Timeline for Connection between LTI filters and damped + driven harmonic oscillator?
Current License: CC BY-SA 4.0
8 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 30, 2023 at 20:51 | answer | added | TimWescott | timeline score: 1 | |
| Dec 30, 2023 at 11:11 | comment | added | bluenote10 | @TimWescott: I had already done so, but perhaps the edit was too subtle. I've emphasized it now. | |
| Dec 30, 2023 at 9:02 | history | edited | bluenote10 | CC BY-SA 4.0 | added 68 characters in body |
| Dec 29, 2023 at 22:15 | comment | added | TimWescott | You may wish to edit your question to make it clear that you're talking about sampled-time filters. | |
| Dec 28, 2023 at 15:11 | comment | added | Peter K.♦ | Absolutely! The usual technique is to transform from a continuous-time, $s$-domain, description of the system into a discrete-time, $z$-domain description of the system. The match won't be exact because of sampling and associated effects, but it can generally get as close as needed. For example, this answer shows how the bi-linear transform works. | |
| Dec 28, 2023 at 13:49 | comment | added | bluenote10 | I should mention that I'm referring to digital filters. So of course a key difference between the two concepts is that time is continuous in a harmonic oscillator, but discrete in a digital filter. The connection between the two may actually come down to numerical approximation of the derivative in the differential equation: I'd expect that e.g. the dx/dt term (associated with damping) can be approximated by the difference of y_n and y_n-1, which can be associated with "velocity". The d^2x/dt^2 term may require a second order numerical approximation. | |
| Dec 28, 2023 at 11:13 | history | edited | bluenote10 | CC BY-SA 4.0 | added 8 characters in body |
| Dec 28, 2023 at 8:45 | history | asked | bluenote10 | CC BY-SA 4.0 |