ECE 101 lab_solution3

# ECE 101 lab_solution3 - ECE 101 Linear Systems...

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ECE 101 – Linear Systems Fundamentals, Winter 2008 Lab # 3 Solutions February 5, 2008 (send questions/comments to psiegel@ucsd.edu) In this lab assignment, you are asked to develop a simple deblurring filter to apply to a blurry image of a car, in order to obtain the undistorted license plate number. The blurring is assumed to be horizontal, so that each pixel in the output image is a linear combination of previous pixels in the same row. This is effectively a convolution operation. The convolution can be written as Y = XH T , where Y is the output (blurry) image matrix, X is the input (original) image matrix, and H is the convolution matrix (i.e., two-dimensional impulse response) which works on the elements of the input X . The structure of the H matrix is: You can see that this matrix has a very particular structure to it, namely that every left-right diagonal of the matrix has the same value. For example, the main diagonal is occupied by h[0], the diagonal underneath it has the value h[1], and so on, so that each left-right diagonal has the same value. This type of matrix structure is known as a Toeplitz matrix . Toeplitz matrices have nice properties, such as reduced computational complexity, and come up often in digital signal processing. The first task in this lab is to create this

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## This note was uploaded on 03/16/2009 for the course ECE 101 taught by Professor Siegel during the Fall '08 term at UCSD.

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ECE 101 lab_solution3 - ECE 101 Linear Systems...

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