/* ---------------------------------------------------------------------- * 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 * COPYRIGHT OWNER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, * INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, * BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; * LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER * CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT * LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN * ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE * POSSIBILITY OF SUCH DAMAGE. * -------------------------------------------------------------------- */ /** * @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, a[n] and b[n], 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 (n1+n2-1) * and is a power of 4 as FFT implementation is radix-4. * The convolution of a[n] and b[n] 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: * 
 A[k] = FFT(a[n],N)
 * B[k] = FFT(b[n],N)
 * conv(a[n], b[n]) = IFFT(A[k] * B[k], N)
* where A[k] and B[k] are the N-point FFTs of the signals a[n] * and b[n] respectively. * The length of the convolved signal is (n1+n2-1). * * \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, (srcALen + srcBLen - 1) * \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() * * Refer * \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 */