EEE 391
Basics of Signals and Systems
Computer Assignment II
Due: 4 November 2011, Friday by 17:00 in the homework box
Consider the following periodic waveforms:
i) a square wave with period
T
◦
, duty cycle 40%, and average value 2,
ii) a triangular waveform with period
T
◦
and average value –1,
iii) a sawtooth waveform with period
T
◦
and average value zero,
iv) a halfwave rectified sine function with period
T
◦
and average value –2.
a) Sketch these waveforms as accurately as possible and label them as needed.
b) Find all
of the Fourier series coefficients of these waveforms through analysis by hand
and express them as compactly as possible.
c) If all
of the Fourier series coefficients are used, the synthesis equation is as follows:
x
(
t
) =
∞
summationdisplay
k
=
−∞
a
k
e
−
j
2
πkf
◦
t
where
f
◦
= 1
/T
◦
is the fundamental frequency of the waveform. However, infinite limits are not
practical when trying to synthesize the signal on a computer. Try to approximate the periodic
signal
x
(
t
) by truncating the synthesis equation using different values of
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 Spring '11
 dat
 Fourier Series, Periodic function, Square wave, Fourier series coefficients, Triangle wave

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