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ME360 homework assignments, Spring 2010. HW9, April 9, due Monday, April 19
Reading
Text 1 –3.7, 6.1  6.4, 6.8, 6.10, 7.1, 7.9, 9.1, 9.2.0, 9.2.1, 9.2.3, 9.2.4, 9.2.5, 9.2.6, Table
9.2 (convolution, conjugation, correlation, autocorrelation), 9.3, 9.4, 9.5, 9.6.3, 16.6,
16.7.4, 16.9. Text 3 Ch. 9.
Problems
1. For signals x(t)=4 rect(t+3) and h(t)=(t+1) rect(t1), find
a) the autocorrelation r
xx
(t),
b) the autocorrelation r
hh
(t),
c) the crosscorrelation r
hx
(t),
d) the crosscorrelation r
xh
(t).
e) How are r
hx
(t) and r
xh
(t)related?
2. Find the Fourier transform X(f) and sketch the magnitude and phase spectra
│
X(f)
│
and
—
X(f), respectively, for
a) x(t)= 82cos(8
π
t)+7sin(19
π
t),
b) x(t)=2
Σδ
(t6k),
c) x(t)=
│
3sin(6
π
t)
│
.
3. Sketch the PSD (power spectral density) of x(t)=8+9sin(4
π
t
π
/5)6cos(8
π
t).
4. Consider a sawtooth waveform x
p
(t) of project 1 with period T=4, and x
p
(t)=
2t, 0
≤
t
≤
4.
a) Derive the autocorrelation function of this waveform in time domain, give the
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This note was uploaded on 04/18/2010 for the course ME 360 taught by Professor Staff during the Spring '08 term at University of Illinois, Urbana Champaign.
 Spring '08
 Staff

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