# ps9 - MIT OpenCourseWare http/ocw.mit.edu 2.161 Signal...

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MIT OpenCourseWare http://ocw.mit.edu 2.161 Signal Processing: Continuous and Discrete Fall 2008 For information about citing these materials or our Terms of Use, visit: http://ocw.mit.edu/terms .

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MASSACHUSETTS INSTITUTE OF TECHNOLOGY DEPARTMENT OF MECHANICAL ENGINEERING 2.161 Signal Processing - Continuous and Discrete Fall Term 2008 Problem Set 9 Assigned: November 20, 2008 Due: December 4, 2008 Problem 1: Given a waveform x ( t ) with a pdf of the form p ( x ) = λe λx x > 0 = 0 otherwise calculate (a) the mean µ x , and (b) the variance σ x 2 . Problem 2: White noise is passed through an ideal low-pass ﬁlter with a cut-oﬀ frequency of ω c . Find the autocorrelation function of the ﬁltered noise. Problem 3: A Mini-project: Deblurring the Hubble Telescope Images Read the Class Handout: Introduction to Two-Dimensional/Image Processing be- fore attempting this mini-project. As you know, the scientiﬁc world was shocked by the poor quality of the initial images from the Hubble Space Telescope after its launch April 24, 1990. After it went into orbit, it became clear that something was wrong. While the pictures were clearer than those of ground-based telescopes, they were blurry, and not the pristine images promised. The telescope’s primary mirror had been polished with a ”spherical aberration” ﬂaw. It was just slightly the wrong shape, causing the light that reﬂected from the center of the mirror to focus in a diﬀerent place than the light reﬂected from the edge. The tiny ﬂaw about 1/50th the thickness of a sheet of paper, was enough to seriously degrade the images. While the problem was well understood, the hardware ﬁx was time consuming and very expensive. The rest is history, we now look in awe at the images from Hubble. In
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ps9 - MIT OpenCourseWare http/ocw.mit.edu 2.161 Signal...

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