7/27/2019 EXP2 DSP pracitcal
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DTSP Practical VIT SMK
EXPERIMENT NO.2
Spectral Analysis using DFT
AIM: To study the spectral analysis using DFT
SOFTWARE: MATLAB
THEORY:
Discrete Fourier Transform: It is a finite duration sequence
which is obtained by sampling one
period of Fourier transform. Sampling is done at N equally
spaced points.
Mathematical Equation: The DFT of discrete sequence x(n) is
denoted by X(k).It is given by
Where k= 0,1,2,...N-1
Since this summation is taken for Npoints, it is called N point
DFT.
One of the most important properties for DFT is convolution of
two sequences .The
multiplication of two DFTs is equivalent to the convolution of
their sequences in time domain.
MATLAB functions: MATLAB defines the following functions:
a. fft: Fast Fourier transform
Syntax
Y = fft(x)
Y = fft(X,n)
Y = fft(x) returns the discrete Fourier transform (DFT) of
vector x, computed with a fast Fourier
transform (FFT) algorithm.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 nonsingleton dimension. If the length of X is less
than n, X is padded with trailing zeros
to length n. If the length of X is greater than n, the sequence
X is truncated. When X is a matrix,the length of the columns are
adjusted in the same manner.
b. ifft: Inverse fast Fourier transform
