how to creat periodic function

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rahman sajadi
rahman sajadi 2015-8-24
评论： Star Strider 2015-8-24
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

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回答（2 个）

James Tursa
James Tursa 2015-8-24
编辑：James Tursa 2015-8-24
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
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rahman sajadi
rahman sajadi 2015-8-24
the anger are inputs function
James Tursa
James Tursa 2015-8-24
编辑：James Tursa 2015-8-24
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);

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Star Strider
Star Strider 2015-8-24
编辑：Star Strider 2015-8-24
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.
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Star Strider
Star Strider 2015-8-24
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.

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