initParamExponential.m
54e98ff0e849TekRSA-Freq-vs-Time

initParamExponential.m
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			function [p_in,lim_lower,lim_upper]=initParamExponential(x,y)
			%Assumes form a*exp(-bx)+c

			%Setting upper and lower limits
			[amp_max,ind_max]=max(y);
			[amp_min,ind_min]=min(y);

			lim_upper=[Inf,Inf,Inf];
			lim_lower=-lim_upper;

			if abs(amp_max)>abs(amp_min)
			lim_upper(1)=Inf;
			lim_lower(1)=0;
			else
			lim_upper(1)=0;
			lim_lower(1)=-Inf;
			end

			if (ind_max>ind_min && abs(amp_max)>abs(amp_min))...
			\|\| (ind_max<ind_min && abs(amp_max)<abs(amp_min))
			lim_upper(2)=Inf;
			lim_lower(2)=0;
			else
			lim_upper(2)=0;
			lim_lower(2)=-Inf;
			end

			%Method for estimating initial parameters taken from
			%http://www.matrixlab-examples.com/exponential-regression.html. Some
			%modifications required to account for negative y values
			% y=y-amp_min;
			if all(y>0)
			y=y-amp_min+eps;
			n=length(x);
			y2=log(y);
			j=sum(x);
			k=sum(y2);
			l=sum(x.^2);
			r2=sum(x .* y2);
			p_in(2)=(n * r2 - k * j)/(n * l - j^2);
			p_in(1)=exp((k-p_in(2)*j)/n);
			y=y+amp_min;
			elseif abs(amp_max)>abs(amp_min) && amp_max>0
			p_in(1)=amp_max;
			p_in(2)=-1;
			else
			p_in(1)=amp_min;
			p_in(2)=-1;
			end

			if abs(amp_max)>abs(amp_min)
			p_in(3)=amp_min;
			else
			p_in(3)=amp_max;
			end

			end