Difference between revisions of "HW 3 Question 1" - Rhea

Revision as of 18:28, 10 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)

An answer to this 1a) question is stated in the discussion [1]

This actually doesn't make sense to me using multiplication theorom (mimis version seen below)

$ F(x_1(t)x_2(t)) = \frac {1} {2\pi} X_1(\omega)*X_2(\omega) $

I took $ x_1(t) = \cos(\frac{\pi}{2}) $ and $ x_2(t) = rect(\frac{t}{2}) $
This resulted in
$ x_1(f) = \frac{1}{2}( \delta (f - \frac{1}{4}) + \delta (f + \frac{1}{4})) $
$ x_2(f) = 2sinc(2f) $ By The multiplication theorem I get that these 2 functions need convolved but do not understand how that results in it being multiplied by sinc(t/2)

--Drestes 22:28, 10 February 2009 (UTC)

b)

$ x_(t) \,\!= repT[x0_(t)] = \frac {1}{T} \sum_{k} cos(\frac{\pi}{2})rect(\frac{t}{4}) $

Based on the Prof Alen's note page 184

$ x_(f) \,\!= \frac{1}{T}\sum_{k} ( \delta (f - \frac{1}{4}) + \delta (f + \frac{1}{4}))( \delta (f - \frac{k}{4})) $

• Can you write your answer using a comb operator? --Mboutin 10:45, 9 February 2009 (UTC)
• How did you get to that answer? Please add some intermediate steps. --Mboutin 10:50, 9 February 2009 (UTC)