File:Nyquist example.svg

Original file (SVG file, nominally 443 × 428 pixels, file size: 53 KB)

Summary

Description The Nyquist Plot for a sample function that can be converted to frequency by replacing with (imaginary frequency) and . Created using Python and matplotlib.
Date
Source Own work
Author Utkarsh Upadhyay,--Krishnavedala (talk) 20:21, 3 June 2011 (UTC) (python version)
Permission
(Reusing this file)
Public Domain
 
W3C-validity not checked.
Source Code
from numpy import *
from matplotlib.pyplot import *

def nyquist(w):		# compute the complex Nyquist response
	s = complex(0,w)
	return (1/(s**2+s+1))
	
fig = figure(figsize=(5,5))
ax = fig.add_subplot(111)
ax.grid(True)

t, N = linspace(0,5*pi,200), [] # 5*pi is approx. to infinity. 
for i in t:			# compute the complex response for +ve omega
	N = append(N,nyquist(i))
ax.plot(real(N),imag(N),label=r"$0\leq\omega\leq\infty$")
t, N = linspace(-5*pi,0,200), []
for i in t:			# compute the complex response for -ve omega
	N = append(N,nyquist(i))
ax.plot(real(N),imag(N),label=r"$-\infty\leq\omega\leq 0$")
ax.legend(frameon=False)
setp(ax.get_legend().get_texts(),fontsize='small')
ax.set_xlabel(r"$\mathrm{Re}\left[G\left(\omega\right)\right]$")
ax.set_ylabel(r"$\mathrm{Im}\left[G\left(\omega\right)\right]$")
ax.text(0.6,-1.25,r"$G(s)=\frac{1}{s^2+s+1}$",\
	fontsize=15)

#fig.show()
fig.savefig("Nyquist example.svg",bbox_inches="tight",\
	pad_inches=.15)

Licensing

Public domain I, the copyright holder of this work, release this work into the public domain. This applies worldwide.
In some countries this may not be legally possible; if so:
I grant anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law.

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27 March 2006

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Date/TimeThumbnailDimensionsUserComment
current20:10, 3 June 2011Thumbnail for version as of 20:10, 3 June 2011443 × 428 (53 KB)Krishnavedalacorrected the equation in the curve
20:04, 3 June 2011Thumbnail for version as of 20:04, 3 June 2011443 × 428 (53 KB)Krishnavedalaa well defined curve
20:55, 1 July 2010Thumbnail for version as of 20:55, 1 July 20101,000 × 1,000 (7 KB)DieBucheBotTrying to fix SVG using scour
02:36, 27 March 2007Thumbnail for version as of 02:36, 27 March 20071,000 × 1,000 (11 KB)Musically ut{{Information |Description=The Nyquist Plot for a sample function. |Source=Octave and GNU Plot |Date=27/03/06 |Author=Utkarsh Upadhyay |Permission=Public Domain |other_versions= - }}

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