Revision as of 06:24, 27 October 2009

Discrete-time Fourier Transform Pairs and Properties

Please feel free to add onto this table!

DT Fourier transform and its Inverse
DT Fourier Transform_ECE301Fall2008mboutin	$\,\mathcal{X}(\omega)=\mathcal{F}(x[n])=\sum_{n=-\infty}^{\infty}x[n]e^{-j\omega n}\,$
DT Inverse Fourier Transform_ECE301Fall2008mboutin	$\,x[n]=\mathcal{F}^{-1}(\mathcal{X}(\omega))=\frac{1}{2\pi} \int_{0}^{2\pi}\mathcal{X}(\omega)e^{j\omega n} d \omega\,$
DT Fourier Transform Pairs
DT Fourier Transform Pair_ECE301Fall2008mboutin	$e^{jw_0n} \longrightarrow 2\pi\sum_{l=-\infty}^{+\infty}\delta(w-w_0-2\pi l) \$
DT Fourier an_ECE301Fall2008mboutin	$a^{n} u[n], \|a\|<1 \longrightarrow \frac{1}{1-ae^{-j\omega}} \$

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+=Discrete-time Fourier Transform Pairs and Properties=
+Please feel free to add onto this table!
-=DTFourierTransformCollectedfromECE301=
+{|
+! colspan="2" style="background: #eee;" | DT Fourier transform and its Inverse
+|-
+| align="right" style="padding-right: 1em;" | [[DT Fourier Transform_ECE301Fall2008mboutin]] || {{:DT Fourier Transform_ECE301Fall2008mboutin}}
+|-
+| align="right" style="padding-right: 1em;" | [[DT Inverse Fourier Transform_ECE301Fall2008mboutin]] || {{:DT Inverse Fourier Transform_ECE301Fall2008mboutin}}
+|-
+! colspan="2" style="background: #eee;" | DT Fourier Transform Pairs
+|-
+| align="right" style="padding-right: 1em;" | [[:DT Fourier Transform Pair_ECE301Fall2008mboutin]] || {{:DT Fourier Transform Pair_ECE301Fall2008mboutin}}
+|-
+|-
+| align="right" style="padding-right: 1em;" | [[:DT Fourier an_ECE301Fall2008mboutin]] || {{:DT Fourier an_ECE301Fall2008mboutin}}
+|-
+|}
-Put your content here . . .
+----
-[[ MegaCollectiveTableTrial1|Back to MegaCollectiveTableTrial1]]
+[[ MegaCollectiveTableTrial1|Back to Collective Table]]