Well you has done a lot of question, I'll try to explain:
1ªwhat is the difference between phase shift and delay shift, phase shitf:is when you change the phase in a sine or cosine fase, e.g. sin(x)->hasn't got a gap in the phase
sin(x+-phi)->here, phi is a phase gap, due to you're adding or subtract the value phi, see this link http://en.wikipedia.org/wiki/Phase_(waves)#Phase_shift On the other hand, a delay in the singal means that the signal starts after a quatum of time, in your case 4seconds or samples depending on the units you are working with, the diference between this and the phase shift, is that all the signal is moved or shifted 4seconds/samples. 2ª Here,I've not done anything that you haven't done before, only I have plotted the ordinate of signal1 ,Y, on the abscissa of signal X, and with 'b' I command matlab to plot in blue
In this code:
lambda =@(x)( sin(x)*(20+30));
S = Trial(lambdaMax,lambda,T)
hold on
X = linspace(min(S),max(S),100);
Y = pchip(S,lambda(S),X);
Signal1=[X;Y]
plot(X,Y,'b')
3ªIn this case,I have imposed the phase shift in the signal, notice that if I had set sin(x+4)*(20+30), the shitf will be to the left. Then I used this variable with your code and lastly with the new axe values(X1,Y2) plot again,here I have not to touch the 'x' axe because I have modified it in the sine expression,so it isn't necessary do it again. With 'r' command matlab to plot in red the singal.
lambdaFirst =@(x) (sin(x-4)*(20+30));
S1 = Trial(lambdaMax,lambdaFirst,T);
X1 = linspace(min(S1),max(S1),100);
Y1 = pchip(S1,lambdaFirst(S1),X1);
Signal2 = [X1;Y1];
plot(X1,Y1,'r')
4ªThe delay of the signal is done with the command below,as you can imagine before 4s(I'm going to asume time units) there is not delay signal due to the fact that it hasn't arrived yet, so the values of x axe should be zero, for that I use the command "zeros(n,m)" which set a matrix of nxm zeros elements.After this 4seconds there is singal, so I'have copied the values of the x-axe Singal1 given that we want to be the same in signal2, so as to do this I copy the values of X, but realizing that if we want to draw with plot, the vector must have the same length, so I have to subtract the 4 last values of the X axe and that is done with "X(1:end-4)", I'm telling matlab to take the values of X from 1 to last value less the 4 last. Finally we have to get together the first four values of x(which ones were zero) and the rest, and that we make with the "[ ]", this way our x axe will be:
xDelay=[zeros(1,4) X(1:end-4)];
plot(xDelay,Y1,'black')
or in one sole command as I've used:
plot([zeros(1,4) X(1:end-4)],Y1,'black')
I suggest that you read the documentation of "plot" to have a clear idea of this command, you can do that by typing "help plot" on matlab prompt
Regards
