midscomp

Purpose

Mid-point construction used in the interference diagram.

Synopsis

[ti,fi] = midpoint(t1,f1,t2,f2,K)

Description

midscomp gives the coordinates in the time-frequency plane of the interference-term corresponding to the points (t1,f1) and (t2,f2), for a distribution in the affine class perfectly localized on power-law group-delays of the form $t_x(\nu)=t_0+c\ \nu^{K-1}.$ This function is mainly called by plotsid.

Name	Description
t1	time-coordinate of the first point
f1	frequency-coordinate of the first point ($>0$)
t2	time-coordinate of the second point
f2	frequency-coordinate of the second point ($>0$)
K	power of the group-delay law. Example of distributions satisfying this interference construction :
	K = 2 : Wigner-Ville distribution
	K = 1/2 : D-Flandrin distribution
	K = 0 : Bertrand (unitary) distribution
	K = -1 : Unterberger (active) distribution
	K = Inf : Margenau-Hill-Rihaczek distribution
ti	time-coordinate (abscissa) of the interference-point
fi	frequency-coordinate (ordinate) of the interference-point

Example

Here is the locus of the interference terms between two points, for K going from -15 to 15:

         t1=10; f1=0.45; t2=90; f2=0.05; hold on
         for K=-15:15,
          [ti(2*K+31),fi(2*K+31)]=midscomp(t1,f1,t2,f2,K);
         end

         plot(ti,fi,'g*'); plot(t1,f1,'go'); plot(t2,f2,'go');
         line([t1,t2],[f1,f2]); hold off
         xlabel('Time'); ylabel('Normalized frequency');

See Also

plotsid.

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