29-06-2012, 02:06 PM
Properties of Discrete Fourier Transform
10Properties of Discrete Fourier transform.ppt (Size: 756.5 KB / Downloads: 35)
Periodicity:
The discrete Fourier transform and its inverse are periodic with period N, i.e.,
Distributivity & Scaling:
From the definition of continuous and discrete Fourier transform pair
F{f1(x,y)+f2(x,y)}=F{f1(x,y)}+F{f2(x,y}
and in general,
F{f1(x,y).f2(x,y)}≠F{f1(x,y)}.F{f2(x,y}
The Fourier transform and its inverse are distributive over addition but not over multiplication
Discrete Convolution:
Let f(x,y)and g(x,y) are discrete arrays of size A x B and C X D. These arrays must be assumed periodic with some period M and N in the x and y directions. Choose,
Summary:
The properties of one dimensional and two dimensional Fourier Transform are studied.
Circular and linear convolution are studied
Linear and circular correlation are studied