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![File:Onfreq.png](https://upload.wikimedia.org/wikipedia/commons/thumb/2/2f/Onfreq.png/800px-Onfreq.png)
Size of this preview: 800 × 373 pixels. Other resolutions: 320 × 149 pixels | 640 × 298 pixels | 1,274 × 594 pixels.
Original file (1,274 × 594 pixels, file size: 83 KB, MIME type: image/png)
Summary
DescriptionOnfreq.png |
English: This image shows the real and imaginary parts of an oscillating function times the complex exponential with the same oscillation. |
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Date | ||||
Source | Own work | |||
Author | Bob K | |||
Permission (Reusing this file) |
I, the copyright holder of this work, hereby publish it under the following license:
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Other versions |
This file was derived from: |
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Octave/QTplot source InfoField | click to expand
This graphic was created by the following Octave script: graphics_toolkit("qt") % has "insert text" option
% standardize the dimensions of all 3 plots
set(0, "DefaultAxesXlim",[-2 +2])
set(0, "DefaultAxesYlim",[-1 +1])
dt = .01;
t = -2:dt:2;
carrier = cos(2*pi*3*t);
envelope = e.^(-pi*t.^2);
signal = carrier.*envelope;
figure("position", [1 1 1500 600]);
subplot(1,3,1)
plot(t, signal)
set(gca, 'xtick', -2:2, 'fontsize',16)
xlabel('t', 'fontsize',24, 'fontweight','normal')
ylabel('oscillates at 3 Hz', 'fontsize',18, 'fontweight','normal')
str = 'f(t) = cos(2\pi 3 t) e^{-\pi t^2}';
title(str,'Interpreter','tex', 'fontsize',28, 'fontweight','normal')
mixer = e.^(-i*2*pi*3*t);
mixed = mixer.* signal;
sum(real(mixed))*dt % integrate the product
subplot(1,3,2)
plot(t, real(mixed))
set(gca, 'xtick', -2:2, 'fontsize',16)
xlabel('t', 'fontsize',24, 'fontweight','normal')
ylabel('Integrates to 0.5', 'fontsize',20, 'fontweight','normal')
str = 'Re( f(t) e^{-i2\pi 3 t} )';
title(str,'Interpreter','tex', 'fontsize',28, 'fontweight','normal')
subplot(1,3,3)
plot(t, imag(mixed))
set(gca, 'xtick', -2:2, 'fontsize',16)
xlabel('t', 'fontsize',24, 'fontweight','normal')
ylabel('Integrates to 0.', 'fontsize',20, 'fontweight','normal')
str = 'Im( f(t) e^{-i2\pi 3 t} )';
title(str,'Interpreter','tex', 'fontsize',28, 'fontweight','normal')
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Captions
A signal at 3 Hz, and the corresponding integrands of the Fourier transform at 3 Hz.
Items portrayed in this file
depicts
creator
some value
author name string: Bob K
Wikimedia username: Bob K
copyright status
copyrighted, dedicated to the public domain by copyright holder
copyright license
Creative Commons CC0 License
source of file
original creation by uploader
inception
2 January 2024
media type
image/png
File history
Click on a date/time to view the file as it appeared at that time.
Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 18:49, 2 January 2024 | ![]() | 1,274 × 594 (83 KB) | Bob K | Uploaded own work with UploadWizard |
File usage
The following pages on the English Wikipedia use this file (pages on other projects are not listed):
Metadata
This file contains additional information, probably added from the digital camera or scanner used to create or digitize it.
If the file has been modified from its original state, some details may not fully reflect the modified file.
Horizontal resolution | 37.78 dpc |
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Vertical resolution | 37.78 dpc |
Software used |
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