Faster way of getting 2D frequency amplitudes than DFT?

1. How FFT is faster than DFT?
2. How many times faster is an FFT than a DFT for a block size of 256 samples?
3. What is the advantage of FFT instead of direct computation of DFT?

How FFT is faster than DFT?

For a sample set of 1024 values, the FFT is 102.4 times faster than the discrete Fourier transform (DFT). The basis for this remarkable speed advantage is the `bit-reversal' scheme of the Cooley-Tukey algorithm. Eliminating the burden of `degeneracy' by this means is readily understood using vector graphics.

How many times faster is an FFT than a DFT for a block size of 256 samples?

This means FFT is 32 times faster than DFT.

What is the advantage of FFT instead of direct computation of DFT?

FFT helps in converting the time domain in frequency domain which makes the calculations easier as we always deal with various frequency bands in communication system another very big advantage is that it can convert the discrete data into a contionousdata type available at various frequencies.