## Fourier coefficients (xx minutes)

• Following the class activities about projecting functions comes an interactive lecture where students help the instructor to project a function (say a sawtooth) onto a particular harmonic function (say the second harmonic), to derive the coefficient for that particular term. Choose the sine or cosine form, and later discuss the need for both.
• Obtain $a_{n}=\frac{2}{T}\int_{0}^{T}{f\left( t \right)\cos \left( n\omega _{0}t \right)dt}$ and $b_{n}=\frac{2}{T}\int_{0}^{T}{f\left( t \right)\sin \left( n\omega _{0}t \right)dt}$ with careful identification of all terms in the expression. add constant term discussion.
• Record coefficients graphically to illustrate the idea of a spectrum. upload picture to illustrate what I mean

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