1
EE102
Systems and Signals
Fall Quarter 2011
Jin Hyung Lee
Homework #4
Due: Wednesday, November 2, 2011 at 5 PM.
1. Suppose that
f
(
t
)
is a periodic signal with period
T
0
, and that
f
(
t
)
has a Fourier series. If
τ
is a real number, show that
f
(
t

τ
)
can be expressed as a Fourier series identical to that
for
f
(
t
)
except for the multiplication by a complex constant, which you must find.
2. Switching amplifiers are a very efficient way to generate a timevarying output voltage
from a fixed supply voltage. They are particularly useful in highpower applications.
The basic idea is that an output voltage
a
is generated by rapidly switching between zero
and the supply voltage
A
. The output is then lowpass filtered to remove the harmonics
generated by the switching operation. For our purposes we can consider the lowpass filter
as an integrator over many switching cycles, so the output voltage is the average value
of the switching waveform.. Varying the switching rate varies the output voltage. In this
problem we will only consider the case where the desired output voltage is constant.
This preview has intentionally blurred sections. Sign up to view the full version.
View Full Document
This is the end of the preview.
Sign up
to
access the rest of the document.
 Fall '11
 lee
 Fourier Series, Periodic function, output voltage, duty cycle

Click to edit the document details