**Digital Image Processing**

Assignment #1

Assignment Report By:

Ashish Gupta 98131

Ashish Gupta 98130

- Write FFT routine to be used for Fourier transform and its inverse for 2D images. Draw a graph between N (number of points) and the Cutoffmputation time.

The Graph Showing Performance of 2D FFT module designed
for Image Manipulation

Graph is time (us) vs. N

- Ideal low/high pass filter and Butterworth low/high pass filter. Examine the effects when the cutoff frequency is changed, plot the Fourier spectrum (you may have to use Compression of dynamic range). For Butterworth see what happens when the order is changed.

Click on the following links :

- Demonstrate the properties of translation and rotation of Fourier transform.

Properties of Translation

The block image Fourier
of block image

Fourier of block image after applying the translation
transform the translate the block by 50x50 units

Note that the magnitude of the Fourier Plot doesn’t change

Fourier Plot after translation The translated block image ( Inverse FFT of the left Fourier Plot )

Rotation of Fourier Transform

The block image rotated by 45 degrees The Fourier plot of the left image

The Fourier plot is also rotated by 45 degrees.

Code : freq.cpp

End of Report