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Unformatted text preview: Project 2: The Discrete Fourier transform, convolution, and more. Do at least 9 of 10 below. If you do all 10, you will be eligible for a 2 point bonus, which may augment your other grades. 1. Calculate the Fourier series for the hat function f ( t ) = 2 π-| t | on [- 2 π, 2 π ] in two ways. a) By calculating its Fourier series directly. b) By calculating the Fourier series for χ π ( t ) and using the convolution theorem. 2. For N even, show that the sum of the roots of unity is zero, or N k =0 w k N = 0 without using a geometric sum argument. ( Hint: Plot the roots on the unit circle and observe that there is a simple geometric, or arithmetic argument, which can easily be changed into a proof ). 3. Write two self-contained programs which compute the derivative of a one dimensional discrete vector. One will utilize the discrete approximation to the derivative, the other will utilize the formal derivative. These al- gorithms should be written in in a .m file ( see matlab’s explanation ofgorithms should be written in in a ....
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This note was uploaded on 01/06/2011 for the course MAP 4413 taught by Professor Olsen during the Spring '10 term at University of Florida.
- Spring '10