DFT and IDFT using MATLAB

AIM:

To find DFT and IDFT of a sequence.

APPARATUS REQUIRED:

Hard ware: IBM PC or compatible

Soft ware : Matlab 6.5 or higher

THEORY:

In mathematics, the discrete Fourier transform (DFT) is a specific kind of discrete transform, used in Fourier analysis. It 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 DFT requires an input function that is discrete. Such inputs are often created by sampling a continuous function, such as a person's voice. The discrete input function must also have a limited (finite) duration, such as one period of a periodic sequence or a windowed segment of a longer sequence. Unlike the discrete-time Fourier transform (DTFT), the DFT only evaluates enough frequency components to reconstruct the finite segment that was analyzed. The inverse DFT cannot reproduce the entire time domain, unless the input happens to be periodic. Therefore it is often said that the DFT is a transform for Fourier analysis of finite-domain discrete-time functions.

FFT algorithms are so commonly employed to compute DFTs that the term "FFT" is often used to mean "DFT" in colloquial settings. Formally, there is a clear distinction: "DFT" refers to a mathematical transformation or function, regardless of how it is computed, whereas "FFT" refers to a specific family of algorithms for computing DFTs. The terminology is further blurred by the (now rare) synonym finite Fourier transform for the DFT, which apparently predates the term "fast Fourier transform"

The discrete Fourier transform (DFT) is given by:

The inverse discrete Fourier transform (IDFT) is given by:

PROGRAM:

clc;

clear all;

close all;

x=input('enter the sequence');

x1=fft(x);

subplot(2,2,1);

stem(imag(x1));

title('imaginary fft');

disp('fft');

disp(x1);

subplot(2,2,2);

stem(real(x1));

title('real fft');

y=ifft(x1);

 subplot(2,2,3);

stem(imag(y));

title('imaginary ifft');

disp('ifft');

disp(y);

subplot(2,2,4);

stem(real(y));

title('real ifft');

Enter the sequence     [1   2   3   4]

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