File:Chirp.gif
Summary
| Description |
English: A signal whose spectral content changes with time, e.g. the low frequencies arrive before the high frequencies, is said to be "chirped".
Notice that in this simple example the overall spectrum of the chirped pulse is wider than the unchirped one, thus keeping the pulse duration constant. If you keep the bandwidth constant, the chirped pulse will stretch in time. |
| Date | |
| Source | https://twitter.com/j_bertolotti/status/1359088862396612612 |
| Author | Jacopo Bertolotti |
| Permission (Reusing this file) |
https://twitter.com/j_bertolotti/status/1030470604418428929 |
Mathematica 12.0 code
a = 5*Sin[\[Pi]/2 \[Tau]]^2
frames = Table[GraphicsRow[{
ListPointPlot3D[Table[{t, \[Omega], E^(-((\[Omega] - (a t + \[Omega]0))^2/(2 \[Sigma]^2)))/(Sqrt[2 \[Pi]] \[Sigma]) /. {\[Sigma] -> 1, \[Omega]0 -> 10}}, {t, 0, 5, 0.25}, {\[Omega], 5, 40, 0.05}], PlotRange -> All, PlotStyle -> Directive[Black, PointSize[0.01]], Filling -> Bottom, FillingStyle -> Directive[Opacity[0.5], White], ViewPoint -> {2.5, -2.5, 2.5}, AxesOrigin -> {5, 5, 0}, Boxed -> False, Axes -> {True, True, False}, Ticks -> False, Epilog -> {Text[Style["t", Bold], {0.2, 0.2}], Text[Style["\[Omega]", Bold], {0.8, 0.2}]}]
,
Show[
Plot[Abs[E^(-(1/2) t (t \[Sigma]^2 - 2 I (\[Omega]0)))/Sqrt[2 \[Pi]]] /. {\[Sigma] -> 1, \[Omega]0 -> 10}, {t, -4, 4}, PlotRange -> {-0.5, 0.5}, Axes -> False, PlotStyle -> Gray, PlotPoints -> 50]
,
Plot[Re[E^(-(1/2) t (t \[Sigma]^2 - 2 I (a t + \[Omega]0)))/Sqrt[2 \[Pi]]] /. {\[Sigma] -> 1, \[Omega]0 -> 10}, {t, -4, 4}, PlotRange -> {-0.5, 0.5}, Axes -> False, PlotStyle -> Black, PlotPoints -> 50]
]
}]
, {\[Tau], 0, 1, 0.05}];
ListAnimate[Join[Table[frames[[1]], {5}], frames, Table[frames[[-1]], {5}],
Reverse[frames]]]
Licensing
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This file is made available under the Creative Commons CC0 1.0 Universal Public Domain Dedication. |
| The person who associated a work with this deed has dedicated the work to the public domain by waiving all of their rights to the work worldwide under copyright law, including all related and neighboring rights, to the extent allowed by law. You can copy, modify, distribute and perform the work, even for commercial purposes, all without asking permission.
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