ENEE 322
Sections 0101 & 0102 Homework #1 All plots should be done by hand, not by computer (a calculator, if needed, is OK). 1) Consider the continuous signal: x(t) = C0 sin ( 2! f0t ) a) Compute the power of x(t) b) Compute the energy in x(t) between t1

ENEE 322
Sections 0101 & 0102 Homework #2 All plots should be done by hand, not by computer (a calculator, if needed, is OK). 1) Consider the discrete signal x[n] = sin ( n! 8 ) a) Compute b) Compute c) Compute d) Compute e) Compute Spring 2008
n = "#
$ x

ENEE 322
Sections 0101 & 0102 Homework #3 1) Consider the following systems, where x ! [System] ! y a) y(t) = cosh ( x(t) =
1 2
Spring 2008
(e
x(t )
+ e ! x(t )
x[ n# ]
)
b) y[n] = Run !" ( x[n]) =
n # = !"
$
n
c) y[n] = x[n + 1] ! x[n] d)
d y(t) + ! y(t)

ENEE 322
Sections 0101 & 0102 Homework #4 Spring 2008
Useful identities:
cos(x) = (e jx + e ! jx ) 2 sin(x) = (e jx ! e ! jx ) 2 j f ( s ) = u(s) f (s) + u(!s) f (!s)
1) Consider the discrete LTI system with Impulse Response h[n] = u[n] : a) For x[n] = u[

ENEE 322
Sections 0101 & 0102 Homework #5 Useful identities: Spring 2008
cos(x) = (e jx + e ! jx ) 2 sin(x) = (e jx ! e ! jx ) 2 j f ( s ) = u(s) f (s) + u(!s) f (!s)
Also, feel free to use properties of convolution (e.g. associativity) whenever it helps.

ENEE 322
Sections 0101 & 0102 Homework #7 1) Consider the function x(t) = sin(! 0 t) + 1 sin(2! 0 t) : 2 a) What is its fundamental period? b) Compute its Fourier coefficients ak c) Compute its average power per period from x(t) . d) Compute its average p

ENEE 322
Sections 0101 & 0102 Homework #8 Important Attach a hardcopy of all MATLAB code. 1) As done in class, the zero-DC square wave function, with period T = 1 , is
x(t) = ! 1 +u t + 1 !u t ! 1 4 4 2
k
Spring 2008
( ) ( )
for t <
1 , extended periodica

ENEE 322
Sections 0101 & 0102 Homework #9 1) Consider the RLC circuit pictured in Figure P3.20 (page 254) in Oppenheim & Willsky, except that R, L, and C are unknown (i.e. keep them as "R", "L", and "C"). a) Using an input signal of V0 exp( j!t) , and kno

ENEE 322
Sections 0101 & 0102 Homework #10 1) For each of these functions, plot it for the range [!2T1 , +2T1 ] and compute its Fourier Transform. Use the properties of the Fourier Transform to simplify the calculation whenever possible. a) xa (t) = t "u