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Nyquist_sampling.gif (576 × 189 pixels, file size: 821 KB, MIME type: image/gif, looped, 86 frames, 10 s)
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Summary
| Description |
English: The figure on the left shows a function (in gray/black) being sampled and reconstructed (in gold) at steadily increasing sample-densities, while the figure on the right shows the frequency spectrum of the gray/black function, which does not change. The highest frequency in the spectrum is ½ the width of the entire spectrum. The width of the steadily-increasing pink shading is equal to the sample-rate. When it encompasses the entire frequency spectrum it is twice as large as the highest frequency, and that is when the reconstructed waveform matches the sampled one.
Italiano: Nella figura a sinistra si può osservare una funzione (in grigio/nero) la quale viene campionata e ricostruita (in oro) con una densità di campioni in costante aumento, mentre la figura a destra mostra lo spettro delle frequenze della funzione grigio/nera, che non varia. La frequenza più alta nello spettro è la metà della larghezza dell'intero spettro. La larghezza dell'ombreggiatura rosa in costante aumento è uguale alla frequenza di campionamento. Quando racchiude l'intero spettro di frequenza essa sarà il doppio della frequenza più alta, ed è allora che la forma d'onda ricostruita diventa corrispondente a quella campionata. |
| Date | |
| Source | https://twitter.com/j_bertolotti/status/1217060092757061632 |
| Author | Jacopo Bertolotti |
| Permission (Reusing this file) |
https://twitter.com/j_bertolotti/status/1030470604418428929 |
Mathematica 11.0 code
pnyq = Table[nyq = Table[{z, g}, {z, -7, 7, sample}];
\[CapitalDelta] = nyq[[-1, 1]] - nyq[[-2, 1]];
rec = Sum[nyq[[j, 2]] Sin[\[Pi] (z + 7 + \[CapitalDelta] - j \[CapitalDelta])/\[CapitalDelta]]/(\[Pi] (z + 7 + \[CapitalDelta] - j \[CapitalDelta])/\[CapitalDelta]), {j, 1, Dimensions[nyq][[1]]}];
GraphicsRow[{
Plot[{g, rec}, {z, -7, 7}, AxesLabel -> {"t", "f(t)"}, LabelStyle -> {Black, Bold}, PlotStyle -> {Directive[Thick, Gray], Directive[Thick, Orange]}, PlotRange -> {-0.8, 1}, Epilog -> {PointSize[0.02], Point[nyq]}]
,
Show[
Plot[Abs[fg]^2, {k, -10, 10}, AxesLabel -> {"\[Omega]", "|F[f]\!\(\*SuperscriptBox[\(|\), \(2\)]\)"}, LabelStyle -> {Black, Bold}, PlotStyle -> {Thick, Red}, PlotRange -> {0, 0.5}]
,
Plot[Abs[fg]^2, {k, -2/\[CapitalDelta], 2/\[CapitalDelta]}, AxesLabel -> {"\[Omega]", "|F[f]\!\(\*SuperscriptBox[\(|\), \(2\)]\)"}, LabelStyle -> {Black, Bold}, PlotStyle -> {Thick, Red},
PlotRange -> {0, 0.5}, Filling -> Bottom]
]
}, ImageSize -> Large]
, {sample, 1, 0.15, -0.01}];
ListAnimate[pnyq]
Licensing
I, the copyright holder of this work, hereby publish it under the following license:
 
|
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.
|
File history
Click on a date/time to view the file as it appeared at that time.
| Date/Time | Thumbnail | Dimensions | User | Comment | |
|---|---|---|---|---|---|
| current | 14:06, 26 February 2020 | | 576 × 189 (821 KB) | AkanoToE | Changed so that the last frame lasts 1.5 seconds to give time between loops. |
| 10:10, 15 January 2020 |  | 576 × 189 (1.11 MB) | Berto | User created page with UploadWizard |
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