Hi Stephen,
I don't know how a slope detector on a triggering 'scope works but here is an attempt at something similar. Your signal seems ideal for this and something with a softer leading edge might not work as well. I added some extra baseline to both signals since the method requires it. I don't have xcorr so I use a homemade function called xcor. You will have to go in and change those to xcorr, and I left it that way as a reminder that you may have to swap the two inputs to the function to make it work.
After detection there are two methods to get the time delay and they seem to agree pretty well.
% your signals with baseline
baseline = 32;
signal1 = 6 + ...
(-0.1 + (0.1+0.1).*rand([1399,1])); %base signal + noise
%simulates the base noisefloor
timeDelay = baseline + randi(700);%quantify a random delay
exponentialContrib = log(1:1399) + ...
(-0.1 + (0.1+0.1).*rand([1399,1]))';
signal1(timeDelay:end,1) = signal1(timeDelay:end,1)' + ...
exponentialContrib(1,1:1399-timeDelay+1);
%Second signal with the exponential starting right away
signal2 = 6 + ...
(-0.1 + (0.1+0.1).*rand([1399,1]));
%aligned to zero time
timeDelay2 = baseline;
exponentialContrib = log(1:1399) + ...
(-0.1 + (0.1+0.1).*rand([1399,1]))';
signal2(timeDelay2:end,1) = signal2(timeDelay2:end,1)' + ...
exponentialContrib(1,1:1399-timeDelay2+1);
new part:
s1 = signal1; % easier names
s2 = signal2;
t = 1:length(s1);
figure(1)
plot(t,s1,t,s2)
% slope detector
detec = zeros(size(s1));
detec(1:10) = -1; % 10 somewhat arbitrary but works;
detec(11:20) = 1; % 20 must be < length of baseline
[d1 lag] = (xcor(s1,detec));
d2 = (xcor(s2,detec));
llag = length(lag); % get rid of unwanted detections associated
ind = (llag+1)/2:llag-baseline; % with the ends of the time record
d1 = d1(ind);
d2 = d2(ind);
lag = lag(ind);
figure(2)
plot(lag,d1,lag,d2)
% find the delay time
% method 1
[~, T1] = max(abs(d1));
[~, T2] = max(abs(d2));
Tdelay1 = T1-T2 % delay of s1 (blue) compared to s2 (red)
% method 2, cross correlation
[dcor lag] = xcor(d1,d2);
[~, ind] = max(abs(dcor));
Tdelay2 = lag(ind)
figure(3)
plot(lag,dcor)
