A Fourier Series Problem
Problem Freq4P00BInt

        This is a guided problem to help you with basic Fourier Series concepts.  If you click here you can get a calculator that allows you to enter Fourier coefficients and see the resulting signal.  Use that calculator for the questions below, as needed.

        In this problem, we assume that the Fourier Series is given by:

Problems

P1  The Fourier Series for a triangle wave - shown below - has components that are given by:

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P2  What is the value of the third harmonic?

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P3  What is the value of the sine term in the third harmonic?

        Now, compute the first five coefficients (for harmonics 1,3,5,7,9) for a triangle wave with an amplitude of one, and with even symmetry (cosine expansion), and insert your computed values into the simulator.  Then run the simulator and observe the quality of the triangle wave.

        Next, do the same for a square wave.  Use the same simulator, or you can use the special square wave calculator.  Click here for the square wave simulator.  Then answer this question.


P4  Is the quality better for the triangle wave with harmonics 1,3,5,7 & 9, or for the square wave with the same harmonics?

        Now,  consider what happens when the triangle signal is shifted in time so that the positive-going zero crossing occurs at the time origin as shown in the figure below.

P5  Answer the following questions.
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P6  You should be able to address these issues.