Fail:Window function (rectangular).png

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See fail ja sellest kastist allapoole jääv kirjeldus pärinevad kesksest failivaramust Wikimedia Commons.

Faili lehekülg Commonsis

Projektist en.wikipedia Commonsisse teisaldanud Tiaguito.

Lühikirjeldus

Kirjeldus

rectangular window and frequency response

Kuupäev

17. detsember 2005

Allikas

Üleslaadija oma töö

Autor

Bob K (original version), Olli Niemitalo

Luba
(Faili edasikasutus)

Selle teose autoriõiguste valdajana annan selle teose avalikku omandisse. See kehtib üleilmselt.
Kui see pole mõnes riigis õiguslikult võimalik:
Annan kõigile õiguse seda teost kasutada ükskõik mille jaoks, ilma ühegi tingimuseta, kui seadus neid just ei sea.

Teised versioonid

Vektorkujutis (SVG) sellest pildist on saadaval. Kui SVG-pilt paremat kvaliteeti võimaldab, tuleks seda rasterkujutise asemel kasutada.

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

Vektorgraafika kohta loe lisaks Commonsi abilehelt, metaviki abilehelt ja Vikipeediast.

Teistes keeltes

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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.

See PNG-rasterkujutis on valmistatud rakendusega GNU Octave, tegi Olli Niemitalo

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")

Lähtekood

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")

Faili ajalugu

Klõpsa kuupäeva ja kellaaega, et näha sel ajahetkel kasutusel olnud failiversiooni.

	Kuupäev/kellaaeg	Mõõtmed	Kasutaja	Kommentaar
viimane	9. veebruar 2013, kell 19:48	2500 × 1123 (83 KB)	Olli Niemitalo	Antialiasing, layout changes, larger font
	18. detsember 2005, kell 00:07	1038 × 419 (7 KB)	Tiaguito~commonswiki	file size. color source: http://en.wikipedia.org/wiki/Window_Function
	17. detsember 2005, kell 23:48	1038 × 419 (8 KB)	Tiaguito~commonswiki	source: http://en.wikipedia.org/wiki/Window_Function author: http://en.wikipedia.org/wiki/User:Bob_K

Faili kasutus

Seda faili kasutab järgmine lehekülg:

Kasutaja:U.schults/Aknafunktsioon

Globaalne failikasutus

Järgmised muud vikid kasutavad seda faili:

Faili kasutus vikis da.wikipedia.org
- Bruger:Peh-herlev/sandkasse-Vinduesfunktion

Fail:Window function (rectangular).png

Lühikirjeldus

Matlab

Octave

Pealdised

Selles failis kujutatud üksused

kujutab

looja

Teatud väärtus ilma Vikiandmete üksuseta

autoriõiguslik seisund

copyrighted, dedicated to the public domain by copyright holder ^inglise

litsents

released into the public domain by the copyright holder ^inglise

asutamise või loomise aeg

17. detsember 2005

source of file ^inglise

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media type ^inglise

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Faili ajalugu

Faili kasutus

Globaalne failikasutus

Fail:Window function (rectangular).png

Lühikirjeldus

Matlab

Octave

Pealdised

Selles failis kujutatud üksused

kujutab

looja

Teatud väärtus ilma Vikiandmete üksuseta

autoriõiguslik seisund

copyrighted, dedicated to the public domain by copyright holder inglise

litsents

released into the public domain by the copyright holder inglise

asutamise või loomise aeg

17. detsember 2005

source of file inglise

original creation by uploader inglise

media type inglise

image/png

Faili ajalugu

Faili kasutus

Globaalne failikasutus

copyrighted, dedicated to the public domain by copyright holder ^inglise

released into the public domain by the copyright holder ^inglise

source of file ^inglise

original creation by uploader ^inglise

media type ^inglise