File:Amplitude & phase vs frequency for 3-term boxcar filter.svg

Summary

Description
English: These graphs depict the same transfer function as File:Frequency response of 3-term boxcar filter.gif. But here, the amplitude is a signed quantity. And where it is negative, the quantity π has been added to the phase plot (before computing the principal value). The purpose is to illustrate the linear-phase property of the FIR filter.
Русский: Амлитудно-частотная и фазовая характеристики фильтра с конечной импульсной характеристикой скользящего среднего
Date
Source Own work based on: Amplitude & phase vs frequency for a 3-term boxcar filter.gif:  by Bob K
Author
Original:
Vector:
Category:Vectorizations
Other versions
SVG development
InfoField
Python source
InfoField
click to expand

This script is a translation of the original Octave script into Python, for the purpose of generating an SVG file to replace the GIF version.

import scipy
from scipy import signal
import numpy as np
from matplotlib import pyplot as plt

N = 256
h = np.array([1., 1., 1.]) / 3
H = scipy.fftpack.shift(scipy.fft(h, n=N), np.pi)
w = np.linspace(-N/2, N/2-1, num=N) * 2 * np.pi / N

amplitude = abs(H)
L = int(np.floor(N/6))
negate1 = np.array(range(L)) + 1
negate2 = N - np.array(range(L)) - 1
amplitude[negate1] = -amplitude[negate1]
amplitude[negate2] = -amplitude[negate2]
H[negate1] = -H[negate1]
H[negate2] = -H[negate2]

fig = plt.figure(figsize=[5,5])
plt.subplot(211)
plt.plot(w, amplitude, 'blue')
plt.grid(True)
plt.ylabel('Amplitude')
plt.xlim([-np.pi,np.pi])
plt.xticks([-np.pi, -2*np.pi/3,0,2*np.pi/3,np.pi], [])
plt.subplot(212)
plt.plot(w, np.angle(H), 'blue')
plt.grid(True)
plt.ylabel('Phase (radians)')
plt.xlabel('$\\longleftarrow$ Frequency ($\\omega$) (radians/sample) $\\longrightarrow$')
plt.xticks([-np.pi, -2*np.pi/3,0,2*np.pi/3,np.pi], ['-$\pi$','-2$\pi$/3','0','2$\pi$/3','$\pi$'])
plt.xlim([-np.pi,np.pi])
plt.yticks([-np.pi, -2,-1,0,1,2,np.pi], ['-$\pi$','-2','-1','0','1','2','$\pi$'])
plt.ylim([-np.pi,np.pi])
plt.subplots_adjust(hspace=0.1)
plt.savefig('Amplidue & phase vs frequency response of 3-term boxcar filter.svg', bbox_inches='tight', transparent=True)
Octave/gnuplot source
InfoField
click to expand
This script was derived from the original in order to address some GNUplot bugs: a missing title and two missing axis labels.  And to add an Octave print function, which creates an SVG file.  Alternatively, the gnuplot screen image has an export function that produces an SVG file, but the π characters aren't as professional-looking.  I think the resultant quality produced by this script is now better than the file produced by the Python script.
graphics_toolkit gnuplot
clear all; close all; clc
  
hfig = figure("position",[100 100 509 509]);

x1 = .12;               % left margin for name of Y-variable
x2 = .02;               % right margin
y1 = .10;               % bottom margin for ticks
y2 = .08;               % top margin for title
dy = .08;               % vertical space between rows

width = 1-x1-x2;
height= (1-y1-y2-dy)/2; % space allocated for each of 2 rows

x_origin = x1;
y_origin = 1;           % start at top of graph area
%=======================================================
  N= 256;
  h = [1 1 1]/3;              % impulse response
  H = fftshift(fft(h,N));     % samples of DTFT
  abscissa = (-N/2:N/2-1)*2*pi/N;  % normalized frequency

% Specify the bins that are to show a negative amplitude
  L = floor(N/6);
  negate = [1+(0:L) N-(0:L-1)];
  amplitude = abs(H);
  amplitude(negate) = -amplitude(negate);
  H(negate) = -H(negate);   % compensate the phase of those bins
  phase = angle(H);
%=======================================================
  y_origin = y_origin -y2 -height;        % position of top row
  subplot("position",[x_origin y_origin width height])
  plot(abscissa, amplitude, "linewidth", 2);
% Default xaxislocation is "bottom", which is where we want the tick labels.
% set(gca, "xaxislocation", "origin")
  hold on
  plot(abscissa, zeros(1,N), "color", "black")  % draw x-axis
  xlim([-pi pi])
  ylim([-.4 1.2])
  set(gca, "XTick", [-pi -2*pi/3 0 2*pi/3 pi])
  set(gca, "YTick", [-.2 0 .2 .4 .6 .8 1])
  grid("on")

  ylabel("Amplitude")
% set(gca, "ticklabelinterpreter", "tex")	% tex is the default
  set(gca, "XTickLabel", ['-\pi'; '-2\pi/3'; '0'; '2\pi/3'; '\pi';])
  set(gca, "YTickLabel", ['-.2'; '0'; '.2'; '.4'; '.6'; '.8'; '1';])
  title("Frequency response of 3-term boxcar filter", "fontsize", 12)
%=======================================================
  y_origin = y_origin -dy -height;
  subplot("position",[x_origin y_origin width height])
  plot(abscissa, phase, "linewidth", 2);
  xlim([-pi pi])
  ylim([-pi pi])
  set(gca, "XTick", [-pi -2*pi/3 0 2*pi/3 pi])
  set(gca, "YTick", [-pi -2 -1 0 1 2 pi])
  grid("on")

  xlabel('\leftarrow Frequency (\omega) (radians/sample) \rightarrow')
  ylabel("Phase (radians)")
% set(gca, "ticklabelinterpreter", "tex")	% tex is the default
  set(gca, "XTickLabel", ['-\pi'; '-2\pi/3'; '0'; '2\pi/3'; '\pi';])
  set(gca, "YTickLabel", ['-\pi'; '-2'; '-1'; '0'; '1'; '2'; '\pi';])

% The print function results in nicer-looking "pi" symbols
% than the export function on the GNUPlot figure toolbar.
print(hfig,"-dsvg", "-S509,509","-color", ...
'C:\Users\BobK\Amplitude & phase vs frequency for a 3-term boxcar filter.svg')

Licensing

Krishnavedala, 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#Amplitude%20&%20phase%20vs%20frequency%20for%203-term%20boxcar%20filter.svgCategory:Self-published work
Category:Phase plots Category:Bode plots Category:Created with GNU Octave Category:Images with Octave source code Category:Images with Gnuplot source code Category:Images with Python source code
Category:Bode plots Category:CC-Zero Category:Created with GNU Octave Category:Images with Gnuplot source code Category:Images with Octave source code Category:Images with Python source code Category:Phase plots Category:Self-published work Category:Valid SVG created with Python Category:Vectorizations