Image:Phase Plots.svg

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[edit] Summary

This svg file is made by Ugur Zongur using GNU Octave and Gnuplot in order to demonstrate linearity or non-linearity of phase plots of various filters.

These are the phase plots of:

a) FIR Filter (Type II) with impulse response: h[n] = δ[n − 3] + δ[n − 2] + δ[n − 1] + δ[n]

b) FIR Filter (Type IV) with impulse response: h[n] = δ[n − 3] + δ[n − 2] − δ[n − 1] − δ[n]

c) IIR Filter with impulse response:

d) FIR Filter with impulse response: h[n] = 4δ[n − 3] + 3δ[n − 2] + 2δ[n − 1] + δ[n]

All plots are Arg[H(e^jω)] vs normalized ω with pi .

GNU Octave and Gnuplot codes used to create the file is given below:

GNU Octave Code:

% Phase Demonstration of basic Filters
% Written By: Ugur Zongur

a=[1 1 1 1]; % Symmetrical (So this has got Linear Phase)
[pp_1,w] = freqz(a,1);

a=[1 1 -1 -1]; % Symmetrical (So this has got Linear Phase)
[pp_2,w] = freqz(a,1);

a=[1 2]; % Numerator
b=[3 4]; % Denominator
[pp_3,w] = freqz(a,b);

a=[4 3 2 1]; % Not Symmetrical (So this hasn't got Linear Phase)
[pp_4,w] = freqz(a,1);

data = [w/pi ; arg(pp_1); arg(pp_2); arg(pp_3); arg(pp_4)]';

save -ascii 'Phase_Plots.dat' data;

Gnuplot Code:

# set the output
set terminal svg
set output "Phase_Plots.svg"

# axis properties
set xrange [0:1]
set key off

# Set up a four-pane multiplot
set size 1, 1
set origin 0, 0
set multiplot

set title "a) FIR Filter (Type II) having Linear Phase"
set size 0.5,0.5
set origin 0 , 0.5
plot "Phase_Plots.dat" using 1:2 with lines linewidth 2

set title "b) FIR Filter (Type IV) having Linear Phase"
set size 0.5, 0.5
set origin 0.5 , 0.5
plot "Phase_Plots.dat" using 1:3 with lines linewidth 2

set title "c) IIR Filter having Non-Linear Phase"
set size 0.5, 0.5
set origin 0 , 0
plot "Phase_Plots.dat" using 1:4 with lines linewidth 2

set title "d) FIR Filter having Non-Linear Phase"
set size 0.5, 0.5
set origin 0.5 , 0
plot "Phase_Plots.dat" using 1:5 with lines linewidth 2

[edit] Licensing

I, the creator of this work, hereby release it into the public domain. This applies worldwide.
In case this is not legally possible,
I grant any entity the right to use this work for any purpose, without any conditions, unless such conditions are required by law.

File history

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• (del) (cur) 12:20, 8 April 2006 . . Zongur (Talk | contribs) . . 600×480 (29,212 bytes) (Made by Ugur Zongur using GNU Octave and Gnuplot in order to demonstrate linearity or non-linearity of phase plots of various filters. )

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• Linear phase