How do I find Fourier series coefficients for triangular and sawtooth waveforms?

[phsyics_197]

Triangular and sawtooth waveforms.

I solved for the coeffiecients for the square wave, and was wondering if you do the same for triangular and sawtooth. I keep getting large/messy integrals that do not seem to simplify.

The thing that is messing me up is that the waveform is linear with a slope, as opposed to just 1/-1. Which would require us to solve by integration by parts.

Are there any worked up examples regarding these. I would like to see the answer I am supposed to get and try to work through it.

 

[Bob S]

This article on pages 605 and 606 gives the cosine-like Fourier transform coefficients for triangular, square, cosine-squared, parabolic, and Gaussian shapes. The equations for deriving the coefficients shown on page 606 are shown on page 605.

http://www.bnl.gov/edm/review/files/references/rshafer_aip_249_601_1992.pdf