Signals.and.Systems.with.MATLAB.Computing.and.Simulink.Modeling.4th_Part41

# Signals.and.Systems.with.MATLAB.Computing.and.Simulink.Modeling.4th_Part41

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Signals and Systems with MATLAB Computing and Simulink Modeling, Fourth Edition 8 41 Copyright © Orchard Publications The System Function and Applications to Circuit Analysis Thus, (8.122) We observe that (8.122) is in agreement with (8.116). 1 a 2 x 2 + ---------------- x d 1 a -- x a atan C + = W R 9 π 1 2 ω 2 --- atan   0 9 2 π ------ π 2 2.25 joules == =

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Chapter 8 The Fourier Transform 8 42 Signals and Systems with MATLAB Computing and Simulink Modeling, Fourth Edition Copyright © Orchard Publications 8.9 Summary The Fourier transform is defined as The Inverse Fourier transform is defined as The Fourier transform is, in general, a complex function. We can express it as the sum of its real and imaginary components, or in exponential form as We often use the following notations to express the Fourier transform and its inverse. If is real, is, in general, complex. If is real and even, is also real and even. If is real and odd, is imaginary and odd. If is imaginary, is, in general, complex. If is imaginary and even, is also imaginary and even. If is imaginary and odd, is real and odd. If , is real. The linearity property states that The symmetry property states that The scaling property states that F ω () ft e j ω t t d = 1 2 π ------ F ω e j ω t ω d = F ω Re F ω {} jIm F ω + F ω e j ϕω == F F ω = F 1 F ω = F ω F ω F ω F ω F ω F ω F ω F ω = a 1 f 1 t a 2 f 2 t () … a n f n t ++ + a 1 F 1 ω a 2 F 2 ω a n F n ω + Ft 2 π f ω fa t 1 a -----F ω a ---  
Signals and Systems with MATLAB Computing and Simulink Modeling, Fourth Edition 8 43 Copyright © Orchard Publications Summary The time shifting property states that The frequency shifting property states that The Fourier transforms of the modulated signals and are

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## This note was uploaded on 11/20/2009 for the course EE EE 102 taught by Professor Bar during the Fall '09 term at UCLA.

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Signals.and.Systems.with.MATLAB.Computing.and.Simulink.Modeling.4th_Part41

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