C11-FT - C11: The Fourier Theorem Due Thursday, December 10...

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C11: The Fourier Theorem Due Thursday, December 10 Objective: Gain some familiarity with the principles of Fourier analysis. You will see how to determine the Fourier frequency components of a simple time signal (a square wave) and then show that these components add together to reproduce the signal. The Fourier theorem states that any continuous, periodic function, S(t), can be described by a sum of sine and cosine functions: S(t) = (a n sin (2 π ν n t) + (b n cos (2 π ν n t) where, in this case, we take S to be a function of time and the sine and cosine terms to be waves with particular frequencies. (Note, however, that the Fourier principle is not restricted only to time/frequency domains.) The coefficients, or amplitude factors, of the various waves can be found from a n = 2/T S(t) sin (2 π ν n t) dt b 0 = 1/T S(t) dt b n>0 = 2/T S(t) cos (2 π ν n t) dt where the integration is over a full period for the function, T, and the frequencies are just those that would fit into this period, ν n = n/T .
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C11-FT - C11: The Fourier Theorem Due Thursday, December 10...

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