File:Window function (rectangular).png

本预览的尺寸：800 × 359像素。其他分辨率：320 × 144像素 | 640 × 287像素 | 1,024 × 460像素 | 1,280 × 575像素 | 2,500 × 1,123像素。

原始文件（2,500 × 1,123像素，文件大小：83 KB，MIME类型：image/png）

本文件并非来自中文维基百科，而是来自维基共享资源。请参阅维基共享资源上的详细描述、讨论页、页面历史、日志。

维基共享资源是一个储存自由版权作品的项目。您可以向此项目作出贡献。

本檔案是由Tiaguito從en.wikipedia轉移到維基共享資源。

摘要

描述

rectangular window and frequency response

日期

2005年12月17日

来源

自己的作品

作者

Bob K (original version), Olli Niemitalo

授权
(二次使用本文件)

我，本作品著作权人，释出本作品至公有领域。这适用于全世界。
在一些国家这可能不合法；如果是这样的话，那么：
我无条件地授予任何人以任何目的使用本作品的权利，除非这些条件是法律规定所必需的。

其他版本

File:Window function and frequency response - Rectangular.svg是此文件的矢量版本。如果此文件质量不低于原点阵图，就应该将这个PNG格式文件替换为此文件。

File:Window function (rectangular).png → File:Window function and frequency response - Rectangular.svg

更多信息请参阅Help:SVG/zh。

其他语言

Alemannisch ∙ العربية ∙ беларуская (тарашкевіца) ∙ български ∙ বাংলা ∙ català ∙ нохчийн ∙ čeština ∙ dansk ∙ Deutsch ∙ Ελληνικά ∙ English ∙ British English ∙ Esperanto ∙ español ∙ eesti ∙ euskara ∙ فارسی ∙ suomi ∙ français ∙ Frysk ∙ galego ∙ Alemannisch ∙ עברית ∙ hrvatski ∙ magyar ∙ հայերեն ∙ Bahasa Indonesia ∙ Ido ∙ italiano ∙ 日本語 ∙ ქართული ∙ 한국어 ∙ lietuvių ∙ македонски ∙ മലയാളം ∙ Bahasa Melayu ∙ norsk bokmål ∙ Plattdüütsch ∙ Nederlands ∙ norsk nynorsk ∙ norsk ∙ occitan ∙ polski ∙ prūsiskan ∙ português ∙ português do Brasil ∙ română ∙ русский ∙ sicilianu ∙ Scots ∙ slovenčina ∙ slovenščina ∙ српски / srpski ∙ svenska ∙ தமிழ் ∙ ไทย ∙ Türkçe ∙ татарча / tatarça ∙ українська ∙ vèneto ∙ Tiếng Việt ∙ 中文 ∙ 中文（中国大陆） ∙ 中文（简体） ∙ 中文（繁體） ∙ 中文（马来西亚） ∙ 中文（新加坡） ∙ 中文（臺灣） ∙ 中文（臺灣） ∙ +/−

Source code

The script below generates these .png images:

This script has not been tested in MATLAB. See the individual file histories for the simpler MATLAB scripts that were the basis of this script.

Generation of svg files by minor modification of the script displayed visual artifacts and renderer incompatibilities that could not be easily fixed. The current script fixes the visual artifacts in the png file as a post-processing step. The script generates a semi-transparent grid by taking a weighted average of two images, one with the grid and one without.

N

本PNG 位图由Olli Niemitalo使用GNU Octave创作。

Matlab

function plotWindowLayer (w, N, gridded, wname, wspecifier)
 
  M=32;
  k=0:N-1;
  dr = 120;

  H = abs(fft([w zeros(1,(M-1)*N)]));
  H = fftshift(H);
  H = H/max(H);
  H = 20*log10(H);
  H = max(-dr,H);
 
