File:Onfreq.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)
Bob K, the copyright holder of this work, hereby publishes 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.

Category:CC-Zero#Onfreq.png
Category:Self-published work
Other versions Own work based on: Onfreq.svg:  and Function ocsillating at 3 hertz.svg: 
PNG development
InfoField
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')
Category:CC-Zero Category:PNG created with Octave Category:Self-published work