This is a puzzle for those who know Fourier transform math. Suppose you want to do a circular convolution of two complex-valued sequences A and B, each of length n. It's well known that you can do it by:
- Use a forward FFT to transform A and B into sequences a and b respectively.
- Do elementwise multiplication of a and b.to generate a sequence c.
- Use a backward (inverse) FFT on c to get the product C=A*B
Now suppose you are stranded on a desert isle with a computer that does only forward FFTs. Can you still do convolutions using a process similar to the above, without using a backward FFT? How?