  figure('Position',[1 1 1200 520])
  subplot(1,2,1)
  set(gca,'FontSize',28)
  area(k,w,'FaceColor', [0 1 1],'edgecolor', [1 1 0],'linewidth', 2)
  xlim([0 N-1])
  if (min(w) &gt;= -0.01)
    ylim([0 1.05])
    set(gca,'YTick', [0 : 0.1 : 1])
    ylabel('amplitude','position',[-16 0.525 0])
  else
    ylim([-1 5])
    set(gca,'YTick', [-1 : 1 : 5])
    ylabel('amplitude','position',[-16 2 0])
  endif
  set(gca,'XTick', [0 : 1/8 : 1]*(N-1))
  set(gca,'XTickLabel',[' 0'; ' '; ' '; ' '; ' '; ' '; ' '; ' '; 'N-1'])
  grid(gridded)
  set(gca,'LineWidth',2)
  set(gca,'gridlinestyle','-')
  xlabel('samples')
  if (strcmp (wspecifier, ""))
    title(cstrcat(wname,' window'))
  else
    title(cstrcat(wname,' window (', wspecifier, ')'))
  endif
  set(gca,'Position',[0.08 0.11 0.4 0.8])
  set(gca,'XColor',[1 0 1])
  set(gca,'YColor',[1 0 1])
  
  subplot(1,2,2)
  set(gca,'FontSize',28)
  h = stem(([1:M*N]-1-M*N/2)/M,H,'-');
  set(h,'BaseValue',-dr)
  ylim([-dr 6])
  set(gca,'YTick', [0 : -10 : -dr])
  set(findobj('Type','line'),'Marker','none','Color',[0 1 1])
  xlim([-M*N/2 M*N/2]/M)
  grid(gridded)
  set(findobj('Type','gridline'),'Color',[.871 .49 0])
  set(gca,'LineWidth',2)
  set(gca,'gridlinestyle','-')
  ylabel('decibels')
  xlabel('bins')
  title('Frequency response')
  set(gca,'Position',[0.59 0.11 0.4 0.8])
  set(gca,'XColor',[1 0 1])
  set(gca,'YColor',[1 0 1])

endfunction

function plotWindow (w, wname, wspecifier = "", wfilespecifier = "")

  if (strcmp (wfilespecifier, ""))
    wfilespecifier = wspecifier;
  endif

  N = size(w)(2);
  B = N*sum(w.^2)/sum(w)^2   % noise bandwidth (bins), set N = 4096 to get an accurate estimate
  
  plotWindowLayer(w, N, "on", wname, wspecifier);  % "gridded" = "on"
  print temp1.png -dpng "-S2500,1165"
  close
  plotWindowLayer(w, N, "off", wname, wspecifier);  % "gridded" = "off"
  print temp2.png -dpng "-S2500,1165"
  close
% I'm not sure what's going on here, but it looks like the author might have been able
% to save himself some time by using set(gca,"Layer","top") and set(gca,"Layer","bottom").
  I = imread ("temp1.png");
  J = imread ("temp2.png");
  info = imfinfo ("temp1.png");
  w = info.Width;
  c = 1-(double(I(:,1:w/2,1))+2*double(J(:,1:w/2,1)))/(255*3);
  m = 1-(double(I(:,1:w/2,2))+2*double(J(:,1:w/2,2)))/(255*3);
  y = 1-(double(I(:,1:w/2,3))+2*double(J(:,1:w/2,3)))/(255*3);
  c = ((c != m) | (c != y)).*(c &gt; 0).*(1-m-y);
  I(:,1:w/2,1) = 255*(1-c-m-y + 0*m + 0*y + 0*c);
  I(:,1:w/2,2) = 255*(1-c-m-y + 0*m + 0*y + 0.4*c);
  I(:,1:w/2,3) = 255*(1-c-m-y + 0*m + 0*y + 0.6*c);
  c = 1-(double(I(:,w/2+1:w,1))+2*double(J(:,w/2+1:w,1)))/(255*3);
  m = 1-(double(I(:,w/2+1:w,2))+2*double(J(:,w/2+1:w,2)))/(255*3);
  y = 1-(double(I(:,w/2+1:w,3))+2*double(J(:,w/2+1:w,3)))/(255*3);
  c = ((c != m) | (c != y)).*c;
  I(:,w/2+1:w,1) = 255*(1-c-m-y + 0*m + 0*y + 0.8710*c);
  I(:,w/2+1:w,2) = 255*(1-c-m-y + 0*m + 0*y + 0.49*c);
  I(:,w/2+1:w,3) = 255*(1-c-m-y + 0*m + 0*y + 0*c);
  if (strcmp (wfilespecifier, ""))
    imwrite (I, cstrcat('Window function and frequency response - ', wname, '.png'));
  else
    imwrite (I, cstrcat('Window function and frequency response - ', wname, ' (', wfilespecifier, ').png'));
  endif
  
