View source for Table of Formulas and Properties ECE301Fall2008mboutin - Rhea

[[Category:ECE 301]]
[[Category:Fall 2008]]
[[Category:mboutin]]

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{|
|- 
! colspan="2" style="background: #bbb; font-size: 110%;" | General Purpose Formulas
|-
! colspan="2" style="background: #eee;" | Series
|-
| align="right" style="padding-right: 1em;" | [[Finite Geometric Series Formula_ECE301Fall2008mboutin]] || {{:Finite Geometric Series Formula_ECE301Fall2008mboutin}}
|-
| align="right" style="padding-right: 1em;" | [[Infinite Geometric Series Formula_ECE301Fall2008mboutin]] || {{:Infinite Geometric Series Formula_ECE301Fall2008mboutin}}
|-
! colspan="2" style="background: #eee;" | Euler's Formula
|-
| align="right" style="padding-right: 1em;" | [[Complex exponential in terms of sinusoidal signals_ECE301Fall2008mboutin]] || {{:Complex exponential in terms of sinusoidal signals_ECE301Fall2008mboutin}}
|-
| align="right" style="padding-right: 1em;" | [[Cosine function in terms of complex exponential_ECE301Fall2008mboutin]] || {{:Cosine function in terms of complex exponential_ECE301Fall2008mboutin}}
|-
| align="right" style="padding-right: 1em;" | [[Sine function in terms of complex exponential_ECE301Fall2008mboutin]] || {{:Sine function in terms of complex exponential_ECE301Fall2008mboutin}}
|-
! colspan="2" style="background: #eee;" | Other
|-
| align="right" style="padding-right: 1em;" | [[sinc function_ECE301Fall2008mboutin]] || {{:sinc function_ECE301Fall2008mboutin}}
|- 
! colspan="2" style="background: #bbb; font-size: 110%;" | Discrete-Time Domain
|-
! colspan="2" style="background: #eee;" | Useful Formulas
|-
| 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}}
|-
|}

*[[DT Fourier Transform Pair 3_ECE301Fall2008mboutin]] {{:DT Fourier Transform Pair 3_ECE301Fall2008mboutin}}

=== DT Fourier Transform Properties ===
*[[DT Fourier Transform Multiplication_ECE301Fall2008mboutin]] {{:DT Fourier Transform Multiplication_ECE301Fall2008mboutin}}
*[[DT Fourier Transform Convolution_ECE301Fall2008mboutin]] {{:DT Fourier Transform Convolution_ECE301Fall2008mboutin}}
*[[DT Fourier Transform Time Reversal_ECE301Fall2008mboutin]] {{:DT Fourier Transform Time Reversal_ECE301Fall2008mboutin}}
*[[DT Fourier Transform Duality_ECE301Fall2008mboutin]] {{:DT Fourier Transform Duality_ECE301Fall2008mboutin}}

=== Parsevel Relationship for DT signals ===
*[[Parsevel Relationship for DT signals_ECE301Fall2008mboutin]]{{:Parsevel Relationship for DT signals_ECE301Fall2008mboutin}}

== Continuous-time domain ==

=== Useful Formulas ===
*[[CT Fourier Transform_ECE301Fall2008mboutin]] {{:CT Fourier Transform_ECE301Fall2008mboutin}}
*[[CT Inverse Fourier Transform_ECE301Fall2008mboutin]] {{:CT Inverse Fourier Transform_ECE301Fall2008mboutin}}
*[[CT Laplace Transform_ECE301Fall2008mboutin]] {{:CT Laplace Transform_ECE301Fall2008mboutin}}
*[[CT_Fourrier_Coefficients_ECE301Fall2008mboutin]] {{:CT_Fourrier_Coeffiecients_ECE301Fall2008mboutin}}
*[[Time_Shifting_ECE301Fall2008mboutin]] {{:Time Shifting Property_ECE301Fall2008mboutin}}
*[[CT Energy of a Signal_ECE301Fall2008mboutin]]  {{:CT Energy of a Signal_ECE301Fall2008mboutin}}
*[[CT Time-averaged Power of a Signal over an infinite interval_ECE301Fall2008mboutin]]  {{:CT Power of a Signal_ECE301Fall2008mboutin}}

