Problem 1:
Problem 2:
F
Problem 3: Recall that f (x) g(x) F ()G(). Then Y () = X()H().
We know that the Fourier Transform property for time scaling is,
F
f (t)
and that
1
F( )

1
F
sinc(t) rect( )
2
2
Using the (1) and (2) we can nd X() .
1
F
x(t) = si
ee 224: hw 2 solutions
February 3, 2014
1.
s ( t ) = cos 2
(e
( t ) =
0
j0t
+ e j0t
)
4
2
=
e j 20t + e j 20t + 2
4
1 1
1
= + e j 20t + e j 20t
2 4
4
Spectrum of s(t)
1/2
1/4
2w0
0
1/4
2w0 W(rad/s)
2. P 2.7 (a)
3e j 3 + 4ej 6
= 3 cos
+ j sin
+ 4 cos
3
3