endfunction

N=128;
k=0:N-1;

w = 0.42 - 0.5*cos(2*pi*k/(N-1)) + 0.08*cos(4*pi*k/(N-1));
plotWindow(w, "Blackman")

w = 0.355768 - 0.487396*cos(2*pi*k/(N-1)) + 0.144232*cos(4*pi*k/(N-1)) -0.012604*cos(6*pi*k/(N-1));
plotWindow(w, "Nuttall", "continuous first derivative")

w = 1 - 1.93*cos(2*pi*k/(N-1)) + 1.29*cos(4*pi*k/(N-1)) -0.388*cos(6*pi*k/(N-1)) +0.032*cos(8*pi*k/(N-1));
plotWindow(w, "Flat top")

w = 1 - 1.93*cos(2*pi*k/(N-1)) + 1.29*cos(4*pi*k/(N-1)) -0.388*cos(6*pi*k/(N-1)) +0.028*cos(8*pi*k/(N-1));
plotWindow(w, "SRS flat top")

w = ones(1,N);
plotWindow(w, "Rectangular")

w = (N/2 - abs([0:N-1]-(N-1)/2))/(N/2);
plotWindow(w, "Triangular")

w = 0.5 - 0.5*cos(2*pi*k/(N-1));
plotWindow(w, "Hann")

w = 0.53836 - 0.46164*cos(2*pi*k/(N-1));
plotWindow(w, "Hamming", "alpha = 0.53836")

alpha = 0.5;
w = ones(1,N);
n = -(N-1)/2 : -alpha*N/2;
L = length(n);
w(1:L) = 0.5*(1+cos(pi*(abs(n)-alpha*N/2)/((1-alpha)*N/2)));
w(N : -1 : N-L+1) = w(1:L);
plotWindow(w, "Tukey", "alpha = 0.5")

w = sin(pi*k/(N-1));
plotWindow(w, "Cosine")

w = sinc(2*k/(N-1)-1);
plotWindow(w, "Lanczos")

w = ((N-1)/2 - abs([0:N-1]-(N-1)/2))/((N-1)/2);
plotWindow(w, "Bartlett")

sigma = 0.4;
w = exp(-0.5*( (k-(N-1)/2)/(sigma*(N-1)/2) ).^2);
plotWindow(w, "Gaussian", "sigma = 0.4")

w = 0.62 -0.48*abs(k/(N-1) -0.5) +0.38*cos(2*pi*(k/(N-1) -0.5));
plotWindow(w, "Bartlett–Hann")

alpha = 2;
w = besseli(0,pi*alpha*sqrt(1-(2*k/(N-1) -1).^2))/besseli(0,pi*alpha);
plotWindow(w, "Kaiser", "alpha = 2")

alpha = 3;
w = besseli(0,pi*alpha*sqrt(1-(2*k/(N-1) -1).^2))/besseli(0,pi*alpha);
plotWindow(w, "Kaiser", "alpha = 3")

tau = N-1;
epsilon = 0.1;
t_cut = tau * (0.5 - epsilon);
T_in = abs(k - 0.5 * tau);
z_exp = ((t_cut - 0.5 * tau) ./ (T_in - t_cut) + (t_cut - 0.5 * tau) ./ (T_in - 0.5 * tau));
sigma =  (T_in &lt; 0.5 * tau) ./ (exp(z_exp) + 1);        
w = 1 * (T_in &lt;= t_cut) + sigma .* (T_in &gt; t_cut);
plotWindow(w, "Planck-taper", "epsilon = 0.1")

w = 0.35875 - 0.48829*cos(2*pi*k/(N-1)) + 0.14128*cos(4*pi*k/(N-1)) -0.01168*cos(6*pi*k/(N-1));
plotWindow(w, "Blackman-Harris")

w = 0.3635819 - 0.4891775*cos(2*pi*k/(N-1)) + 0.1365995*cos(4*pi*k/(N-1)) -0.0106411*cos(6*pi*k/(N-1));
plotWindow(w, "Blackman-Nuttall")

