EE511 Day 8 Class Notes
Fourier Transform Continued
Laurence Hassebrook
Updated 9-15-03
Monday 9-15-03
Fourier Series (FS) Expansion
Given s(t) = s(t+T) is a periodic function of period T then
st    cn e j 2fot
n
where fo=1/T and
cn 
1 T /2
st e  j 2f ot dt


T
/
2
T
NOTE: Given s(t) then
cn 
1 
1
t 
F rect  st 
 T SafT   S  f 
 Saf o nT   S  f o n 
T 
T   ff n T
f  fon
o
Thus, the FS coefficients are sinc functions convolved with the spectra of the waveform.
FS of a square wave
Consider the periodic part such that
(Draw graph of square wave)
In this case
 t  nT 
s t    rect 

  
n
Using the FT we find the coefficients to be:
1