# Pulse Train Fourier Series Representation

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```					Pulse Train Fourier Series Representation

Amplitude
in Volts
A                              B

Vo

T                                          Time in
seconds

Parameter Definitions

Pulse duration A      Interpulse interval B   Pulse period T = A + B Duty cycle D = A/T
Pulse frequency fo = 1/T     Pulse radian frequency ωo = 2πfo    Pulse amplitude Vo

Fourier Series Equation

ao ∞                   ∞
f(t) = + ∑a n cos(nω o t) + ∑ bn sin(nω ot)
2 n=1                 n =1

where the Fourier parameters are:

2       T                       2       T                                   2       T
ao =       ∫   0
f(t)dt      an =
T
∫   0
f(t)cos(nω ot)dt         bn =
T
∫   0
f(t)sin(nω o t)dt
T

The Fourier parameters for the Pulse Train

2AVo                        Vo                              Vo
ao =                        an =      sin(nω o t)           bn =      [1- cos(nω ot) ]
A +B                        nπ                              nπ

The Fourier Series for the Pulse Train

Vo A Vo ∞  1                         1
f(t) =      +  ∑ n [sin(nω oA)]cos(nω ot) + n [1- cos(nω oA)]sin(nω ot)
A + B π n=1 


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PrF|sc                        *91f,,, Rrr,'els9s

```
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