Store a FFT with a minimal amount of data

1. How many points do you need for FFT?
2. Why is FFT more efficient than DFT?
3. Why FFT is efficient?
4. Is FFT lossless?

How many points do you need for FFT?

Because the FFT function uses a base 2 logarithm by definition, it requires that the range or length of the time series to be evaluated contains a total number of data points precisely equal to a 2-to-the-nth-power number (e.g., 512, 1024, 2048, etc.).

Why is FFT more efficient 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 FFT is efficient?

In an FFT, D and E come entirely from the twiddle factors, so they can be precomputed and stored in a look-up table. This reduces the cost of the complex twiddle-factor multiply to 3 real multiplies and 3 real adds, or one less and one more, respectively, than the conventional 4/2 computation.

Is FFT lossless?

The FFT is lossless, so there's no compression as a result of using it. The compression is gained by perceptual modeling and dumping parts, and by powerful entropy modeling, like CABAC and such.