%generateDictionaries creates to vectors of MATLAB structures. Both hold scale position and frequency of atoms from an optimally sampled dictionary. The first return argument holds atoms metrically equidistant from direct neighbours. The second adds a stochastic element to the parameter values. Usage:
%
%[GaborsFixed,GaborsStochastic]=generateDictionaries(SignalSize,Base);

function [gaborsFixed, gaborStochastic]=generateDictionaries(SignalSize,Base)

    C=0.5*log(0.5*(Base+1./Base));
    ScaleStep=Base;
    numberOfLevels=log(SignalSize)/log(Base);
    scalefloat=SignalSize*ScaleStep;
    EPS=10^(-5);
    k=1;
    for w=1:numberOfLevels

		scalefloat=scalefloat/ScaleStep;
		FreqStep=sqrt(8*pi*C)/scalefloat;
		TimeStep=scalefloat*sqrt(2*C/pi);
		for v=FreqStep/2:FreqStep:pi


			TimeStep=scalefloat*sqrt(2*C/pi);
			for u=(TimeStep/2):TimeStep:SignalSize
				gaborsFixed(k).scale=round(scalefloat/ScaleStep);
				gaborsFixed(k).position=round(u);
				gaborsFixed(k).freq=v;
				k=k+1;
            end
        end
    end
    

    scalefoat=SignalSize*ScaleStep;
    EPS=10^(-10);
    k=1;
    for w=1:numberOfLevels

		scalefloat=scalefloat/ScaleStep;
		FreqStep=sqrt(8*pi*C)/scalefloat;
		TimeStep=scalefloat*sqrt(2*C/pi);
		for v=EPS:FreqStep:FreqStep:pi


			TimeStep=scalefloat;
			for u=EPS::TimeStep:SignalSize
				gaborStochastic(k).scale=round(scalefloat/ScaleStep + rand(1)*(scalefloat-scalefloat/ScaleStep));
				gaborStochastic(k).position=round(u+rand(1)*TimeStep);
				gaborStochastic(k).freq=v+rand(1)*FreqStep;
				k=k+1;
            end
        end
    end