Spectrum: Difference between revisions
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The spectrum of a signal, say <math>u(t)</math>, shows how the variance of this signal is distributed with respect to frequency. If the spectrum of <math>u</math> is <math>\Psi(f)</math>, then the spectrum has the property that the variance of <math>u</math> is | The spectrum of a signal, say <math>u(t)</math>, shows how the variance of this signal is distributed with respect to frequency. If the spectrum of <math>u</math> is <math>\Psi(f)</math>, then the spectrum has the property that the variance of <math>u</math> is | ||
<math> | <math>\overline{u} = \int_0^{\infty}\, \mathrm{d}f </math> | ||
Revision as of 20:33, 13 July 2021
| Short definition of Spectrum |
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| Shows how the variance of a signal is distributed with respect to frequency or wavenumber |
This is the common definition for Spectrum, but other definitions maybe discussed within the wiki.
The spectrum of a signal, say [math]\displaystyle{ u(t) }[/math], shows how the variance of this signal is distributed with respect to frequency. If the spectrum of [math]\displaystyle{ u }[/math] is [math]\displaystyle{ \Psi(f) }[/math], then the spectrum has the property that the variance of [math]\displaystyle{ u }[/math] is
[math]\displaystyle{ \overline{u} = \int_0^{\infty}\, \mathrm{d}f }[/math]
