We have our Fourier expansion. And we're gonna evaluate from zero to pi. The fewer times that a wave cycles, the less certain its frequency is.
A curiosity of the convergence of the Fourier series representation of the square wave is the Gibbs phenomenon. So if n is even, you're gonna have negative three over n pi times Actually let me just do it over here so we have the space. When you look at the shape of the square wave, it actually makes a lot of sense.
But let's now tackle our b-sub-ns. That f-of-t's gonna be zero from pi to two pi and zero times anything is gonna be zero, so the integrals, the definite integrals over this, the second part of the interval, are always going to be zero.
Hi-Fi audio graphic equalizer. So for this particular square wave, I can just worry about from zero to pi. So that's going to be six over five pi. Visualizing the Fourier expansion of a square wave Video transcript - [Voiceover] So this could very well be an exciting video because we start with this idea of a Fourier series that we could take a periodic function and represent it as an infinite sum of weighted cosines and sines and we use that idea to say, "Well can we find formulas "for those coefficients?
The rise and fall times between positive and negative cycles are much steeper now, and the crests of the wave are closer to becoming flat like a squarewave.
Why did I start at zero? Now what is this going to be equal to?