Kenngrößen stochastischer Signale - Digitale Signalverarbeitung mit MATLAB - page 176

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Bild 14-5 Grafische Darstellung der zweidimensionalen WDF einer Normalverteilung (oben) und ihrer

Höhenlinien (unten) ( dsplab14_5 )

Programmbeispiel 14-2 Schätzung der zweidimensionalen WDF
% Estimation of the bidimensional probability density function (pdf)
% dsplab14_4.m * mw * 13Feb2011
N = 1e7; % number of samples
M1 = 30; M2 = 30; % number of bins for (1-dim.) pdfs 1 or 2
MIN1 = -4; MIN2 = -4; % minimum value of bin centers
MAX1 = 4; MAX2 = 4; % maximum value of bin centers
h2d = [M1,MIN1,MAX1,M2,MIN2,MAX2]; % parameter vector for function hist2
% 2-dim. histogram (absolute frequency)
x1 = randn(N,1);
x2 = randn(N,1) + x1;
[c1,c2,f2d] = hist2d(x1,x2,h2d);

% 2D histogram

% Normalization (pdf)
D1 = (MAX1-MIN1)/(M1-1); % width of bins for x1

D2 = (MAX2-MIN2)/(M2-1); % width of bins for x2

f2d = f2d/(D1*D2*N); % normalization (relative frequency)

%% Graphics
FIG1 = figure( 'Name' , 'dsplab14_4 : bidimensional
pdf' , 'NumberTitle' ,...
'off' , 'Units' , 'normal' , 'Position' ,[.4 .4 .45 .45]);
surfl(c1,c2,f2d); % pdf

xlabel( '{\itx} \rightarrow' ), ylabel( '\leftarrow {\ity}' )
zlabel( '{\itf}({\itx},{\ity}) \rightarrow' )
FIG2 = figure( 'Name' , 'dsplab14_4 : contour lines of bidim. pdf' ,...
'NumberTitle' , 'off' , 'Units' , 'normal' , 'Position' ,[.4 .37 .45 .45]);
V = [.01 .05 .10 .15 .2];
[CS,CH] = contour(c1,c2,f2d,V); grid % contour lines

clabel(CS,CH,V);
xlabel( '{\itx} \rightarrow' ), ylabel( '{\ity} \rightarrow' )

Programmbeispiel 14-3 Bivariates Histogramm
function [c1,c2,f2d] = hist2d(x,y,h2d)
% Bivariate histogram with equidistant bin center spacing
% function [c1,c2,f2d] = hist2d(x,y,h2d)
% x : input sequence 1
% y : input sequence 2
% if y is scalar, y is used as shift parameter, i.e.