# Homework Help: Charateristic equation of a discrete system

1. Aug 7, 2010

### lmasterz

Calculate value(s) of the root(s) of the charateristic equation of a discrete system that correspond(s) to a time constant of 0.03 seconds when the sample period is 0.02 seconds.

I'm not sure if I should use a first order or 2nd order equation. Either/or, why is it? Any ideas on how I should go about it

2. Aug 7, 2010

### Staff: Mentor

Welcome to the PF.

Your problem statement seems a bit under-specified, at least for me. Can you please post the full question text? You don't specify the order of the characteristic equation, for example. What other details are you given in this problem statement?

3. Aug 7, 2010

### lmasterz

that is exactly the question. word for word. nothing less nor more.

I mean, it also states to plot the roots on a graph. but mainly I am looking for the roots

4. Aug 7, 2010

### xcvxcvvc

Maybe something like this if you were doing impulse invariant design
$$h(t)=e^{\frac{t}{\tau}}u(t)$$
$$h[n]=e^{\frac{nT_s}{\tau}}u[n]=(e^{\frac{T_s}{\tau}})^nu[n]$$
$$h[n]\longleftrightarrow \frac{z}{z-e^{\frac{T_s}{\tau}}}$$

so the pole is at $$e^{\frac{T_s}{\tau}}$$

I think that the pole locations do not change for a system's characteristic equation regardless of order if it must have a certain time constant. You'll just have repeated poles.

5. Aug 7, 2010

### lmasterz

ya that's what I got too,

e^-(0.02/0.03) = 0.513

anyone care to confirm?

Last edited: Aug 7, 2010