FAST FOURIER TRANSFORM
DEFINATION:
The FFT is a faster version of the Discrete Fourier Transform (DFT).It is an efficient algorithm for computing the
Discrete Fourier Transform.
Syntax:
Y = fft(x)
Y = fft(X,n)
Y = fft(X,[],dim)
Y = fft(X,n,dim)
Description:
•Y = fft(x) returns the discrete Fourier transform (DFT) of vector x.
•If the input X is a matrix, Y = fft(X) returns the Fourier transform of each column of the matrix.
•If the input X is a multidimensional array, fft operates on the first nonsingleton dimension.
•Y = fft(X, n) returns the n-point DFT. fft(X) is equivalent to fft(X, n) where n is the size of X in the first no
singleton dimension.
•Y = fft(X, [], dim) and Y = fft(X,n,dim) applies the FFT operation across the dimension dim.
FFT ALGORITHM:
There are two main families of FFT algorithms:
•the Cooley-Tukey algorithm
• the Prime Factor algorithm
FFT is a divide and conquer algorithm.
The window length is the length of the input data vector. It is determined by the size of an external buffer.
The transform length is the length of the output, the computed DFT.
An FFT algorithm pads or chops the input to achieve the desired transform length.
The execution time of an FFT algorithm depends on the transform length.
It is fastest when the transform length is a power of two and has only small prime factors.
APPLICATIONS:
•Image processing
•Signal analysis
•Sound filtering
•Partial differential equations
