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*[[DT Fourier Transform Multiplication_ECE301Fall2008mboutin]] {{:DT Fourier Transform Multiplication}} | *[[DT Fourier Transform Multiplication_ECE301Fall2008mboutin]] {{:DT Fourier Transform Multiplication}} | ||
*[[DT Fourier Transform Convolution_ECE301Fall2008mboutin]] {{:DT Fourier Transform Convolution}} | *[[DT Fourier Transform Convolution_ECE301Fall2008mboutin]] {{:DT Fourier Transform Convolution}} | ||
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| + | === Parsevel Relationship for DT signals === | ||
| + | <math>\frac {1}{N} \sum_{n=<N>}^{}|x[n]|^2 dt = \sum_{k=<N>}{}|a_k|^2</math> | ||
== Continuous-time domain == | == Continuous-time domain == | ||
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*[[CT Time Reversal_ECE301Fall2008mboutin]]{{:CT Time Reversal}} | *[[CT Time Reversal_ECE301Fall2008mboutin]]{{:CT Time Reversal}} | ||
*[[CT Multiplication Property Mimis Version_ECE301Fall2008mboutin]]{{:CT Multiplication Property Mimis Version}} | *[[CT Multiplication Property Mimis Version_ECE301Fall2008mboutin]]{{:CT Multiplication Property Mimis Version}} | ||
| + | |||
| + | === Parsevel Relationship for CT signals === | ||
| + | <math>\frac {1}{T} \int_{0}^{T}|x(t)|^2 dt = \sum_{k=-\inf}{inf}|a_k|^2</math> | ||
| + | |||
*put a property here following syntax described at top of page. | *put a property here following syntax described at top of page. | ||
Revision as of 09:26, 15 October 2008
Please follow the following model to add your formulas:
{{:name of the page with your formula}}
in the place where you want your formula to appear in this table. (Look at the syntax of the geometric series below for an example.) This will allow other people to refer to your formula later on (by refering to the corresponding page) while still being able to view all formulas on this page.
General Purpose Formulas
Series
- Finite Geometric Series Formula_ECE301Fall2008mboutinFinite Geometric Series Formula
- Infinite Geometric Series Formula_ECE301Fall2008mboutinInfinite Geometric Series Formula
Discrete-time domain
Useful Formulas
- DT Fourier Transform_ECE301Fall2008mboutin DT Fourier Transform
- DT Inverse Fourier Transform_ECE301Fall2008mboutin DT Inverse Fourier Transform
- put a formula here following syntax described at top of page.
DT Fourier Transform Pairs
- put a pair here following syntax described at top of page.
- put a pair here following syntax described at top of page.
DT Fourier Transform Properties
- DT Fourier Transform Multiplication_ECE301Fall2008mboutin DT Fourier Transform Multiplication
- DT Fourier Transform Convolution_ECE301Fall2008mboutin DT Fourier Transform Convolution
Parsevel Relationship for DT signals
$ \frac {1}{N} \sum_{n=<N>}^{}|x[n]|^2 dt = \sum_{k=<N>}{}|a_k|^2 $
Continuous-time domain
Useful Formulas
- CT_Fourrier_Coefficients_ECE301Fall2008mboutin CT Fourrier Coeffiecients
- Time_Shifting_ECE301Fall2008mboutin Time Shifting Property
- put a formula here following syntax described at top of page.
CT Fourier Transform Pairs
- CT_Fourier Pairs 1_ECE301Fall2008mboutinCT Fourier Pairs 1
- CT_Fourier Pairs 2_ECE301Fall2008mboutinCT Fourier Pairs 2
- put a pair here following syntax described at top of page.
CT Fourier Transform Properties
- CT_Fourier_Int/Diff_ECE301Fall2008mboutinCT Fourier Int/Diff
- CT Time and Frequency Scaling_ECE301Fall2008mboutin : $ x(at) \leftarrow \rightarrow \frac{1}{|a|}X(\frac{j\omega }{a})\, $
- CT Convolution_ECE301Fall2008mboutin : $ F(x_1(t)*x_2(t)) = X_1(\omega)X_2(\omega) \! $
- CT Frequency Shifting_ECE301Fall2008mboutin : $ F(e^{jw0t}x(t)) = X(j(w - w0)) \! $
- CT Time Reversal_ECE301Fall2008mboutinCT Time Reversal
- CT Multiplication Property Mimis Version_ECE301Fall2008mboutinCT Multiplication Property Mimis Version
Parsevel Relationship for CT signals
$ \frac {1}{T} \int_{0}^{T}|x(t)|^2 dt = \sum_{k=-\inf}{inf}|a_k|^2 $
- put a property here following syntax described at top of page.
