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UCLA, Electrical Engineering Department
Winter Quarter, 2011
EE 114, Part 2: Image Processing
Due: Feb. 16, 2011
Computer Assignment #5
1. Introduction
In this assignment, you will experiment with the two-dimensional Fourier Transform of digital
images.
2. Preliminary
The following tools in Matlab will be useful in this assignment:
Fast Fourier Transform of a 2-D array (
fft2
)
The Fourier Transform of a 2-D array can be performed by
fft2
.
a_ft = fft2(array);
Inverse Fast Fourier Transform of a 2-D array (
ifft2
)
The Inverse Fourier Transform of a 2-D array can be performed by
ifft2
.
iarray = ifft2(a_ft);
Shift (
fftshift
and
ifftshift
)
The coefficient array produced by the Fourier Transform has the lower frequency
components at the corners of the 2D array
and the higher frequency components at the center as
shown in Figure 1.
Lower

This
** preview**
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Figure1. FT coefficients before
fftshift
fftshift
performs a 2D circular shift that moves the zero-frequency component of fast Fourier
transform to center of the array as shown in Figure 2.
ifftshift

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