Sinusoid plots, XTick

I've plotted a couple periods of y=5*sqrt(2)*cos(2*pi*t+pi/4) and I would like to use XTick (preferably, if it works) to set the labels on the x-axis to be all of the values of t such that y is at a maximum, minimum, or zero. I could do it manually, but I need it to be generic (i.e. I could change the function and the labels would conform to it). It could do it if there wasn't a phase shift, but there is. Does anyone know how to do this? Thanks.

For clarification: This image is the plot as it is now: http://img684.imageshack.us/img684/7678/whatihaveb.png I drew vertical lines where I want tick marks in this image: http://img838.imageshack.us/img838/1121/whatiwant.png

[Jan]

What exactly does "generic" mean here? What should be recognized automatically?

[Patrick Star]

"Generic" means that I could change nothing in the m-file except the value of y and it would still work the way I want it to.

The maximums, minimums, and zeros are what I'm trying to get recognized.

[Walter Roberson]

When you change y, is the function still certain to be sinusoid? Finding all the zeros of an arbitrary "black box" function is impossible.

What is the highest frequency that needs to be dealt with?

[Patrick Star]

y will always be a sinusoid. If possible, I would like it to function at any frequency, but leaving it at a frequency of 1 Hz will be fine.

[Walter Roberson]

If you push the frequency high enough, the labels will overlap. Higher still and it will be a terrible mess to plot, when you start approaching one cycle per pixel.

Answer 1

[Paulo Silva]

clf
t=0:0.01:2*pi;
y=5*sqrt(2)*cos(2*pi*t+pi/4);
%hold on %in case you want to draw your own y lines instead of using GRID
plot(t,y,'r'); 
mx=max(y); %find the maximum value of y
mxm=min(y); %find the minimum value of y
%draw your own lines 
% line(get(gca,'Xlim'),[mx mx],'LineStyle','--','Color',[0 0 0]);
% line(get(gca,'Xlim'),[-mx -mx],'LineStyle','--','Color',[0 0 0]);
% line(get(gca,'Xlim'),[0 0],'LineStyle','--','Color',[0 0 0]);
t1=find(y>=(mx-0.01)); %dirty way to find maximum
t2=find(y>=-0.23 & y<=0.23); %dirty way to find zeros
t3=find(y<=(mxm+0.01)); %dirty way to find minimum
ti=[t1 t2 t3]; %put all the interesiting values on a vector
ti=sort(ti); %put the values in ascending order
v=[find(diff(ti)~=1) numel(ti)]; %remove unwanted values and add last one
%set the ticks and turn on grids
set(gca,'XTick',t(ti(v)))
set(gca,'XTickLabel',t(ti(v)))
set(gca,'XGrid','on')
set(gca,'YTick',[mxm 0 mx])
set(gca,'YTickLabel',[mxm 0 mx])
set(gca,'YGrid','on')
axis([0 max(t(ti(v))) mxm-0.2*abs(mxm) mx+0.2*mx]) %adjust axis

[Patrick Star]

Thanks! This works.

Answer 2

[the cyclist]

This code will identify just the maximum (not the minimum or zeros), but you should be able to see how to generalize it.

A cautionary note: you'll see in the plot from my code that it does not identify the second occurrence of the true maximum of the sine wave. This is because when I have sampled at every 0.01 interval of x, it is not a maximum of y there. You may need to code around that in your own data.

x = 0:0.01:4*pi;
y = sin(x);

figure
plot(x,y)
set(gca,'YLim',[-2 2])

[ymax indexToYmax] = max(y);

xAtMaxY = x(indexToYmax);

set(gca,'XTick',xAtMaxY);
set(gca,'XTickLabel',num2str(xAtMaxY));
set(gca,'XGrid','On')