how to creat periodic function

y=f(x)

y=0 for 0<x<pi/8

y=1 for pi/8<x<pi/4

y=0 for pi/4<x<pi/3

y=1 for pi/3<x<pi/2

and also this function is even ratio to pi/2 and odd ratio to pi and this function is periodic with 2*pi Periodicity

Answer 1

[James Tursa]

Mod the input x with 2*pi and then do your testing above to generate the output, making sure to cover all cases for x between 0 and 2*pi. If you know x isn't going to be too large you could use x = mod(x,2*pi). But if you want to be robust you can use the following function to do the mod(,2*pi) operation (forces the result to match what MATLAB does in the background for its trig functions):

function y = mod2pi(x) % Result is in range 0 to 2*pi
y = atan2(sin(x),cos(x));
g = y < 0;
y(g) = y(g) + 2*pi;
end

[rahman sajadi]

this function is periodic with 2*pi Periodicity

[rahman sajadi]

the anger are inputs function

[James Tursa]

Does this work for you? (CAUTION, untested)

x = mod2pi(x);
g = x > pi;
x(g) = 2*pi - x(g);
h = x > pi/2;
x(h) = pi - x(h);
y = double((x > pi/8 & x < pi/4) | (x > pi/3));
y(g) = -y(g);

Answer 2

[Star Strider]

I don’t know what you mean by: ‘this function is even ratio to pi/2 and odd ratio to pi and this function is periodic with 2*pi Periodicity.’

Otherwise, see if this does what you want:

x = linspace(0, 5*pi, 200);

y = [((mod(x,pi)>pi/8) & (mod(x,pi)<pi/4)) + ((mod(x,pi)>pi/3) & (mod(x,pi)<pi/2))].*(-1).^fix(x/pi);

figure(1)
plot(x, y)
grid

EDIT — Minor alteration in ‘y’ to reflect to ‘even-odd’ clarification.

EDIT #2 — Added plot figure.

[rahman sajadi]

this function is periodic with 2*pi Periodicity

the anger are inputs function

[rahman sajadi]

do you now my mean?

[Star Strider]

The function in my edited Answer (1) creates the function in your Question, (2) has the appropriate ‘even-odd’ behaviour, and (3) will work for all ‘x’ greater than or equal to 0.

I added the plot figure to my original Answer.