10/10,13,16,17 - Fourier Transform Properties: Difference between revisions
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|<math> \Longrightarrow </math> |
|<math> \Longrightarrow </math> |
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|<math> H(f)\cdot e^{j\,2\,\pi f\,\lambda}</math> |
|<math> H(f)\cdot e^{j\,2\,\pi f\,\lambda}</math> |
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|Time Invariance |
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|<math> x(\lambda)\cdot 1\cdot e^{j\,2\,\pi f\,\lambda}</math> |
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|<math> \Longrightarrow </math> |
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|<math> x(\lambda)\cdot H(f)\cdot e^{j\,2\,\pi f\,\lambda}</math> |
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|Proportionality |
|Proportionality |
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|- |
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|<math> \int_{-\infty}^{\infty}x(\lambda)\cdot 1\cdot e^{j\,2\,\pi f\,\lambda}\,d\lambda=X^{-1??}(F)</math> |
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|<math> \Longrightarrow </math> |
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|<math> \int_{-\infty}^{\infty}x(\lambda)x(\lambda)\cdot H(f)\cdot e^{j\,2\,\pi f\,\lambda}\,d\lambda=X^{-1??}(F)\,H(f)</math> |
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|Superposition |
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Revision as of 01:51, 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? | Time Invariance | ||
Proportionality | |||
Superposition |