Digital Signal Processing Reference
In-Depth Information
(d)
Is the circuit low pass? Why?
(e)
The period of the square wave is changed to State the effects of this
change on the answers to parts (a) and (c), without solving these parts again. Give
the reasons for your answers.
T
0
= p.
2
Output
Input
0.5 F
Figure P4.26
4.27.
Consider the
RL
circuit of Figure P4.27.
2
Input
1 H
Output
Figure P4.27
(a)
The square wave of Table 4.3 is applied to the input of this circuit, with
and Solve for the frequency spectrum of the output signal. Give nu-
merical values for the amplitudes and phases of the first three nonzero sinusoidal
harmonics.
(b)
Verify the results in part (a), using MATLAB.
(c)
Let the input of the circuit be as in part (a), but with a dc value of 20 V added to the
square wave. Solve for the frequency spectrum of the output signal. Give numeri-
cal values for the dc component and the first three nonzero sinusoidal harmonics.
(d)
Is the circuit low pass? Why?
(e)
The period of the square wave is changed to State the effects of this
change on the answers to parts (a) and (c), without solving these parts again. Give
the reasons for your answers.
T
0
= ps
X
0
= 10 V.
T
0
= 2p.
4.28.
Consider the general time transformation
y(t) = x(at + b).
Show that the Fourier coefficients for the signal
y
(
t
) are given by
C
kx
e
jkw
0
b
,
a 7 0
b
C
ky
=
a 6 0
,
[C
kx
e
jkw
0
b
]
*
,
where
C
kx
are the Fourier coefficients for
x
(
t
).
