ECE
HW13

# HW13 - ECE 301 Homework#13 due date...

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ECE 301, Homework #13, due date: 4/21/2010 chihw/10ECE301S/10ECE301S.html Question 1: [Basic] Find and plot the DTFT of x [ n ] = k = -∞ δ [ n - 4 k ]. Find and plot the CTFT of y ( t ) = k = -∞ δ ( t - πk ). Observe the similarity between both your answers. Hint: you should use the generalized DTFT and CTFT formulas. Namely, find the coefficients of DTFS and CTFS first and then convert them to DTFT and CTFT by inspection. Question 2: [Basic] Consider a signal w ( t ) = sin(0 . 5 t ) πt . Plot w ( t ). The impulse-train sam- pling of w ( t ) with sample period T s = π 2 is z ( t ) = w ( t ) y ( t ) = w ( t ) X k = -∞ δ ( t - π 2 k ) = X k = -∞ w ( π 2 k ) δ ( t - π 2 k ) . Plot z ( t ) for the range - 1 . 5 π < t < 1 . 5 π . Question 3: [Basic] Continue from the previous question. Use the multiplication property of CTFT to plot Z ( ). Hint: You need to use the observation that “convolving a shifted impulse is equivalent to shifting the original signal.” Question 4: Consider an AM-DSB signal y ( t ) = ( x ( t ) + 0 . 5) cos(3 πt ) is sent by a trans- mitter.

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