What's wrong with my FFT implementation?

1. How does fast Fourier transform algorithm work?
2. Why is FFT faster than DFT?
3. How can you compute DFT using FFT algorithm?

How does fast Fourier transform algorithm work?

The FFT algorithm decomposes the DFT into log2 N stages, each of which consists of N/2 butterfly computations. Each butterfly takes two complex numbers p and q and computes from them two other numbers, p + αq and p − αq, where α is a complex number. Below is a diagram of a butterfly operation.

Why is FFT 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 can you compute DFT using FFT algorithm?

fft , with a single input argument, x , computes the DFT of the input vector or matrix. If x is a vector, fft computes the DFT of the vector; if x is a rectangular array, fft computes the DFT of each array column. Compute the DFT of the signal and the magnitude and phase of the transformed sequence.