| /* ---------------------------------------------------------------------- |
| * 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 |
| * are met: |
| * - Redistributions of source code must retain the above copyright |
| * 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 |
| * LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS |
| * FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE |
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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 */ |
