Convolution example: inputA[64],InputB[64] and Output[128]

Hi all,

I need help to reproduce a convolution example presented here:

https://www.keil.com/pack/doc/CMSIS/DSP/html/group__ConvolutionExample.html

A[k] = FFT(a[n],N)

B[k] = FFT(b[n],N)

conv(a[n], b[n]) = IFFT(A[k] * B[k], N)

/* ----------------------------------------------------------------------

* Test input data for Floating point Convolution example for 32-blockSize

* Generated by the MATLAB randn() function

* ------------------------------------------------------------------- */

float32_t Ak[MAX_BLOCKSIZE]; /* Input A */

float32_t Bk[MAX_BLOCKSIZE]; /* Input B */

float32_t AxB[MAX_BLOCKSIZE * 2]; /* Output */

[Bruno Luong]

None of the standard (MATLAB) shape produce output of length nA+nB where nA and nB are the lenghs of a and b respectively (64 in the thread subject) , but

• 'full': nA+nB-1
• 'same': nA
• 'valid': nA-nB+1

Answer 1

[Paul]

Hi AndyK,

I'm going to assume that N = na + nb - 1, where na and nb are the lengths of a[n] and b[n] respectively. Under this assumption, the code would look like this. If we make N > na + nb - 1, like to the nextpower of 2, then ci should have N - (na + nb - 1) trailing zeros (to within rounding error)

rng(100)
na = 5;
nb = 5;
a = rand(1,na);
b = rand(1,nb);
c = conv(a,b);
N = na + nb - 1;
A = fft(a,N);
B = fft(b,N);
C = A.*B;
ci = ifft(C);
c

c = 1×9

0.0661 0.3983 0.6871 0.6916 1.2684 0.9189 0.3635 0.4865 0.0027

ci

ci = 1×9

0.0661 0.3983 0.6871 0.6916 1.2684 0.9189 0.3635 0.4865 0.0027