PHY354H1 Lecture Notes - Square Wave, Phenylalanine, Gibbs Phenomenon
Document Summary
Lecture 14: fourier series examples: last time: if we represent a function f (t) that is periodic on t as a fourier series: f (t) = a0 + (cid:20) T then we derived formulas for the amplitudes of the sinusoids in the fourier series: (cid:90) t (cid:90) t. T dt dt f (t) sin f (t) cos (cid:90) t. < t 2 : as an example, we found the amplitudes for the square wave: (1) (2) (3) (4) (5) (6) This last one can be simpli ed a bit to read: N for n odd: so our fourier series for the square wave can be written: 4f0 n sin nt: today we will investigate how this sum gives us the square wave. We will also try to develop some intuition about why a0 and an were 0 in this example, and we will do another example.
