Lecture 35 Blog, ECE438 Fall 2011, Prof. Boutin

Monday November 14, 2011 (Week 13) - See Course Outline.

After "fleeing from the tornado" into a nearby classroom (yes, it WAS a tornado shelter, as per the sign posted on the wall), we discussed how all the 1D transform formulas that we have already seen can be generalized to space (2D) signals. We also mentioned how both rotationally symmetric space signals and separable space signals can be analyzed using 1D transform formulas.

After that, we moved to the topic of image processing. We stated the formula for 2D convolution (in discrete-space). We used this formula to express the output of a discrete-space LTI system in terms of the input image f[m,n] and the unit input response h[m,n]. We then proceed to demonstrate how to use the formula using an average filter and a 6x6 digital image. The issue of the boundary conditions was discussed.

Relevant Rhea pages

• Table of CSFT pairs and properties
• a pdf file of the notes of Hector Santos on 2D signals and CSFT

Action items

• Solve the following problems on Spectral Analysis of discrete-space (2D) signals and share your answers for feedback
  • Obtain the discrete-space Fourier transform of a rectangle
  • Compute the discrete-space Fourier transform of this function
  • Compute the discrete-space Fourier transform of this cosine

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