Final Exam 2004

# 1 20 consider a 1d signal f x with values f 025

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Unformatted text preview: 0%) Consider a 1D signal f (x) with values f (0:25) = 3, f (0:5) = 2, f (0:75) = 2 and f (1:0) = 3. We can write this as f (x0 + 0 x) = 3, f (x0 + 1 x) = 2, f (x0 + 2 x) = 2 and f (x0 + 3 x) = 3, where both x0 = 0:25 and x = 0:25, or more simply denoted as f (0) = 3, f (1) = 2, f (2) = 2 and 1 f (3) = 3. Figure 1 shows the details. Similarly, frequencies, u, have values ? 2 , Figure 1: Discretized x values. ? 1 , 0 and 1 or u0 + 0 u, u0 + 1 u, u0 + 2 u and u0 + 3 u, where u0 = ?0:5 4 4 and u = 1 , or more simply denoted as u = 0; 1; 2 and 3. Compute the FT 4 of this signal, F (u), u = 0; ::; 3, with and without translation to 0 for f (x), x = 0; :::; 3, on the next two pages. Show all your work plus formulae used in your answers. CS630a In-Class Final Exam, Monday, December 13th, 4-6pm, 2004, MC320 3 (1a) (10%) FT without translation to 0. Show all formulae used and all work. CS630a In-Cl...
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