W3C-validity not checked.

I, the copyright holder of this work, hereby publish it under the following licenses:

This file is licensed under the Creative Commons Attribution-Share Alike 3.0 Unported, 2.5 Generic, 2.0 Generic and 1.0 Generic license.

You are free:

• to share – to copy, distribute and transmit the work
• to remix – to adapt the work

Under the following conditions:

• attribution – You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
• share alike – If you remix, transform, or build upon the material, you must distribute your contributions under the same or compatible license as the original.

https://creativecommons.org/licenses/by-sa/3.0CC BY-SA 3.0 Creative Commons Attribution-Share Alike 3.0 truetrue

Permission is granted to copy, distribute and/or modify this document under the terms of the GNU Free Documentation License, Version 1.2 or any later version published by the Free Software Foundation; with no Invariant Sections, no Front-Cover Texts, and no Back-Cover Texts. A copy of the license is included in the section entitled GNU Free Documentation License.http://www.gnu.org/copyleft/fdl.htmlGFDLGNU Free Documentation Licensetruetrue

You may select the license of your choice.

This image is a derivative work of the following images:

• File:Hilbert_transform.png licensed with Cc-by-sa-3.0,2.5,2.0,1.0, GFDL
  • 2005-07-02T18:54:12Z Omegatron 1600x1120 (123072 Bytes) Image of the Hilbert transform of a square wave.
  • 2005-06-26T19:53:50Z Omegatron 608x433 (4690 Bytes) A graph or diagram made by [[User:Omegatron]]. (Uploaded with Wikimedia Commons.) Source: Created by [[User:Omegatron]] {{GFDL}}{{cc-by-sa-2.0}} [[Category:Diagrams]]\

Created entirely in GNUPlot using:

set term svg size 1600,1100 fsize 32
set out "Hilbert_transform.svg"

unset key
set samples 1000

set xrange [0:6]
set yrange [-1:1]
set xtics 1
set ytics 1

set grid lw 2 lc rgb "grey"

# set style of Hilbert transform
set style line 1 lw 2 lc rgb "red" 
# set style of rectangular function
set style line 2 lw 2 lc rgb "blue"

set border -1 lw 3

# Heaviside step function
u(t) = 0.5 * (1 + sgn(t))

# Rectangular function
rect(t) = u(t + 0.5) - u(t - 0.5)

# Hilbert transform of rectangular function
hrect(t) = log(abs((t + 0.5)/(t - 0.5)))/pi

# Sums from a to b of the above functions
hrectsum(t,a,b) = (a >= b) ? 0 : (hrectsum(t,a+1,b) + hrect(t - 2*a))
rectsum(t,a,b) = (a >= b) ? 0 : (rectsum(t,a+1,b) + rect(t - 2*a))

plot hsum(x,-500,500) ls 1, rectsum(x,-10,20)-0.5 ls 2

Uploaded with derivativeFX