Timeline for How do I analyze a sum of decaying exponentials?
Current License: CC BY-SA 2.5
6 events
| when toggle format | what | by | license | comment | |
|---|---|---|---|---|---|
| Dec 6, 2010 at 8:10 | vote | accept | kaleidomedallion | ||
| Dec 5, 2010 at 3:55 | comment | added | Joseph O'Rourke | Pull out $\epsilon_0/\tau_m$. If $t_{pre}=0,1,2,\ldots$, then what remains is a sum of powers of $e$, and if I've calculated correctly, it sums to $\frac{e^{-\frac{t}{\tau_m}}}{e^{\frac{1}{\tau_m}}-1}$. | |
| Dec 5, 2010 at 2:51 | answer | added | drbobmeister | timeline score: 7 | |
| Dec 5, 2010 at 1:25 | comment | added | kaleidomedallion | No, the $t_{pre}$ are a series of previous times, evenly spaced. So it is the sum of several decaying exponentials of a given rate. What I want to do is relate the rate at which the $t_{pre}$s occur to the value of $V(t)$ using a single exponential, without having to take the sum over each point in time of the previous events. | |
| Dec 5, 2010 at 1:10 | comment | added | Jerry | Not sure that I understand -- otherwise the question is entirely trivial. Are the $t_{pre}$ terms constants? If so, your definition implies $\epsilon(t-t_{pre}) = \exp(t_{pre}/\tau_m)\epsilon(t)$. Apply the distribution law. This can't be what you really mean, right? | |
| Dec 5, 2010 at 0:15 | history | asked | kaleidomedallion | CC BY-SA 2.5 |