w = 1 - 1.93*cos(2*pi*k/(N-1)) + 1.29*cos(4*pi*k/(N-1)) -0.388*cos(6*pi*k/(N-1)) +0.032*cos(8*pi*k/(N-1));
plotWindow(w, "Flat top")

tau = (N/2);
w = exp(-abs(k-(N-1)/2)/tau);
plotWindow(w, "Exponential", "tau = N/2", "half window decay")

tau = (N/2)/(60/8.69);
w = exp(-abs(k-(N-1)/2)/tau);
plotWindow(w, "Exponential", "tau = (N/2)/(60/8.69)", "60dB decay")

alpha = 2;
w = 1/2*(1 - cos(2*pi*k/(N-1))).*exp(alpha*abs(N-2*k-1)/(1-N));
plotWindow(w, "Hann-Poisson", "alpha = 2")

源代码

Octave

Source code

function plotWindowLayer (w, N, gridded, wname, wspecifier)
 
  M=32;
  k=0:N-1;
  dr = 120;

  H = abs(fft([w zeros(1,(M-1)*N)]));
  H = fftshift(H);
  H = H/max(H);
  H = 20*log10(H);
  H = max(-dr,H);
 
  figure('Position',[1 1 1200 520])
  subplot(1,2,1)
  set(gca,'FontSize',28)
  area(k,w,'FaceColor', [0 1 1],'edgecolor', [1 1 0],'linewidth', 2)
  xlim([0 N-1])
  if (min(w) &gt;= -0.01)
    ylim([0 1.05])
    set(gca,'YTick', [0 : 0.1 : 1])
    ylabel('amplitude','position',[-16 0.525 0])
  else
    ylim([-1 5])
    set(gca,'YTick', [-1 : 1 : 5])
    ylabel('amplitude','position',[-16 2 0])
  endif
  set(gca,'XTick', [0 : 1/8 : 1]*(N-1))
  set(gca,'XTickLabel',[' 0'; ' '; ' '; ' '; ' '; ' '; ' '; ' '; 'N-1'])
  grid(gridded)
  set(gca,'LineWidth',2)
  set(gca,'gridlinestyle','-')
  xlabel('samples')
  if (strcmp (wspecifier, ""))
    title(cstrcat(wname,' window'))
  else
    title(cstrcat(wname,' window (', wspecifier, ')'))
  endif
  set(gca,'Position',[0.08 0.11 0.4 0.8])
  set(gca,'XColor',[1 0 1])
  set(gca,'YColor',[1 0 1])
  
  subplot(1,2,2)
  set(gca,'FontSize',28)
  h = stem(([1:M*N]-1-M*N/2)/M,H,'-');
  set(h,'BaseValue',-dr)
  ylim([-dr 6])
  set(gca,'YTick', [0 : -10 : -dr])
  set(findobj('Type','line'),'Marker','none','Color',[0 1 1])
  xlim([-M*N/2 M*N/2]/M)
  grid(gridded)
  set(findobj('Type','gridline'),'Color',[.871 .49 0])
  set(gca,'LineWidth',2)
  set(gca,'gridlinestyle','-')
  ylabel('decibels')
  xlabel('bins')
  title('Frequency response')
  set(gca,'Position',[0.59 0.11 0.4 0.8])
  set(gca,'XColor',[1 0 1])
  set(gca,'YColor',[1 0 1])

endfunction

function plotWindow (w, wname, wspecifier = "", wfilespecifier = "")

  if (strcmp (wfilespecifier, ""))
    wfilespecifier = wspecifier;
  endif

  N = size(w)(2);
  B = N*sum(w.^2)/sum(w)^2   % noise bandwidth (bins), set N = 4096 to get an accurate estimate
  
