DFT/FFT What did N stand for again?

1. What is DFT and FFT?
2. Why is FFT faster than DFT?
3. Why is my FFT symmetric?

What is DFT and FFT?

The discrete Fourier transform, or DFT, is the primary tool of digital signal processing. The foundation of the product is the fast Fourier transform (FFT), a method for computing the DFT with reduced execution time.

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.

Why is my FFT symmetric?

Because both the positive and negative frequency sinusoids are 90 degrees out of phase and have the same magnitude, they will both respond to real signals in the same way.