# Difference equation vs differential equation

1. Oct 12, 2009

### swraman

Hi,

Im trying to go back and relearn material from a signals class I took to prepare for my controls class.

In the controls class we always deal with CT systems, whereas in the systems class we focused on DT.

My prof derived a frequency response that was H(w) = 1/(1-a*exp(i*w)).

This dint look farmiliar as in my controls class we never have exponentials in the frequency response.

The complex exponential in the Freq response came from y(n) = y(n-1) + x(n), more particularly the y(n-1) part. Now im guessing the reason this doenst look farmiliar to my controls work is that we always use CT in controls, so there will never be a y(n-1) in our answer. So my question is: What is the CT parallel for the DT term y(n-1)? What makes a CT model have a complex exponential in the solution (aside from actually having y(t) = y(t-1), as y(t-1) doesnt mean the same thing in DT as CT)?

Thanks

2. Oct 21, 2009

### swraman

no one?

3. Oct 21, 2009

### oufa

hi
i think that the i.f t is coming from ..
y(t)-ay(t-1)=x(t)
so take f.t
y(w)*(1-aexp-jw)=x(w)
That's it i think where exp comes where no unit step function is found here
any question again if you need ...

Last edited by a moderator: Oct 21, 2009