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Unformatted text preview: ENEE 241 02 * HOMEWORK PROBLEM 29 Due Fri 04/18 Generate the 20-point signal vector x using the MATLAB script below. n = (0:19).’ ; f0 = 0.15 + 0.25*rand(1) ; A = 10*rand(1) ; phi = pi*rand(1) ; x = A*cos(2*pi*f0*n + phi) + 0.3*A*randn(size(n)) ; Following the same steps as in the example given in class (Reading Assignment 28, Item 7): (i) (5 pts.) Compute and plot (using stems) the amplitude spectrum of x against f = ω/ (2 π ). (ii) (6 pts.) Compute and plot (on the same graph, using a continuous curve) the amplitude spectrum resulting from zero-padding x to length N = 512. (iii) (3 pts.) Using the continuous graph in (ii) , obtain an estimate ˆ f of f . How does it compare to the true value? (iv) (6 pts.) Use the least squares technique developed in Reading Assignment 17 (also in Home- work Assignment 17) to approximate x by a linear combination of the vectors [cos(2 π ˆ f n )] and [- sin(2 π ˆ f n )], where ˆ f is the value obtained in part (iii) and n = 0 : 15. Hence obtain estimates= 0 : 15....
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This note was uploaded on 03/21/2010 for the course ENEE 241 taught by Professor Staff during the Spring '08 term at Maryland.
- Spring '08