I want to convolve two discrete functions $f$ and $g$ using convolution stride size $a$ to get the result as $s_{a, i}$:
$$s_{i,a} = \sum_i g_k f_{ai-k}$$
I know that simple convolution with $a=1$ can be calculated via FFT. I can do it even now, but I have to drop out all the points except $ai$. I think this way is not the best.
Cannot you advice me something better?