Matlab define several step functions - matlab

Question

I would like to define a Matlab function like the one shown in the figure below, but repeating regularly along the t axis.
So far I tried two different codes:
function Borne = borne(p)
pxt = x;
Borne = zeros(size(pxt));
i0 = (pxt <= 0.1);
i1 = (pxt > 0.1 & pxt < 0.3);
i2 = (pxt > 0.3 & pxt < 0.5);
i3 = (pxt > 0.5 & pxt < 0.7);
i4 = (pxt > 0.7 & pxt < 0.9);
i5 = (pxt > 0.9 & pxt < 1.1);
Borne(i0) = 3;
Borne(i1) = -1;
Borne(i2) = 3;
Borne(i3) = -1;
Borne(i4) = 3;
Borne(i5) = -1;
This one works, but I might be obliged to go to time=100 perhaps.
function Borne = borne(p)
x=0:0.2:100;
y=ones(1,length(x));
for i=1:length(x)
if mod(i,2) == 1;
y(i)=3;
else
y(i)=-1;
end
end
Borne=stairs(x,y);
This one doesn't work at all, it gives me a constant function at 147 circa. Also, at the end of the for loop both x and y have length=1, and I don't know why.
Is there a better way to define my function, maybe? If not, how can I improve my codes?
Thank you very much!

Answer 1

You can do it one-shot with the remainder (rem) function and logical indexing:
%// Data
period = 1;
up_start = .1;
up_stop = .4;
up_value = 3;
down_value = -1;
x = linspace(0,10,200); %// x axis
%// Generate function
Borne = zeros(size(x)); %// initiallize
aux = rem(x,period);
ind = (aux>=up_start) & (aux<up_stop); %// index of "up" values
Borne(ind) = up_value;
Borne(~ind) = down_value;

Answer 2

If you want steps at 2, 4, 6 etc. you could use cumsum:
t = (1:14).*0.1;
x(2:4:12) = -4;
x(4:4:14) = 4;
x(1) = 3;
y = cumsum(x);
[t; y] =
1 2 3 4 5 6 7 8 9 10 11 12 13 14
0 1 1 0 0 1 1 0 0 1 1 0 0 1
The way this works is, you first create a vector that is +1 and -1 where you want the step to be. cumsum will take the cumulative sum of this vector, thus altering between 1 and 0.
If you want, you can plot this using stairs.
Update
With your values, this will be:
n = 8; % Don't know the length of t
t = (0:n).*0.1;
x = zeros(1, length(t));
x(2:4:length(t)) = -4;
x(4:4:length(t)) = 4;
x(1) = 3;
y = cumsum(x);
[t; y] =
0.00000 0.10000 0.20000 0.30000 0.40000 0.50000 0.60000 0.70000
3.00000 -1.00000 -1.00000 3.00000 3.00000 -1.00000 -1.00000 3.00000

Answer 3

No complicated code is needed for something like this. You can use the square function, which is part of the Signal Processing toolbox that comes with most distributions of Matlab:
miny = -1; % Minimum amplitude
maxy = 3; % Maximum amplitude
period = 0.4; % Period in Hz, 1/frequency
duty = 0.5; % Duty cycle, percentage of time spent at maxy
offset = 0.1; % Phase offset in sec.
t = 0:0.01:3;
y = 0.5*(maxy-miny)*square(2*pi*(t-offset)/period,duty*100)-miny;
figure;
plot(t,y)
axis([t(1) t(end) miny-0.1*(maxy-miny) maxy+0.1*(maxy-miny)])