What is difference between FFT and DFT?

What is difference between FFT and DFT?

DFT or Discrete Fourier Transform is an algorithm that computes the Fourier transform of a digitized (discrete) signal. FFT (Fast Fourier Transform) is an optimized implementation of this transform.

What is output of FFT?

You can find more information on the FFT functions used in the reference here, but at a high level the FFT takes as input a number of samples from a signal (the time domain representation) and produces as output the intensity at corresponding frequencies (the frequency domain representation).

What is the result of an FFT?

Just as the sampled time data represents the value of a signal at discrete points in time, the result of a (forward) Fast Fourier Transform represents the spectrum of the signal at discrete frequencies.

What is the output of FFT in Matlab?

Y = fft( X ) computes the discrete Fourier transform (DFT) of X using a fast Fourier transform (FFT) algorithm. If X is a vector, then fft(X) returns the Fourier transform of the vector. If X is a matrix, then fft(X) treats the columns of X as vectors and returns the Fourier transform of each column.

What are the applications of FFT algorithm?

There are many different FFT algorithms based on a wide range of published theories, from simple complex-number arithmetic to group theory and number theory. Fast Fourier transforms are widely used for applications in engineering, music, science, and mathematics.

Why we use FFT instead of DFT?

The Fast Fourier Transform (FFT) is an implementation of the DFT which produces almost the same results as the DFT, but it is incredibly more efficient and much faster which often reduces the computation time significantly. It is just a computational algorithm used for fast and efficient computation of the DFT.

Where is DFT used?

The DFT is also used to efficiently solve partial differential equations, and to perform other operations such as convolutions or multiplying large integers. Since it deals with a finite amount of data, it can be implemented in computers by numerical algorithms or even dedicated hardware.