ECE 380 Introduction to Communication Systems
Homework Assignment 7 Due: 14:00pm Tuesday, Mar. 21, 2023
Problem 1. Specify the Nyquist rate and the Nyquist interval for the signal g(t) = sinc2(400t).
Problem 2. Consider sampling of the sinusoidal wave g(t) = sin(πt). Determine the Fourier transform of the instantaneous sampled signal for the following sampling periods and draw the magnitude spectrum:
(a) Ts = 0.25 second;
(b) Ts = 1.5 seconds.
Problem 3. A baseband signal g(t) with bandwidth 50 Hz is sampled at the Nyquist rate and the re-
sulting sampled values are
g(nTs) = (a) Find g(0.015) from its reconstruction.
− 1 n = − 1 , − 2 ,
1 n = 1,2 . 0 otherwise
(b) Is the signal g(t) a power signal or energy signal? Problem 4. A PAM wave is produced by the message
m(t) = 2 sin(2πfmt).
Assume that the modulation frequency fm = 0.2 Hz, sampling period Ts = 1s, and pulse duration
(with rectangular pulse shape)
(a) Plot the PAM wave (time-domain): s(t) = ∞n=−∞ m(nTs)h(t − nTs).
T = 0.4s. (b) Find the frequency spectrum of the PAM wave S(f).
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