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hw3_600 - ECE-600 Introduction to Digital Signal Processing...

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ECE-600 Introduction to Digital Signal Processing Autumn 2011 Homework #3 Oct. 8, 2011 HOMEWORK ASSIGNMENT #3 Due Fri. Oct. 14, 2011 (in class) 1. The following matlab routine ( phasor.m ) helps to visualize the sampling of a complex sinusoid: f0 = -1; T = 0.1; n = [0:5/T]; x = exp(j*2*pi*T*f0*n); figure(gcf) for i=1:length(n), plot([0,real(x(i))],[0,imag(x(i))],’o-’); axis([-1,1,-1,1]); axis(’square’) title([’exp(j*2*pi*T*f0*n) for T=’,num2str(T),... ’ and f0=’,num2str(f0),’ and n=’,num2str(n(i))]) drawnow; pause(T) end; In particular, it illustrates what happens when the complex sinusoid x ( t ) = e j 2 πf 0 t is sampled every T seconds to yield x [ n ] = x ( nT ). Here, f 0 (written as “ f0 ” in the code) represents the signal frequency in Hz. (a) Run the code for f 0 = 1, and describe how many radians the angle changes per sample. Does this agree with the DTFT frequency ω 0 = 2 πf 0 T ? (b) Run the code for f 0 = 11, and describe how many radians the angle changes per sample. Does this agree with the DTFT frequency ω 0 = 2 πf 0 T ? How does it compare to part (a)?
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