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# HW12 - ECE 301 Homework#12 due date...

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ECE 301, Homework #12, due date: 12/11/2008 http://www.ece.purdue.edu/ chihw/ECE301 08F.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. One distinct feature, however, is that any DTFT X ( e ) is always of period 2 π (although the fundamental period of X ( e ) is not 2 π . For comparison, the period of CTFT Y ( ) is not 2 π . 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 ) is z ( t ) = w ( t ) y ( t ) = w ( t ) X k = -∞ δ ( t - πk ) = X k = -∞ w ( πk ) δ ( t - πk ) .

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HW12 - ECE 301 Homework#12 due date...

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