RoseHulman ECE 300  Fourier Series and Filtering Periodic Signals (7 pages)
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Fourier Series and Filtering Periodic Signals
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 RoseHulman Institute of Technology
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 Ece 300  Continuoustime signal systems
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ROSE HULMAN INSTITUTE OF TECHNOLOGY Department of Electrical and Computer Engineering ECE 300 Signals and Systems Winter 2007 Fourier Series and Filtering Periodic Signals Lab 06 by Robert Throne Objectives A variety of interesting waveforms can be expressed as sums of complex exponentials of different frequencies The pulse trains used in communication systems speech waveforms and the waveforms produced by musical instruments can be modeled in this way It is also important to determine how these periodic signals are modified when they are the input to a linear time invariant system The four main objectives of this lab are 1 Improve your knowledge of programs in MATLAB and 2 Understand how Fourier series coefficients are changed when a periodic signal goes through a system 3 Review filtering of signals and develop an understanding of the relationship between the phase of a system and the time delay in the output signal Procedure 1 Plotting a Periodic Signal using the Complex Fourier Series a Copy your code Complex Fourier Series m from the previous homework to a new file lab6 m and then use it to determine and plot the Complex Fourier series representation of the following periodic function defined over one period using 20 terms of the series 0 2 t 1 1 1 t 2 x t 3 2 t 3 0 3 t 4 Procedure 2 Filtering Periodic Signals One of the reasons for using a Fourier Series representation of a periodic signal instead of a different type of representation is that we get a frequency domain representation of the original signal x t If x t is a periodic signal with period T then it has the Fourier series k 2 1 representation x t ck e jk ot where 0 and ck x t e jk ot dt Using the fact that TT T k the magnitude of the ck is even and the phase of the ck is odd we can rewrite the complex Fourier series as a Fourier cosine series Page 1 of 7 ECE 300 Signals and Systems x t Fall 2007 k k k ck e jk ot co 2 ck cos k o t ck k 1 Assume next we have a periodic signal x t A cos 0t We can
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