Dft and fft

1. What is difference between DFT and FFT?
2. What is the use of DFT and FFT?
3. Why FFT is better than DFT?
4. Which is better FFT or DFT?

What is difference between DFT and FFT?

Discrete Fourier Transform (DFT) is the discrete version of the Fourier Transform (FT) that transforms a signal (or discrete sequence) from the time domain representation to its representation in the frequency domain. Whereas, Fast Fourier Transform (FFT) is any efficient algorithm for calculating the DFT.

What is the use of 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 FFT is better 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.

Which is better FFT or DFT?

FFT algorithms are faster ways of doing DFT. It is a family of algorithms and not a single algorithm. How it becomes faster can be explained based on the heart of the algorithm: Divide And Conquer.