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= Discrete Fourier Transform =
 
= Discrete Fourier Transform =
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Please help building this page!
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*Let's try to follow the same table syntax as for [[CT_Fourier_Transform_(frequency_in_hertz)|this table]]
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*You can copy and paste the formulas from these pages:
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**[[Student_summary_Discrete_Fourier_transform_ECE438F09]]
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**[[Discrete_Time_Fourier_Transform_Properties_(DTFT)_-_Mohammed_Almathami]]
  
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Definition: let x[n] be a DT signal with Period N.
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{|
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|-
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<math> X [k] = \sum_{k=0}^{N-1} x[n].e^{-J.2pi.kn/N}</math>
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! style="background: none repeat scroll 0% 0% rgb(228, 188, 126); font-size: 110%;" colspan="2" | Discrete Fourier Transform Pairs and Properties  [[More on CT Fourier transform|(info)]]
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|-
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! style="background: none repeat scroll 0% 0% rgb(238, 238, 238);" colspan="2" | Definition CT Fourier Transform and its Inverse
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|-
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| align="right" style="padding-right: 1em;" | [[Discrete Fourier Transform|Discrete Fourier Transform]]
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| <math>X [k] = \sum_{k=0}^{N-1} x[n]e^{-j 2\pi \frac{k n}{N}} \, </math>
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|-
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| align="right" style="padding-right: 1em;" | Inverse Discrete Fourier Transform
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| <math>\,x [n] = (1/N) \sum_{k=0}^{N-1} X[k] e^{j 2\pi\frac{kn}{N}} \,</math>
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|}
  
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<math> x [n] = (1/N) \sum_{k=0}^{N-1} X[k].e^{J.2pi.kn/N}</math>
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{|
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|-
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! style="background: none repeat scroll 0% 0% rgb(238, 238, 238);" colspan="4" | Discrete Fourier Transform Pairs [[Discrete Fourier Transform| (info)]]
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|-
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| align="right" style="padding-right: 1em;" |
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| <span class="texhtml">''x''[''n'']</span>
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| <math>\longrightarrow</math>
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| <math> X[k] </math>
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|-
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| align="right" style="padding-right: 1em;" | name
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| <math>type signal here\ </math>  
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|
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| <math> type transform here \! \ </math>
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|-
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| align="right" style="padding-right: 1em;" | name
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| <math>type signal here \ </math>
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|
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| <math>type transform here</math>
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|}
  
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Please help building this page!
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{|
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|-
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*You can copy the table syntax from [[CT_Fourier_Transform_(frequency_in_hertz)|this page]]
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! style="background: none repeat scroll 0% 0% rgb(238, 238, 238);" colspan="4" | Discrete Fourier Transform Properties
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*You can copy and paste the formulas from these pages:
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|-
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**[[Student_summary_Discrete_Fourier_transform_ECE438F09]]
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| align="right" style="padding-right: 1em;" |
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**[[Discrete_Time_Fourier_Transform_Properties_(DTFT)_-_Mohammed_Almathami]]
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| <span class="texhtml">''x''[''n'']</span>
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| <math>\longrightarrow</math>
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| <math> X[k] </math>
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|-
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| align="right" style="padding-right: 1em;" | multiplication property
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| <math>x[n]y[n] \ </math>
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|
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| <math> write DFT here</math>
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|-
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| align="right" style="padding-right: 1em;" | convolution property
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| <math>x(t)*y(t) \!</math>
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|
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| <math> X(f)Y(f) \!</math>
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|-
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| align="right" style="padding-right: 1em;" | time reversal
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| <math>\ x(-t) </math>
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|
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| <math>\ X(-f)</math>
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|}
  
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{|
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|-
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! style="background: none repeat scroll 0% 0% rgb(238, 238, 238);" colspan="2" | Other Discrete Fourier Transform Properties
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|-
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| align="right" style="padding-right: 1em;" | property
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| <math>type math here</math>
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|}
 
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----
 
[[Collective_Table_of_Formulas|Back to Collective Table]]
 
[[Collective_Table_of_Formulas|Back to Collective Table]]
  
 
[[Category:Formulas]]
 
[[Category:Formulas]]

Revision as of 06:11, 23 September 2011

Discrete Fourier Transform

Please help building this page!

Discrete Fourier Transform Pairs and Properties (info)
Definition CT Fourier Transform and its Inverse
Discrete Fourier Transform $ X [k] = \sum_{k=0}^{N-1} x[n]e^{-j 2\pi \frac{k n}{N}} \, $
Inverse Discrete Fourier Transform $ \,x [n] = (1/N) \sum_{k=0}^{N-1} X[k] e^{j 2\pi\frac{kn}{N}} \, $
Discrete Fourier Transform Pairs (info)
x[n] $ \longrightarrow $ $ X[k] $
name $ type signal here\ $ $ type transform here \! \ $
name $ type signal here \ $ $ type transform here $
Discrete Fourier Transform Properties
x[n] $ \longrightarrow $ $ X[k] $
multiplication property $ x[n]y[n] \ $ $ write DFT here $
convolution property $ x(t)*y(t) \! $ $ X(f)Y(f) \! $
time reversal $ \ x(-t) $ $ \ X(-f) $
Other Discrete Fourier Transform Properties
property $ type math here $

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