, 1.564249, -1.564297, -1.296760, 8.904013,
-3.230109, 6.878013, -7.819823, 3.369909, -1.657410, -2.007358,
-4.112825, 1.370685, -3.420525, -6.276605, 3.244873, -3.352638,
1.545372, 0.902211, 0.197489, -1.408732, 0.523390, 0.348440, 0
};
/* ----------------------------------------------------------------------
* Declare Global variables
* ------------------------------------------------------------------- */
uint32_t srcALen = 64; /* Length of Input A */
uint32_t srcBLen = 64; /* Length of Input B */
uint32_t outLen; /* Length of convolution output */
float32_t snr; /* output SNR */
int32_t main(void)
{
arm_status status; /* Status of the example */
arm_cfft_radix4_instance_f32 cfft_instance; /* CFFT Structure instance */
/* CFFT Structure instance pointer */
arm_cfft_radix4_instance_f32 *cfft_instance_ptr =
(arm_cfft_radix4_instance_f32*) &cfft_instance;
/* output length of convolution */
outLen = srcALen + srcBLen - 1;
/* Initialise the fft input buffers with all zeros */
arm_fill_f32(0.0, Ak, MAX_BLOCKSIZE);
arm_fill_f32(0.0, Bk, MAX_BLOCKSIZE);
/* Copy the input values to the fft input buffers */
arm_copy_f32(testInputA_f32, Ak, MAX_BLOCKSIZE/2);
arm_copy_f32(testInputB_f32, Bk, MAX_BLOCKSIZE/2);
/* Initialize the CFFT function to compute 64 point fft */
status = arm_cfft_radix4_init_f32(cfft_instance_ptr, 64, 0, 1);
/* Transform input a[n] from time domain to frequency domain A[k] */
arm_cfft_radix4_f32(cfft_instance_ptr, Ak);
/* Transform input b[n] from time domain to frequency domain B[k] */
arm_cfft_radix4_f32(cfft_instance_ptr, Bk);
/* Complex Multiplication of the two input buffers in frequency domain */
arm_cmplx_mult_cmplx_f32(Ak, Bk, AxB, MAX_BLOCKSIZE/2);
/* Initialize the CIFFT function to compute 64 point ifft */
status = arm_cfft_radix4_init_f32(cfft_instance_ptr, 64, 1, 1);
/* Transform the multiplication output from frequency domain to time domain,
that gives the convolved output */
arm_cfft_radix4_f32(cfft_instance_ptr, AxB);
/* SNR Calculation */
snr = arm_snr_f32((float32_t *)testRefOutput_f32, AxB, srcALen + srcBLen - 1);
/* Compare the SNR with threshold to test whether the
computed output is matched with the reference output values. */
if ( snr > SNR_THRESHOLD)
{
status = ARM_MATH_SUCCESS;
}
if ( status != ARM_MATH_SUCCESS)
{
while (1);
}
while (1); /* main function does not return */
}
/** \endlink */