10/10,13,16,17 - Fourier Transform Properties: Difference between revisions
Jump to navigation
Jump to search
(→??) |
|||
Line 76: | Line 76: | ||
|} |
|} |
||
===The Game (frequency domain)=== |
===The Game (frequency domain)=== |
||
{| border="1" cellpadding="5" cellspacing="0" |
|||
|- |
|||
|Input |
|||
|LTI System |
|||
|Output |
|||
|Reason |
|||
|- |
|||
|<math> \delta (t) \,\!</math> |
|||
|<math> \Longrightarrow </math> |
|||
|<math> h(t) \,\!</math> |
|||
|Given |
|||
|- |
|||
|<math> \delta (t)\,e^{-j\,2\,\pi f\,t}</math> |
|||
|<math> \Longrightarrow </math> |
|||
|<math> h(t)\,e^{-j\,2\,\pi f\,t}</math> |
|||
|Proportionality |
|||
|- |
|||
|<math> \int_{-\infty}^{\infty}\delta (t)\,e^{-j\,2\,\pi f\,t}\,dt=F[\delta(t)]=1</math> |
|||
|<math> \Longrightarrow </math> |
|||
|<math> \int_{-\infty}^{\infty}h(t)\,e^{-j\,2\,\pi f\,t}\,dt=H(f) How??</math> |
|||
|Superposition |
|||
|- |
|||
|<math> F[\delta(t-\lambda)]=1\cdot e^{j\,2\,\pi f\,\lambda}</math> The notes have <math>e^{-j\,2\,\pi f\,\lambda}</math> Is this an error? |
|||
|<math> \Longrightarrow </math> |
|||
|<math> H(f)\cdot e^{j\,2\,\pi f\,\lambda}</math> |
|||
|Proportionality |
|||
|} |
Revision as of 01:47, 22 November 2008
Properties of the Fourier Transform
Linearity
Time Invariance (Delay)
Let and | ||
??
??
??
Thus is a linear filter with transfer function |
The Game (frequency domain)
Input | LTI System | Output | Reason |
Given | |||
Proportionality | |||
Superposition | |||
The notes have Is this an error? | Proportionality |