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1 a) | 1 a) | ||
| − | <math> | + | <math>x(t) \,\!= \cos(\frac{\pi}{2})rect(\frac{t}{2})</math> |
Based on the Prof Alen's note page 179 | Based on the Prof Alen's note page 179 | ||
| − | <math> | + | <math>x(f) \,\!= \frac{1}{2}( \delta (f - \frac{1}{4}) + \delta (f + \frac{1}{4}))sinc(t/2)</math> |
| + | *<span style="color:red">Would you know how to compute this FT without a table if asked? </span> --[[User:Mboutin|Mboutin]] 10:45, 9 February 2009 (UTC) | ||
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| + | *<span style="color:red">This answer is incorrect and does not match the answer we acquired..Please check the answer stated in the discussion below [https://kiwi.ecn.purdue.edu/rhea/index.php/Talk:HW_3_Question_1]</span>--[[User:Drestes|Drestes]] 10:47, 11 February 2009 (UTC) | ||
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| + | An answer to this 1a) question is stated in the discussion [https://kiwi.ecn.purdue.edu/rhea/index.php/Talk:HW_3_Question_1]--[[User:Drestes|Drestes]] 10:41, 11 February 2009 (UTC) | ||
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b) | b) | ||
| − | <math> | + | This is how I came to my conclusion, I think it makes morse sense then the previous mentioned answer. |
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| + | First take the x(t) from part a and call it <math>x_1(t)</math><br/> | ||
| + | *The answer from part a please check the referred link as the answer stated above is incorrect. | ||
| + | <math>x1(t) \,\!= \cos(\frac{\pi t}{2})rect(\frac{t}{2})</math> | ||
| + | |||
| + | Now since this is a repeating function use the rep function to get | ||
| + | <math>x(t) = rep_4(x_1(t))</math> | ||
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| + | We know that the CTFT of x1(t) is:<br/> | ||
| + | <math>x1(f) = sinc(2(f-\frac{1}{4} ) + sinc(2(f + \frac{1}{4})</math><br/> | ||
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| + | *<span style="color:green"> -- i am a little confused with this step. </span> | ||
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| + | *<span style="color:green">In part a we did the CTFT of x1(t) and we get </span> | ||
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| + | <math>x(f) \,\!= \frac{1}{2}( \delta (f - \frac{1}{4}) + \delta (f + \frac{1}{4}))sinc(t/2)</math> | ||
| + | |||
| + | *<span style="color:green">so why here do you say the CTFT of x1(t) is </span> | ||
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| + | <math>x1(f) = sinc(2(f-\frac{1}{4} ) + sinc(2(f + \frac{1}{4})</math><br/> --[[User:Jwromine|Jwromine]] 23:45, 10 February 2009 (UTC) | ||
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| + | We also know from alabechs notes section 1.4.1 that | ||
| + | <math> rep_T(x_1(t)) \Rightarrow \frac{1}{T} comb_{1/T}(X_1(f))</math><br/> | ||
| + | |||
| + | Put all the pieces together and you get something that looks like<br/> | ||
| + | <math> X(f) = \frac{1}{4} comb_{1/4}(sinc(2(f-\frac{1}{4} ) + sinc(2(f + \frac{1}{4}))</math> | ||
| + | --[[User:Drestes|Drestes]] 22:53, 10 February 2009 (UTC) | ||
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| − | < | + | *<span style="color:red"> Can you write your answer using a comb operator? </span> --[[User:Mboutin|Mboutin]] 10:45, 9 February 2009 (UTC) |
| + | * <span style="color:red"> How did you get to that answer? Please add some intermediate steps. </span> --[[User:Mboutin|Mboutin]] 10:50, 9 February 2009 (UTC) | ||
Latest revision as of 05:47, 11 February 2009
1 a)
$ x(t) \,\!= \cos(\frac{\pi}{2})rect(\frac{t}{2}) $
Based on the Prof Alen's note page 179
$ x(f) \,\!= \frac{1}{2}( \delta (f - \frac{1}{4}) + \delta (f + \frac{1}{4}))sinc(t/2) $
- Would you know how to compute this FT without a table if asked? --Mboutin 10:45, 9 February 2009 (UTC)
- This answer is incorrect and does not match the answer we acquired..Please check the answer stated in the discussion below [1]--Drestes 10:47, 11 February 2009 (UTC)
An answer to this 1a) question is stated in the discussion [2]--Drestes 10:41, 11 February 2009 (UTC)
b)
This is how I came to my conclusion, I think it makes morse sense then the previous mentioned answer.
First take the x(t) from part a and call it $ x_1(t) $
- The answer from part a please check the referred link as the answer stated above is incorrect.
$ x1(t) \,\!= \cos(\frac{\pi t}{2})rect(\frac{t}{2}) $
Now since this is a repeating function use the rep function to get $ x(t) = rep_4(x_1(t)) $
We know that the CTFT of x1(t) is:
$ x1(f) = sinc(2(f-\frac{1}{4} ) + sinc(2(f + \frac{1}{4}) $
- -- i am a little confused with this step.
- In part a we did the CTFT of x1(t) and we get
$ x(f) \,\!= \frac{1}{2}( \delta (f - \frac{1}{4}) + \delta (f + \frac{1}{4}))sinc(t/2) $
- so why here do you say the CTFT of x1(t) is
$ x1(f) = sinc(2(f-\frac{1}{4} ) + sinc(2(f + \frac{1}{4}) $
--Jwromine 23:45, 10 February 2009 (UTC)
We also know from alabechs notes section 1.4.1 that
$ rep_T(x_1(t)) \Rightarrow \frac{1}{T} comb_{1/T}(X_1(f)) $
Put all the pieces together and you get something that looks like
$ X(f) = \frac{1}{4} comb_{1/4}(sinc(2(f-\frac{1}{4} ) + sinc(2(f + \frac{1}{4})) $
--Drestes 22:53, 10 February 2009 (UTC)