  plotWindowLayer(w, N, "on", wname, wspecifier);  % "gridded" = "on"
  print temp1.png -dpng "-S2500,1165"
  close
  plotWindowLayer(w, N, "off", wname, wspecifier);  % "gridded" = "off"
  print temp2.png -dpng "-S2500,1165"
  close
% I'm not sure what's going on here, but it looks like the author might have been able
% to save himself some time by using set(gca,"Layer","top") and set(gca,"Layer","bottom").
  I = imread ("temp1.png");
  J = imread ("temp2.png");
  info = imfinfo ("temp1.png");
  w = info.Width;
  c = 1-(double(I(:,1:w/2,1))+2*double(J(:,1:w/2,1)))/(255*3);
  m = 1-(double(I(:,1:w/2,2))+2*double(J(:,1:w/2,2)))/(255*3);
  y = 1-(double(I(:,1:w/2,3))+2*double(J(:,1:w/2,3)))/(255*3);
  c = ((c != m) | (c != y)).*(c &gt; 0).*(1-m-y);
  I(:,1:w/2,1) = 255*(1-c-m-y + 0*m + 0*y + 0*c);
  I(:,1:w/2,2) = 255*(1-c-m-y + 0*m + 0*y + 0.4*c);
  I(:,1:w/2,3) = 255*(1-c-m-y + 0*m + 0*y + 0.6*c);
  c = 1-(double(I(:,w/2+1:w,1))+2*double(J(:,w/2+1:w,1)))/(255*3);
  m = 1-(double(I(:,w/2+1:w,2))+2*double(J(:,w/2+1:w,2)))/(255*3);
  y = 1-(double(I(:,w/2+1:w,3))+2*double(J(:,w/2+1:w,3)))/(255*3);
  c = ((c != m) | (c != y)).*c;
  I(:,w/2+1:w,1) = 255*(1-c-m-y + 0*m + 0*y + 0.8710*c);
  I(:,w/2+1:w,2) = 255*(1-c-m-y + 0*m + 0*y + 0.49*c);
  I(:,w/2+1:w,3) = 255*(1-c-m-y + 0*m + 0*y + 0*c);
  if (strcmp (wfilespecifier, ""))
    imwrite (I, cstrcat('Window function and frequency response - ', wname, '.png'));
  else
    imwrite (I, cstrcat('Window function and frequency response - ', wname, ' (', wfilespecifier, ').png'));
  endif
  
endfunction

N=128;
k=0:N-1;

w = 0.42 - 0.5*cos(2*pi*k/(N-1)) + 0.08*cos(4*pi*k/(N-1));
plotWindow(w, "Blackman")

w = 0.355768 - 0.487396*cos(2*pi*k/(N-1)) + 0.144232*cos(4*pi*k/(N-1)) -0.012604*cos(6*pi*k/(N-1));
plotWindow(w, "Nuttall", "continuous first derivative")

w = 1 - 1.93*cos(2*pi*k/(N-1)) + 1.29*cos(4*pi*k/(N-1)) -0.388*cos(6*pi*k/(N-1)) +0.032*cos(8*pi*k/(N-1));
plotWindow(w, "Flat top")

w = 1 - 1.93*cos(2*pi*k/(N-1)) + 1.29*cos(4*pi*k/(N-1)) -0.388*cos(6*pi*k/(N-1)) +0.028*cos(8*pi*k/(N-1));
plotWindow(w, "SRS flat top")

w = ones(1,N);
plotWindow(w, "Rectangular")

w = (N/2 - abs([0:N-1]-(N-1)/2))/(N/2);
plotWindow(w, "Triangular")

w = 0.5 - 0.5*cos(2*pi*k/(N-1));
plotWindow(w, "Hann")

w = 0.53836 - 0.46164*cos(2*pi*k/(N-1));
plotWindow(w, "Hamming", "alpha = 0.53836")

alpha = 0.5;
w = ones(1,N);
n = -(N-1)/2 : -alpha*N/2;
L = length(n);
w(1:L) = 0.5*(1+cos(pi*(abs(n)-alpha*N/2)/((1-alpha)*N/2)));
w(N : -1 : N-L+1) = w(1:L);
plotWindow(w, "Tukey", "alpha = 0.5")

w = sin(pi*k/(N-1));
plotWindow(w, "Cosine")

w = sinc(2*k/(N-1)-1);
plotWindow(w, "Lanczos")

w = ((N-1)/2 - abs([0:N-1]-(N-1)/2))/((N-1)/2);
plotWindow(w, "Bartlett")

sigma = 0.4;
w = exp(-0.5*( (k-(N-1)/2)/(sigma*(N-1)/2) ).^2);
plotWindow(w, "Gaussian", "sigma = 0.4")

