EE200_Weber_10-16

EE200_Weber_10-16 - EE 200 Fourier Series The Fourier...

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26 EE 200 Fourier Series The Fourier series expansion for a function x(t) is unique. If the expansion of x(t) is given by with coefficients and phase values A k and ! k , then there are no other set of coefficients and phase values B k and " k that is also the expansion of x(t). Note that the phase values are not unique in that ! k and ! k +2 # n are equivalent . x ( t ) = A 0 + A k cos( k " 0 t + # k ) k = 1 $ %
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27 EE 200 Finite Signals We can use the Fourier series for describing finite signals that are not periodic. Construct a periodic signal (period = t 2 - t 1 ) made up of time shifted copies of the finite signal, and find the Fourier series expansion of this periodic signal. t x(t) t x(t) t 1 t 2
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28 EE 200 Aperiodic Signals Fourier series expansion can be used with aperiodic signals also. Divide the aperiodic signal into regions of time and treat each region as a finite signal. Create a periodic signal from this finite signal and apply the Fourier series expansion.
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EE 200 Discrete-Time Signals Discrete time signals (x: Integers $ Reals) can be represented by sinusoids in much the same way as continuous time signals. The frequency of a discrete time signal (domain = Integers) is based samples, not time. Frequency is specified as cycles per sample, or radians per sample. The period of a discrete time signals is a non-zero
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This note was uploaded on 12/03/2008 for the course EE 200 taught by Professor Zadeh during the Fall '08 term at USC.

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EE200_Weber_10-16 - EE 200 Fourier Series The Fourier...

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