(New page: 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.--[[User:Par...) |
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Where can I find first order interpolation? I looked at Prof.Allebach's note and textbook, I couldn't find that. | 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.--[[User:Park1|Park1]] 20:25, 22 February 2009 (UTC) | If anybody knows first order interpolation, please let me know.--[[User:Park1|Park1]] 20:25, 22 February 2009 (UTC) | ||
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Is it zero order? I thought we need to use<math> X(f)=\sum_k(X(f-(\frac{k}{T}))</math> for the first problem. | Is it zero order? I thought we need to use<math> X(f)=\sum_k(X(f-(\frac{k}{T}))</math> for the first problem. | ||
--[[User:Kim415|Kim415]] 16:56, 23 February 2009 (UTC) | --[[User:Kim415|Kim415]] 16:56, 23 February 2009 (UTC) | ||
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| + | Right. Here's what I'm thinking: | ||
| + | For part a, in the time domain we want to comb <math>x_a(t)\!</math> and convolve it with a system whose impulse response is a rect that goes from 0 to T with height 1. So in the <math>f\!</math> domain I got: | ||
| + | <br><math>X_r(f)=rep_\frac{1}{T}[X_a(f)]sinc(Tf)e^{-j{\pi}fT} \!</math> | ||
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| + | Then for part c we want to do the same thing, except the system is a triangle. In the <math>f\!</math> domain I got: | ||
| + | <br><math>X_r(f)=rep_\frac{1}{T}[X_a(f)]sinc^2(Tf) \!</math> | ||
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| + | Let me know if you guys got something different. | ||
| + | <br>--[[User:Pjcannon|Pjcannon]] 23:06, 23 February 2009 (UTC) | ||
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| + | You are right. For the part c, it is | ||
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| + | <br /><math>X_r(t)=comb_T[X_a(t)]tri(\frac{t}{T}) \!</math> | ||
| + | <br /><math>X_r(t)=comb_T[X_a(t)]rect(\frac{t}{T})*rect(\frac{t}{T}) \!</math> | ||
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| + | After CTFT | ||
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| + | <br /><math>X_r(f)=rep_\frac{1}{T}[X_a(f)]sinc(Tf)sinc(Tf) \!</math> .--[[User:Kim415|Kim415]] 12:39, 24 February 2009 (UTC) | ||
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| + | Check out in the link. [http://en.wikipedia.org/wiki/First-order_hold First order hold], [http://en.wikipedia.org/wiki/Triangular_function Triangle Function] from wikipedia | ||
Latest revision as of 07:37, 26 February 2009
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
