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Unformatted text preview: Assignment #13
ECSE—2410 Signals & Systems — Spring 2007 Tue 03/20/07 1(15). The signal x(t) = cos {10 t) has been sampled by multiplying it by an impulse train. The sampled
signal is x5. (I) : C(t) x(t) where XS (t) is the sampled version of x(t) and C(t) is an impulse train k:oo
described by ca) = 2 50—14) .
k: m The spectrum of X S ( a) ) is shown below after sampling and lowpass filtering. a.) (7) What is the sampling rate? Is the Nyquist sampling rate satisfied? b.) (8) What is the actual output, )5, (t), after sampling and lowpass filtering? 2(10). The input to alinear, timeinvariant system is x(t) = 3 + sin( IOt — 45° )and the output is
100 y“) = 75“ sin10t.
If H(a)) = EM—é—ﬁndAandB.
+ J60 3 (10). A certain filter has the following characteristics: IH(0)=0dBand4H(0) = 0°,
H(2)=ldB andAHQ) = 0°,
lH(5)[=~6dB and AH(5) 2 0°, and
IH(10)=10dB and AHUO) 2 0°. Find the output of this filter, y (I), when the input is x(t) = 5 + 3 cos(2t) + 10 sin(51). A#13.p.1 4(15).
2(1+ jw) . 2 '
jw1+ﬂ
10 (c) (5) For the frequency response given in (a), find the phase, in degrees, as a) —9 00. Consider the limit
of H (w) as a) —> 00 as opposed to the exact equation. (a) (5) Write the exact equation for phase, 411(0)) , Where, H (60) = (b) (5) Find the exact AH(a)) when 6!) =1. 5(10). Find the value of a in so that the magnitude of H( a) ) approaches —6 dB as a) —> oo . 6(20). Sketch the straight—line Bode plot (magnitude and phase) for the system with the frequency response
H( a, ) = ___£.0______
1 + 5 J a) 10 + J a)
1 Make sure all terms are in the form of 1 + j a) 1‘ where  2 60b is the break frequency.
T 7(20). Use the “bode” command in MATLAB to make the Bode plot for the system in Problem 6. Label the axes and put a title on the graph with your name in the title, e. g,
“Bode Plot for l/(jw + 10) — A. Desrochers”. Sketch the Straight—line approximation on your MATLAB plots. A#13. p.2 ...
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 Spring '07
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 Signal Processing, sampling rate, Nyquist sampling rate, impulse train

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