EE 350
PROBLEM SET 7
DUE: 5 November 2007
Reading assignment: Lathi Chapter 4, Sections 4.1 through 4.4
Laboratory sections will meet during the week of October 29.
Problem 33:
(20 points)
Figure 1 shows a representation of the triangle waveform used in Laboratory #3.
Figure 1: A triangle waveform with a fundamental period
T
o
and peaktopeak amplitude 2
A
.
1. (10 points) Determine the trigonometric Fourier series coeﬃcients
a
o
,
a
n
, and
b
n
in terms of
T
o
and
A
, and if possible,
use symmetry properties to simplify the calculations.
2. (4 points) Using the results from part 1, determine the compact trigonometric Fourier series coeﬃcients
C
n
and
θ
n
.
3. (6 points) Using the expressions developed in part 2 to compute the coeﬃcients
C
n
and
θ
n
for the triangle wave used
in Laboratory #3, where
T
o
= 1 ms and
A
= 1 V. Construct the following table to compare your theoretical results to
the experimental values obtained in Laboratory #3, where
PE
=
±

C
n

theory

C
n

exp
²

C
n

theory
×
100
.
n
Peak Location [kHz]

C
n

[V
RMS
]
PE
Theory
Experiment
0
1
2
3
4
5
This preview has intentionally blurred sections. Sign up to view the full version.
View Full DocumentProblem 34:
(20 points)
1. (2 points) When
f
(
t
) is a realvalued, periodic signal, show that
D

n
=
D
*
n
.
This is the end of the preview.
Sign up
to
access the rest of the document.
 Fall '07
 SCHIANO,JEFFREYLDAS,ARNAB
 Fourier Series, LTI system theory, Impulse response, Fourier series coefficients

Click to edit the document details