Pulse Train Fourier Series Representation

Parameter Definitions

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

Fourier Series Equation

where the Fourier parameters are:

The Fourier parameters for the Pulse Train

The Fourier Series for the Pulse Train

V

B

T

Amplitude in Volts

Time in seconds

A

o

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f(t) = ao2

+ ancos(nωot)n=1

∞

∑ + bnsin(nωot)n =1

∞

∑

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ao =2T

f(t)dt0

T∫

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an =2T

f(t)cos(nωo0

T∫ t)dt

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bn =2T

f(t)sin(nωot)dt0

T∫

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ao =2AVoA +B

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an =Vonπsin(nωot)

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bn =Vonπ

1- cos(nωot)[ ]

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f(t) = VoAA +B

+Voπ

1nsin(nωoA)[ ]cos(nωot)+

1n1- cos(nωoA)[ ]sin(nωot)

n=1

∞

∑

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