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Unformatted text preview: Midterm 1
Fall 2008 Problem 1 (12 points) Consider the rectangular time signal x(t)=rect(t/4), where [rect(x)] is the common rectangular pulse
function (amplitude is 0 or 1). Sketch X(t), the Fourier transform of x(t), from —1 to +1 on the horizontal
axis. Label all critical points on both axes. Problem 2 (12 points) Consider the modulator shown. The signal y(t) is obtained by sampling the information signal every Ts
seconds. Sketch the Fourier transform of m(t)cos(27tfct). Label all signiﬁcant points. Sampler y(t) z(t)
—B 0 B f Problem 3 (25 points) Consider the voice scrambling system shown, with input voice signal X(f), also as shown. All frequency
components above f1 are passed by highpass ﬁlter H,(f), and all ﬁ'equency components below f. are
removed. The lowpass ﬁlter H20), passes all ﬁ‘equency components below [-B,B], and all other frequency
components are removed. xm 1 zm 1 3) Assume f1 >> B. Sketch Y(f).
i. Find f2 as a function of f1 and B, in order to produce Z(f), as shown.
ii. What must the amplitude response of H2(t) be?
c) Explain how this signal may be descrambled. In other words, show or explain how X(f) may be
recovered from 2(1). Show and label a block diagram of your proposed solution. Page 1 of 2 Midterm 1
ECE 1 0 1
Fall 2008 Problem 4 (25 points) Suppose a white noise signal w(t) with power spectral density (PSD) Sw(t)=No/2 is passed through a ﬁlter
with an impulse response of h(t), as shown. The output signal y(t) has an autocorrelation of
———> PSD: swm PSD: sym a) Find the PSD of y(t).
b) Assuming the angle of H(t)=0, ﬁnd h(t).
c) The random signal y(t) is uncorrelated for what values of T. d) With an increase in T, will the random signal change more slowly or more quickly? Why /
Explain? Problem 5 (16 points) 96 voice and music signals are time-division multiplexed after each being subjected to sampling via a
uniform process. Flat-top samples with a lus duration are used by the sampling operation.
Synchronization is used by the multiplexing operation, and this is implemented by adding one additional pulse, with sufﬁcient amplitude, that is also 1 us in duration. Each voice signal may contain frequency
components of up to 4.2 kHz. a) If the samples are taken at a rate of 9 kHz, what will be the time spacing between successive
pulses of the multiplexed signal? b) If the samples are taken at a Nyquist sampling rate, what will be the time spacing between
successive pulses of the multiplexed signal? Problem 6 (10 points) a) Comparing standard AM modulation to FM modulation, brieﬂy describe one advantage and one
disadvantage of the AM modulation. b) Comparing digital modulation to analog modulation, give one advantage and one disadvantage of
the digital modulation. Page 2 of 2 ...
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- Spring '08