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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