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

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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
Author original: Bob K
vector version: Krishnavedala
Permission
(Reusing this file)
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.

Other versions This file was derived from: Amplitude & phase vs frequency for a 3-term boxcar filter.gif
SVG development
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The SVG code is valid.
 
This vector image was created with Python by Krishnavedala.
Python source
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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
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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')

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16 August 2017

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9f3c3a071591f369e4e0d2c300c59f7bdf6e2841

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400 pixel

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Date/TimeThumbnailDimensionsUserComment
current13:04, 1 October 2020Thumbnail for version as of 13:04, 1 October 2020435 × 400 (20 KB)KrishnavedalaText-to-graph aspect ratio renders poorly in thumbnails with text unreadable.
01:25, 3 July 2019Thumbnail for version as of 01:25, 3 July 2019512 × 512 (42 KB)Bob Kchange graph "linewidth" to 2
13:03, 2 July 2019Thumbnail for version as of 13:03, 2 July 2019512 × 512 (42 KB)Bob KEnlarge image. Add title. Improve rendering of "pi" symbols.
16:23, 22 August 2017Thumbnail for version as of 16:23, 22 August 2017435 × 400 (20 KB)Krishnavedalacorrections on phase plot
16:11, 22 August 2017Thumbnail for version as of 16:11, 22 August 2017435 × 400 (20 KB)Krishnavedalanew version using Matplotlib
15:26, 21 August 2017Thumbnail for version as of 15:26, 21 August 2017512 × 384 (42 KB)Krishnavedalathicker lines and uses unicode text
22:01, 16 August 2017Thumbnail for version as of 22:01, 16 August 2017576 × 432 (43 KB)KrishnavedalaUse Unicode for Greek symbols
21:58, 16 August 2017Thumbnail for version as of 21:58, 16 August 2017576 × 432 (43 KB)KrishnavedalaUnicode symbols corrected
21:52, 16 August 2017Thumbnail for version as of 21:52, 16 August 2017576 × 432 (43 KB)Krishnavedalaregenerate using "gnuplot" backend
21:31, 16 August 2017Thumbnail for version as of 21:31, 16 August 2017576 × 431 (28 KB)KrishnavedalaUser created page with UploadWizard
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