periodic functions

I would like to know how to make a 1 periodic function which is a this fuction times itself is also a periodic function a*a=b a is one periodic b is one periodic too I have a fumction right now is

function piecewise2=piecewphi(x)

z = mod(2*x,2)-1 
piecewise2=abs(1-abs(z)).*(abs(z)<1);
end

and how can I modify it to fit the case? thanks

[Andrew Newell]

I don't understand your question. The function piecewphi is periodic and you want what?

[li]

I want a piecewise linear 1 periodic function

you may refer to this picture http://www.flickr.com/photos/58977081@N02/5579460185/

thanks

[li]

the ak part

Answer 1

[Andrew Newell]

If I understand your question, you want a function like this:

function p=piecewise2d(x,y)
p = piecewphi(x).*piecwphi(y);

Answer 2

[li]

yes but the point is I am also a bit confuse about what I should generate i.e. I donno what is the correct answer to draw that function

[Walter Roberson]

sin(2*pi*mod(x,1)) is 1-periodic, and raising it to any arbitrary positive integer power N also gives a 1-periodic function.

I _suspect_ (but do not know) that for your purposes, that for any given x, at least one of your functions needs to be non-zero, as otherwise no information content would be associated with that x.

[Andrew Newell]

This should be a comment. I'll add a comment to Walter's answer.

Answer 3

[Walter Roberson]

Apologies, in my earlier answer, I did not notice that you had altered your function to z = mod(2*x,2)-1 . What you have now should be 1 periodic, and should be piecewise linear.

However, I do not understand what your question is at this time.

If you want to multiply your piecewphi function by itself, go ahead, but notice that the result will not be piecewise linear: it would be piecewise quadratic instead.