Transcribed Text
1)
H(s) = 35²+205+37 2 I( (s) is the transfer
52+65+9
function of an LTI system.
a) compute the poles and Zevos 9 the
system and plot them on the S plane
b) obtain the partial fraction expansion
of H(S) and compute the Inverse
Laplace trans form 7 H(s), i.e hct).
c) Is the system stable 2 what is the =)
final value of h(t)? i.e h(w)
T
2) Given the following Fourler transforms determine
the corresponding timedomain signals. ( It is not
to use the Inverse Founer Transform and
necessary integral. you can use the Fourier transform its
properties tables In the text.)
a)
X I (w) = Cos (w) Sinc(w)
b) X2(w) = Sinc (low) Sinc (4w)
c)
x3(w) 2 el3w
X4 wo) = II S(w10) w  + TI S(w+10) + ejjww sinc(w)
= 3+jw
d)
)
3) Determine the Founer Transform 9 the following
Signals
a) y,(t)
=
{ SctnT0)
b)
y2 (t) Even part a>o
c) 43(t) = Cos(wot) p(ult+Vult1))
d)
y4((t) = 1o
5)
Let x(t). = c, cos(wot+9). To 2II be the
penod of the signal x(t).
a) show that x(t) is a Power signal
b) Calculate the average Power
6) Consider a periodic signal x(t), shown below,
obtained by halfwave  rectifying a Simusoidal
signal
x(t)
Sin (4TTE)

1
3/4
1/2
1/4
o
1/4
1/2
314
it In secs
a) Determine To, f. swo
b) Find the Fourer Coefficients aneb.
c) Express x(t) in the form
x(t) = in con(nwot+d.) tCO
n=1
d) what, is the dc content of x(t)?
e) sketch the Magmtude/amplitude spectrum
and phase spectrum
f) If x(t) is passed thru a filter (LTI
with the following frequency response
system) H(w), Determine the power in the output
Signal y(t)).
y (f)
x(t)
H(w)
H(w)
30 md/sec
w
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