# Discrete fourier transform in matlab

The following Matlab project contains the source code and Matlab examples used for discrete fourier transform .
This Matlab code can be used for Fourier transforming of any arbitrary discrete data.

The following Matlab project contains the source code and Matlab examples used for to compute dft of a given signal .
Tracing code is intended to perform N point Discrete Fourier Transform of input signal x. Maximum value of N is equal to signal length. It also computes the DFT matrix of order N.

The following Matlab project contains the source code and Matlab examples used for displays a two dimensional discrete fourier transformation..
Easy to use display function for analyzing the FFT of tow-dimensional signals.

The following Matlab project contains the source code and Matlab examples used for two matlab functions for understanding how fast fourier transform works.
Matlab has fft and ifft already to fast calculate discrete Fourier transform and its inverse.

discrete Fourier transform (DFT) converts a finite list of equally spaced samples of a function into the list of coefficients of a finite combination of complex sinusoids, ordered by their frequencies, that has those same sample values.

The following Matlab project contains the source code and Matlab examples used for discrete fourier transform one dimensional.
DFT is the frequency domain representation of a discrete digital signal.

The following Matlab project contains the source code and Matlab examples used for discrete fourier transform of a finite sequence.
DFT transforms one function into another, which is called the frequency domain representation, or simply the DFT, of the original function (which is often a function in the time domain).

The following Matlab project contains the source code and Matlab examples used for radix 2 dft algorithm for real data.
Computes the DFT of N real values and returns the first
N/2+1 DFT coefficients. N is an integral power of two.

The following Matlab project contains the source code and Matlab examples used for circular convolution using dft idft.
Circular convolution using DFT-IDFT
1st sequence(*) 2nd sequence = IDFT(DFT of 1st sequence * DFT of second sequence)

The following Matlab project contains the source code and Matlab examples used for compute n x n dft matrix.
% dftmat = DFT matrix of order N x N;
% N = Order of the matrix
% computes the DFT matrix of orer N x N;
% DFT matrix is a n x n matrix defined as Wn=[(Wn)^km]
% Wn=exp(-j*2*pi/n)
%Reference: Multirate Systems and Filter banks by P.

The following Matlab project contains the source code and Matlab examples used for discrete fourier transform 2d.
Run this program with a small image of about 100x100 pixels its because though it works on image of any size but for large images the execution time is very high.

The following Matlab project contains the source code and Matlab examples used for dft and idft.
finds DFT and IDFT of the discrete signal without using in built functions.It is an alternate algorithm to fast fourier transform(FFT)

The following Matlab project contains the source code and Matlab examples used for extended dft.
EDFT (Extended Discrete Fourier Transform) algorithm produces N-point DFT of sequence X where N is greater than the length of input data.

The following Matlab project contains the source code and Matlab examples used for image filtering.
Image Filtering RGB Spatial Wiener Direct Inverse Discrete Fourier Transform DFT Lucy Richardson Median Laplacian

A fast Fourier transform (FFT) is an algorithm to compute the discrete Fourier transform (DFT) and its inverse. Fourier analysis converts time (or space) to frequency and vice versa; an FFT rapidly computes such transformations by factorizing the DFT matrix into a product of sparse (mostly zero) factors.

Radix-2 FFT