w = 0.62 -0.48*abs(k/(N-1) -0.5) +0.38*cos(2*pi*(k/(N-1) -0.5));
plotWindow(w, "Bartlett–Hann")

alpha = 2;
w = besseli(0,pi*alpha*sqrt(1-(2*k/(N-1) -1).^2))/besseli(0,pi*alpha);
plotWindow(w, "Kaiser", "alpha = 2")

alpha = 3;
w = besseli(0,pi*alpha*sqrt(1-(2*k/(N-1) -1).^2))/besseli(0,pi*alpha);
plotWindow(w, "Kaiser", "alpha = 3")

tau = N-1;
epsilon = 0.1;
t_cut = tau * (0.5 - epsilon);
T_in = abs(k - 0.5 * tau);
z_exp = ((t_cut - 0.5 * tau) ./ (T_in - t_cut) + (t_cut - 0.5 * tau) ./ (T_in - 0.5 * tau));
sigma =  (T_in &lt; 0.5 * tau) ./ (exp(z_exp) + 1);        
w = 1 * (T_in &lt;= t_cut) + sigma .* (T_in &gt; t_cut);
plotWindow(w, "Planck-taper", "epsilon = 0.1")

w = 0.35875 - 0.48829*cos(2*pi*k/(N-1)) + 0.14128*cos(4*pi*k/(N-1)) -0.01168*cos(6*pi*k/(N-1));
plotWindow(w, "Blackman-Harris")

w = 0.3635819 - 0.4891775*cos(2*pi*k/(N-1)) + 0.1365995*cos(4*pi*k/(N-1)) -0.0106411*cos(6*pi*k/(N-1));
plotWindow(w, "Blackman-Nuttall")

w = 1 - 1.93*cos(2*pi*k/(N-1)) + 1.29*cos(4*pi*k/(N-1)) -0.388*cos(6*pi*k/(N-1)) +0.032*cos(8*pi*k/(N-1));
plotWindow(w, "Flat top")

tau = (N/2);
w = exp(-abs(k-(N-1)/2)/tau);
plotWindow(w, "Exponential", "tau = N/2", "half window decay")

tau = (N/2)/(60/8.69);
w = exp(-abs(k-(N-1)/2)/tau);
plotWindow(w, "Exponential", "tau = (N/2)/(60/8.69)", "60dB decay")

alpha = 2;
w = 1/2*(1 - cos(2*pi*k/(N-1))).*exp(alpha*abs(N-2*k-1)/(1-N));
plotWindow(w, "Hann-Poisson", "alpha = 2")

文件历史

点击某个日期/时间查看对应时刻的文件。

	日期/时间	大小	用户	备注
当前	2013年2月9日 (六) 16:48	2,500 × 1,123（83 KB）	Olli Niemitalo	Antialiasing, layout changes, larger font
	2005年12月17日 (六) 21:07	1,038 × 419（7 KB）	Tiaguito~commonswiki	file size. color source: http://en.wikipedia.org/wiki/Window_Function
	2005年12月17日 (六) 20:48	1,038 × 419（8 KB）	Tiaguito~commonswiki	source: http://en.wikipedia.org/wiki/Window_Function author: http://en.wikipedia.org/wiki/User:Bob_K

文件用途

没有页面链接到本图像。

全域文件用途

以下其他wiki使用此文件：

da.wikipedia.org上的用途
- Bruger:Peh-herlev/sandkasse-Vinduesfunktion
et.wikipedia.org上的用途
- Kasutaja:U.schults/Aknafunktsioon

File:Window function (rectangular).png

摘要

Matlab

Octave

说明

此文件中描述的项目

描繪內容

創作作者

某些值没有维基数据项目

著作權狀態

保有知識產權並由其所有者公開於公有領域

许可协议

著作权持有者释出至公有领域 ^{简体中文（已转写）}

成立或建立時間

17 12 2005

文件来源

上传者的原创作品

多媒體型式

image/png

文件历史

文件用途

全域文件用途

摘要

Matlab

Octave

说明

此文件中描述的项目

某些值没有维基数据项目

著作权持有者释出至公有领域 简体中文（已转写）

17 12 2005

image/png

文件历史

文件用途

全域文件用途

著作权持有者释出至公有领域 ^{简体中文（已转写）}