Difference between revisions of "Talk:Student summary CT DT Fourier transform ECE438F09" - Rhea

Latest revision as of 15:11, 1 September 2009

I moved all content to the page itself instead of its discussion page. See here.--Mboutin 20:11, 1 September 2009 (UTC)

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+I moved all content to the page itself instead of its discussion page. See [[Student_summary_CT_DT_Fourier_transform_ECE438F09|here]].--[[User:Mboutin|Mboutin]] 20:11, 1 September 2009 (UTC)
-CTFT ( Continuous Time Fourier Transform )
-Equations**
-*<math>X(w) = \int{x(t)*exp(-jwt) dt }</math>
-*<math>x(t) = (1/2pi)\int{X(w)*exp(jwt) dw }</math>
-Duality Property
-* <math>'''{x(t)-CTFT->X(f)}'''</math>
-* <math>'''{X(t)-CTFT->x(-f)}'''</math>
-Example
-*<math>delta(t-t0) ->CTFT-> exp(-j2pi.f.t0)</math>
-*<math>exp(j.2pi.f0t) -> CTFT -> delta(f-f0)</math>
-Another Example:
-*<math>rect(t) -> CTFT -> sinc(f)</math>
-*<math>sinc(t) -> CTFT -> (rect(-f) = rect(f))</math>
-Cosine and Sine Functions
-*<math>cos(t) = 0.5 . ( delta(f - f0) + delta(f + f0) )</math>
-*<math>sin(t) = 0.5 i .( delta(f + f0) - delta(f - f0))</math>
-Rept and Comb Functions
-* <math>Rept(x(t)) = x(t) * sum(delta(t-kT))</math>
-*<math>Comb(x(t)) = x(t) . sum(delta(t-kT))</math>
-----------------------------------------
-DTFT ( Discrete Time Fourier Transform )
-* <math>X(w) = \sum{x(n)*exp(-jwn) dn }</math>
-* <math>x(t) = (1/2pi)\int{X(w)*exp(jwt) dw }</math>
-* Note that x[n] is always periodic with 2pi
-I will add more later.