1 / 8

Harmonic functions

Harmonic functions. Sines and cosines with the same frequency. The general picture: Asin  x + Bcos  x. (x is usually t). I’ll set A = 1 and B = 0 for examples here. Examples with 0 ≤ x ≤ 1000,  = 2nπ/1000. Sums of harmonic functions with different frequencies are not harmonic.

baris
Download Presentation

Harmonic functions

An Image/Link below is provided (as is) to download presentation Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author. Content is provided to you AS IS for your information and personal use only. Download presentation by click this link. While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server. During download, if you can't get a presentation, the file might be deleted by the publisher.

E N D

Presentation Transcript

  1. Harmonic functions Sines and cosines with the same frequency The general picture: Asinx + Bcos x (x is usually t) I’ll set A = 1 and B = 0 for examples here. Examples with 0 ≤ x ≤ 1000,  = 2nπ/1000

  2. Sums of harmonic functions with different frequencies are not harmonic.

  3. That one was periodic because the n = 6 has the same period as the n = 3 Incommensurate periods give apparently aperiodic sums

  4. But almost all sums of harmonic functions are periodic And almost all periodic functions are sums of harmonic functions (albeit possibly infinite sums) (Can we say “Fourier series” boys and girls? We’ll look at that this evening.)

More Related