Adding zero points on a plot of a damped sine wave - quick question

Greetings all,

 This will probably be a quick one for you experts, but I have a damped sine wave of:

 y1=2*sin(w*t).*exp(-lambda*t);

 The user inputs w and lambda, and I have t=0:.001:1;

 Now, since the sine wave crosses zero, I would like to add a circle or X where that crossing is just to highlight it. I played around with for and if statements, but not getting it, even though it's kinda trivial.

Any assistance?

   Thanks!
    -J

Answer 1

[Geoff Hayes]

Jesse - you could compare each element to its neighbour and see if there is a switch in sign i.e. from positive to negative or negative to positive. The easiest way to do this, without a for loop, is to use arrayfun and just check to see if each neighbour is different. Something like

 idcs = arrayfun(@(k)sign(y1(k))~=sign(y1(k+1)),1:length(y1)-1);

We use sign to check the sign of the number, and if the sign between two neighbouring elements is different then

 sign(y1(k))~=sign(y1(k+1)

is true (or 1). Note how we use the anonymous function

 @(k)sign(y1(k))~=sign(y1(k+1))

to take as an input k which will be an index into y1. The resulting logical array, idcs, will have ones where there is a difference in sign which is the zero crossing. Use find to find those indices as

 find(idcs==1)

which you can then use to draw your X or circle at the zero crossing. Try the above and see what happens!

[Jesse]

Geoff,

Thanks for the response and apologies on the delay on my end. The answer you provided makes sense, but quick question here. When I tried:

plot(idcs, -t, 'or');

   It threw back an error since the vectors are not the same length. True, but I was trying to put it all on the same plot with hold on, etc.

Since I'm new to "find", is there a plotfind command of some sort?

   Thanks again!

[Geoff Hayes]

Jesse - idcs would have one less element than t, so you wouldn't be able to plot the two together. I think that I gave a poor name to this variable and should be something more like

 zeroCrossings = arrayfun(@(k)sign(y1(k))~=sign(y1(k+1)),1:length(y1)-1);

which is a vector of zeros (not a zero crossing) and ones (is a zero crossing). We would then need the indices of this vector that correspond to ones (the zero crossings) so

 zeroCrossingIdcs = find(zeroCrossings==1);

Now we use this array of indices with y1 and t as

 plot(y1(zeroCrossingIdcs), t(zeroCrossingIdcs), 'or');

(I removed the - from the t as I wasn't sure if this was a typo or intentional).

Try with the above and see if that gives a better result.

[Jesse]

Yes that's it. Thanks Geoff!

[Geoff Hayes]

Glad it worked out, Jesse!