10/10,13,16,17 - Fourier Transform Properties: Difference between revisions
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|<math> \int_{-\infty}^{\infty}\delta (t)\,e^{-j\,2\,\pi f\,t}\,dt=F[\delta(t)]=1</math> |
|<math> \int_{-\infty}^{\infty}\delta (t)\,e^{-j\,2\,\pi f\,t}\,dt=F[\delta(t)]=1</math> |
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|<math> \Longrightarrow </math> |
|<math> \Longrightarrow </math> |
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|<math> \int_{-\infty}^{\infty}h(t)\,e^{-j\,2\,\pi f\,t}\,dt=H(f) |
|<math> \int_{-\infty}^{\infty}h(t)\,e^{-j\,2\,\pi f\,t}\,dt=F[h(t)]=H(f)</math> |
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|Superposition |
|Superposition |
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Revision as of 17:17, 23 November 2008
Properties of the Fourier Transform
Linearity
Time Invariance (Delay)
Let and | ||
Frequency Shifting
Double Sideband Modulation
Differentiation in Time
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? | Time Invariance | ||
Proportionality | |||
Superposition |