Evaluating regular Fourier Transform from DFT

1. How is DFT calculated in FFT?
2. What is difference between DFT and FFT?
3. How much faster is FFT compared to DFT?
4. Which is better FFT or DFT?

How is DFT calculated in FFT?

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.

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.

How much faster is FFT compared to DFT?

Graphical explanation for the speed of the Fast Fourier Transform. 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.

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.