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Original file (1,274 × 594 pixels, file size: 83 KB, MIME type: image/png)

Summary

Description
English: This image shows the real and imaginary parts of an oscillating function times the complex exponential with the same oscillation.
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:
Creative Commons CC-Zero 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.

Other versions

This file was derived from:

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')

Captions

A signal at 3 Hz, and the corresponding integrands of the Fourier transform at 3 Hz.

Items portrayed in this file

depicts

2 January 2024

image/png

File history

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Date/TimeThumbnailDimensionsUserComment
current18:49, 2 January 2024Thumbnail for version as of 18:49, 2 January 20241,274 × 594 (83 KB)Bob KUploaded own work with UploadWizard

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