File:Frequency response of 3-term boxcar filter.svg

原始文件 (SVG文件,尺寸为416 × 400像素,文件大小:20 KB)


摘要

描述
English: Frequency response (discrete time Fourier transform) of a 3-tap boxcar filter. To produce these plots, samples of the DTFT are obtained by computing the DFT of the zero-filled impulse response. Alternatively, one can directly sample the closed form of the DTFT:   and plot the magnitude and angle of the samples. (See File:MA2Amp_C.svg)
Note: At the two frequencies where the magnitude goes to zero, there are phase discontinuities of π radians. They are not artifacts of phase wrapping. Rather, they indicate a sign inversion... multiplication by -1. Since that is equivalent to an amplitude modification, it does not affect the filter's property of phase linearity. An illustration of that can be viewed at File:Amplitude & phase vs frequency for 3-term boxcar filter.svg.
日期
来源 自己的作品
作者 original: Bob K
vector version: Krishnavedala
授权
(二次使用本文件)
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其他版本 本檔案衍生自: Frequency response of 3-term boxcar filter.gif
SVG开发
InfoField
 
SVG的源代码为有效代码
 
矢量图Krishnavedala使用Python创作。
Python source
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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
plt.rcParams['svg.fonttype'] = 'none'

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

fig = plt.figure(figsize=[5,5])
plt.subplot(211)
plt.plot(w, np.abs(H), 'blue')
plt.grid(True)
plt.ylabel('Magnitude')
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('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
%=======================================================
  y_origin = y_origin -y2 -height;        % position of top row
  subplot("position",[x_origin y_origin width height])
  plot(abscissa, abs(H), "linewidth",2);
  xlim([-pi pi])
  ylim([0 1.2])
  set(gca, "XTick", [-pi -2*pi/3 0 2*pi/3 pi])
  set(gca, "YTick", [0 .2 .4 .6 .8 1])
  grid("on")

  ylabel("Magnitude")
% set(gca, "ticklabelinterpreter", "tex")	% tex is the default
  set(gca, "XTickLabel", ['-\pi'; '-2\pi/3'; '0'; '2\pi/3'; '\pi';])
  set(gca, "YTickLabel", ['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, angle(H), "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\Frequency response of 3-term boxcar filter.svg')

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日期/时间缩⁠略⁠图大小用户备注
当前2020年10月1日 (四) 13:072020年10月1日 (四) 13:07版本的缩略图416 × 400(20 KB)KrishnavedalaText-to-graph aspect ratio renders poorly in thumbnails with text unreadable.
2019年7月3日 (三) 01:362019年7月3日 (三) 01:36版本的缩略图512 × 512(37 KB)Bob KIncrease graph "linewidth" to 2.
2019年7月2日 (二) 22:112019年7月2日 (二) 22:11版本的缩略图512 × 512(37 KB)Bob KEnlarge image. Add title. Improve rendering of "pi" symbols.
2017年8月22日 (二) 15:352017年8月22日 (二) 15:35版本的缩略图416 × 400(20 KB)KrishnavedalaUser created page with UploadWizard

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