hw6 - 6 2-t(over Assignment#6 p.2 ECSE-2410...

Assignment #6 - p.1
Fri 09/20/05
1(10). Write the complex expression,
( 29
( 29
3 1 1
) 1 (
j j
j j
z
+ +
-
=
, in polar form , i.e.,
) arg( z j e z z =
. Express the
angle of z , i.e., arg( z ), as p
π
radians, where p is a fraction. Assume that the principal value of
arg( z ) is
≤ < - ) arg( z
2(18). Given 3 1 j z + = , evaluate the following. Note that some of these expressions are simplest when
expressed in polar form and others in rectangular form. Some are simply real numbers.
(a)
z
(b)
zz
(c)
2
z (d)
+ z z
(e)
{ }
z e ℜ
(f)
z
z
3(15). Use properties of convolution to find the overall impulse response of the following system in
terms of h
1
, h
2
, and h
3
:
4(20). Sketch the following periodic signals and calculate their average values (dc values).
(a)
) ( sin 2 ) ( t = t x
, which is the output of a half wave rectifier circuit . Sketch several
periods of
) ( t x
.
(b) The signal
) ( t x
of period 4, where one period is given by





< < + -
< <
< < - - -
2 1 , 2
1 0 , 1
0 2 , 1
t t
t
t t
.
Sketch
) ( t x
over the interval,