Where can I find first order interpolation? I looked at Prof.Allebach's note and textbook, I couldn't find that. If anybody knows first order interpolation, please let me know.--Park1 20:25, 22 February 2009 (UTC)
For first order interpolation, $ H_0(f)=Tsinc^2(Tf) \! $
--Pjcannon 13:37, 23 February 2009 (UTC)
Is it zero order? I thought we need to use$ X(f)=\sum_k(X(f-(\frac{k}{T})) $ for the first problem. --Kim415 16:56, 23 February 2009 (UTC)
Right. Here's what I'm thinking:
For part a, in the time domain we want to comb $ x_a(t)\! $ and convolve it with a system whose impulse response is a rect that goes from 0 to T with height 1. So in the $ f\! $ domain I got:
$ X_r(f)=rep_\frac{1}{T}[X_a(f)]sinc(Tf)e^{-j{\pi}fT} \! $
Then for part c we want to do the same thing, except the system is a triangle. In the $ f\! $ domain I got:
$ X_r(f)=rep_\frac{1}{T}[X_a(f)]sinc^2(Tf) \! $
Let me know if you guys got something different.
--Pjcannon 23:06, 23 February 2009 (UTC)
You are right. For the part c, it is
$ X_r(t)=comb_T[X_a(t)]tri(\frac{t}{T}) \! $
$ X_r(t)=comb_T[X_a(t)]rect(\frac{t}{T})*rect(\frac{t}{T}) \! $
After CTFT
$ X_r(f)=rep_\frac{1}{T}[X_a(f)]sinc(Tf)sinc(Tf) \! $ .--Kim415 12:39, 24 February 2009 (UTC)
Check out in the link. First order hold, Triangle Function from wikipedia
