(→DT Fourier Transform Pairs) |
(→CT Fourier Transform Properties) |
||
| Line 68: | Line 68: | ||
=== CT Fourier Transform Properties === | === CT Fourier Transform Properties === | ||
*[[CT_Fourier_Int/Diff_ECE301Fall2008mboutin]]{{:CT_Fourier_Int/Diff}} | *[[CT_Fourier_Int/Diff_ECE301Fall2008mboutin]]{{:CT_Fourier_Int/Diff}} | ||
| + | |||
*[[CT Time and Frequency Scaling_ECE301Fall2008mboutin]] : <math>x(at) \leftarrow \rightarrow \frac{1}{|a|}X(\frac{j\omega }{a})\,</math> | *[[CT Time and Frequency Scaling_ECE301Fall2008mboutin]] : <math>x(at) \leftarrow \rightarrow \frac{1}{|a|}X(\frac{j\omega }{a})\,</math> | ||
| + | |||
*[[CT Differentiation in Frequency_ECE301Fall2008mboutin]]{{:CT Differentiation in Frequency}} | *[[CT Differentiation in Frequency_ECE301Fall2008mboutin]]{{:CT Differentiation in Frequency}} | ||
| + | |||
*[[CT Convolution_ECE301Fall2008mboutin]] : <math> F(x_1(t)*x_2(t)) = X_1(\omega)X_2(\omega) \!</math> | *[[CT Convolution_ECE301Fall2008mboutin]] : <math> F(x_1(t)*x_2(t)) = X_1(\omega)X_2(\omega) \!</math> | ||
| + | |||
*[[CT Frequency Shifting_ECE301Fall2008mboutin]] : <math> F(e^{jw0t}x(t)) = X(j(w - w0)) \!</math> | *[[CT Frequency Shifting_ECE301Fall2008mboutin]] : <math> F(e^{jw0t}x(t)) = X(j(w - w0)) \!</math> | ||
| + | |||
{{:CT Multiplication Property}} | {{:CT Multiplication Property}} | ||
| + | |||
*[[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}} | ||
| + | |||
*[[CT Duality Property_ECE301Fall2008mboutin]] :<math> F(x(t)) = X(w) = 2\pi x(-w) \!</math> {{:CT Duality Property}} | *[[CT Duality Property_ECE301Fall2008mboutin]] :<math> F(x(t)) = X(w) = 2\pi x(-w) \!</math> {{:CT Duality Property}} | ||
| + | |||
| + | *[[CT Conjugate Symmetry_ECE301Fall2008mboutin]] :<math> F(x(t)^*) = X^*(w) \!</math> {{:CT Duality Property}} | ||
=== Parsevel Relationship for CT signals === | === Parsevel Relationship for CT signals === | ||
Revision as of 18:49, 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
Euler's Formula
- Complex exponential in terms of sinusoidal signals_ECE301Fall2008mboutinComplex exponential in terms of sinusoidal signals
- Cosine function in terms of complex exponential_ECE301Fall2008mboutinCosine function in terms of complex exponential
- Sine function in terms of complex exponential_ECE301Fall2008mboutinSine function in terms of complex exponential
Other
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
- DT Fourier Transform Pair_ECE301Fall2008mboutin DT Fourier Transform Pair
- DT Fourier Transform Pair_ECE301Fall2008mboutin DT Fourier an
- DT Fourier Transform Pair 3_ECE301Fall2008mboutin DT Fourier Transform Pair 3
- 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
- DT Fourier Transform Time Reversal_ECE301Fall2008mboutin DT Fourier Transform Time Reversal
- DT Fourier Transform Duality_ECE301Fall2008mboutin DT Fourier Transform Duality
Parsevel Relationship for DT signals
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 Time-averaged Power of a Signal over an infinite interval_ECE301Fall2008mboutin CT Power of a Signal
CT Fourier Transform Pairs
- CT_Fourier Pairs 1_ECE301Fall2008mboutinCT Fourier Pairs 1
- CT_Fourier Pairs 2_ECE301Fall2008mboutinCT Fourier Pairs 2
- CT_Fourier Pairs 3_ECE301Fall2008mboutin CT Fourier Pairs 3
- CT_Fourier Pairs 4_ECE301Fall2008mboutin CT Fourier Pairs 4
- CT_Fourier Pairs 5_ECE301Fall2008mboutin CT Fourier Pairs 5
- CT_Fourier Pairs 6_ECE301Fall2008mboutin CT Fourier Pairs 6
- CT_Fourier Pairs 7_ECE301Fall2008mboutin CT Fourier Pairs 7
- CT_Fourier Pairs 8_ECE301Fall2008mboutin CT Fourier Pairs 8
- CT_Fourier Pairs 9_ECE301Fall2008mboutin CT Fourier Pairs 9
CT Fourier Transform Properties
- 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 Multiplication Property Mimis Version_ECE301Fall2008mboutinCT Multiplication Property Mimis Version
- CT Duality Property_ECE301Fall2008mboutin :$ F(x(t)) = X(w) = 2\pi x(-w) \! $ CT Duality Property
- CT Conjugate Symmetry_ECE301Fall2008mboutin :$ F(x(t)^*) = X^*(w) \! $ CT Duality Property
Parsevel Relationship for CT signals
- Parseval's Relation for Aperiodic Signals_ECE301Fall2008mboutinParseval's Relation for Aperiodic Signals
- put a property here following syntax described at top of page.