=== CT Fourier Transform Pairs ===
*[[CT_Fourier Pairs 1_ECE301Fall2008mboutin| (1)]]{{:CT_Fourier Pairs 1_ECE301Fall2008mboutin}}
*[[CT_Fourier Pairs 2_ECE301Fall2008mboutin| (2)]]{{:CT_Fourier Pairs 2_ECE301Fall2008mboutin}}
*[[CT_Fourier Pairs 3_ECE301Fall2008mboutin| (3)]]  {{:CT_Fourier Pairs 3_ECE301Fall2008mboutin}}
*[[CT_Fourier Pairs 4_ECE301Fall2008mboutin|(4)]]  {{:CT_Fourier Pairs 4_ECE301Fall2008mboutin}}
*[[CT_Fourier Pairs 5_ECE301Fall2008mboutin|(5)]]  {{:CT_Fourier Pairs 5_ECE301Fall2008mboutin}}
*[[CT_Fourier Pairs 6_ECE301Fall2008mboutin|(6)]]  {{:CT_Fourier Pairs 6_ECE301Fall2008mboutin}}
*[[CT_Fourier Pairs 7_ECE301Fall2008mboutin|(7)]]  {{:CT_Fourier Pairs 7_ECE301Fall2008mboutin}}
*[[CT_Fourier Pairs 8_ECE301Fall2008mboutin|(8)]]  {{:CT_Fourier Pairs 8_ECE301Fall2008mboutin}}
*[[CT_Fourier Pairs 9_ECE301Fall2008mboutin|(9)]]  {{:CT_Fourier Pairs 9_ECE301Fall2008mboutin}}
*[[CT_Fourier Pairs 10_ECE301Fall2008mboutin|(10)]]  {{:CT_Fourier Pairs 10_ECE301Fall2008mboutin}}
*[[CT_Fourier Pairs 11_ECE301Fall2008mboutin|(11)]]  {{:CT_Fourier Pairs 11_ECE301Fall2008mboutin}}
*[[CT_Fourier Pairs 12_ECE301Fall2008mboutin|(12)]]  {{:CT_Fourier Pairs 12_ECE301Fall2008mboutin}}

=== CT Fourier Transform Properties ===
*[[CT_Fourier_Int/Diff_ECE301Fall2008mboutin]]{{:CT_Fourier_Int/Diff_ECE301Fall2008mboutin}}

*[[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_ECE301Fall2008mboutin}}

*[[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 Multiplication Property_ECE301Fall2008mboutin}}

*[[CT Time Reversal_ECE301Fall2008mboutin]]{{:CT Time Reversal_ECE301Fall2008mboutin}}

*[[CT Multiplication Property Mimis Version_ECE301Fall2008mboutin]]{{:CT Multiplication Property Mimis Version_ECE301Fall2008mboutin}}

*[[CT Duality Property_ECE301Fall2008mboutin]] :<math> F(x(t)) = X(w) = 2\pi x(-w) \!</math> {{:CT Duality Property_ECE301Fall2008mboutin}}

*[[CT Conjugate Symmetry_ECE301Fall2008mboutin]] {{:CT Conjugate Symmetry_ECE301Fall2008mboutin}}

=== Parsevel Relationship for CT signals ===
*[[Parsevel Relationship for CT signals_ECE301Fall2008mboutin]]{{:Parsevel Relationship for CT signals_ECE301Fall2008mboutin}}

*[[Parseval's Relation for Aperiodic Signals_ECE301Fall2008mboutin]]{{:Parseval's Relation for Aperiodic Signals_ECE301Fall2008mboutin}}
 
*put a property here following syntax described at top of page.

== Some Laplace Transform Pairs ==
{{:LaplaceTransforms_ECE301Fall2008mboutin}}
*[[Laplace Pairs 1_ECE301Fall2008mboutin| (1)]]{{:Laplace Pairs 1_ECE301Fall2008mboutin}}
*[[Laplace Pairs 2_ECE301Fall2008mboutin| (2)]]{{:Laplace Pairs 2_ECE301Fall2008mboutin}}
*[[Laplace Pairs 3_ECE301Fall2008mboutin| (3)]]{{:Laplace Pairs 3_ECE301Fall2008mboutin}}
*[[Laplace Pairs 4_ECE301Fall2008mboutin| (4)]]{{:Laplace Pairs 4_ECE301Fall2008mboutin}}
*[[Laplace Pairs 5_ECE301Fall2008mboutin| (5)]]{{:Laplace Pairs 5_ECE301Fall2008mboutin}}
*[[Laplace Pairs 6_ECE301Fall2008mboutin| (6)]]{{:Laplace Pairs 6_ECE301Fall2008mboutin}}
*[[Laplace Pairs 7_ECE301Fall2008mboutin| (7)]]{{:Laplace Pairs 7_ECE301Fall2008mboutin}}