File:Window function (rectangular).png
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原始檔案 (2,500 × 1,123 像素,檔案大小:83 KB,MIME 類型:image/png)
Transferred from en.wikipedia to Commons by Tiaguito.
摘要
描述Window function (rectangular).png | rectangular window and frequency response | |||
日期 | ||||
來源 | 自己的作品 | |||
作者 | Bob K (original version), Olli Niemitalo | |||
授權許可 (重用此檔案) |
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其他版本 |
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Source code InfoField | 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 Matlabfunction 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) >= -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 > 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 < 0.5 * tau) ./ (exp(z_exp) + 1);
w = 1 * (T_in <= t_cut) + sigma .* (T_in > 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")
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原始碼 InfoField | Octave
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在此檔案描寫的項目
描繪內容
著作權狀態 繁體中文 (已轉換拼寫)
保有知識產權並由其所有者公開於公有領域 繁體中文 (已轉換拼寫)
著作權持有者釋出至公有領域 繁體中文 (已轉換拼寫)
17 12 2005
多媒體型式 繁體中文 (已轉換拼寫)
image/png
檔案歷史
點選日期/時間以檢視該時間的檔案版本。
日期/時間 | 縮圖 | 尺寸 | 用戶 | 備註 | |
---|---|---|---|---|---|
目前 | 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 |
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