What is the difference between FFT and DFT?

What is the difference between FFT and DFT?

The FFT (Fast Fourier Transform) is an efficient algorithm to compute the DFT (Discrete Fourier Transform). While DFT directly computes the frequency components of a signal, FFT reduces the computational complexity significantly, making it faster for large datasets.

Why is FFT preferred over DFT in most applications?

FFT is preferred because it reduces the number of calculations needed from O(N^2) for DFT to O(N log N), making it much faster, especially for large datasets.

Can you give an example of when to use FFT?

Sure! FFT is commonly used in signal processing, such as audio analysis, image processing, and even in solving partial differential equations.

Are there any limitations of using FFT?

Yes, FFT assumes the input signal is periodic and can introduce artifacts if the signal is not properly windowed or if it has discontinuities.