Difference between revisions of "Table of Formulas and Properties ECE301Fall2008mboutin" - Rhea

Revision as of 16:17, 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

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
• 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

• Parsevel Relationship for DT signals_ECE301Fall2008mboutinParsevel 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 Energy of a Signal_ECE301Fall2008mboutin CT Energy of a Signal

• 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 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 Differentiation in Frequency_ECE301Fall2008mboutinCT Differentiation in Frequency
• 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

• CT Time Reversal_ECE301Fall2008mboutinCT Time Reversal
• 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

Parsevel Relationship for CT signals

• Parsevel Relationship for CT signals_ECE301Fall2008mboutinParsevel 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.