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Unformatted text preview: City University of Hong Kong Department of Electronic Engineering EE3210 Lab 3: Periodic Signal Representation by Fourier Series Prelab: Read the Background section. Complete Section 2.2(b) , which asks you to derive the exponential Fourier series coefficients for x ( t ) defined in (6). Verification: The Warm-Up section must be completed during your assigned lab time. The steps marked Instructor Verification must also be signed off during the lab time. When you have completed a step that requires verification, simply demonstrate the step to the instructor. Lab Report: It is only necessary to turn in a report on the Experiment section with graphs and explanations. 1. Background The Fourier Series representation applies to periodic signals. The Fourier synthesis equation for a periodic signal x ( t ) = x ( t + T ) is ∑ ∞ −∞ = = n t jn n e D t x ) ( ω , ( 1 ) where / 2 T π ω = is the fundamental frequency. To determine the Fourier series coefficients from a time-domain formula for the signal over one period, we must evaluate the analysis integral for every integer value of n : ∫ − = ) ( 1 T t jn n dt e t x T D ω , ( 2 ) where / 2 ω π = T is the fundamental period. The power of a real periodic signal is defined as ∫ = 2 ) ( 1 T x dt t x T P . ( 3 ) Parseval’s theorem says that it can be expressed in terms of its exponential Fourier series coefficients as ∑ ∞ −∞ = = n n x D P 2 . ( 4 ) 2. Warm-up 2.1 Getting Familiar with fplot and stem MATLAB provides a function called fplot , which can be used to plot a function. Try the following: fplot(‘x.^2’,[0,1]) Type “ help fplot ” to learn more on it....
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- Spring '09