Choosing middle points in discrete function

I have a set of experimental data y=f(x), this set looks like a discrete function means for y=a there are several corresponding x, the overall variation is sin(x) like shape like steps going up and down along with x axis. My question is, can any one help me to remove the repeated y from each step and create another set newy=f(newx) that passes through the middle point of each step, so then I will plot both as plot(x,y,'x',newx,newy) and I have the plot(newx,newy) passing exactly in the middle point of each step; thanks in advance and sorry for the long explanation

[Zine]

I tried to use this function but it takes only the last point from the step

function [ norepx,norepy ] = norep( xdata,ydata)

n=length(xdata);

j=0;

k=0;

for i=1:n-1

    j=j+1;

    k=k+1;

    if abs(ydata(i)-ydata(i+1))>0  

           ny(k)=ydata(i);

           nx(j)=xdata(i);    
    end       
end
ind=find(nx);
norepx=nx(nx>0);

 for i=1:length(ind)

norepy(i)=ny(ind(i));

 end

norepx=[xdata(1) norepx xdata(length(xdata))];

norepy=[ydata(1) norepy ydata(length(ydata))];

norepx(2)=[]; norepy(2)=[];

end

[mohammed]

can you give a simple example or can post your result means of some image?

[Zine]

see attached hand drawing where the black lines are my original set of data, and the blue stars are the desired new set and the red line is the link between new set points, I did not put my data because it is huge array of data, in my function it takes the last point of each step but I need the middle point,(x points in one step is variable from 1 to around 60)

Answer 1

[Zine]

The problem is solved by introducing a counter in the algorithm that calculates the number of repeated data and than divide that number by two as follows

function [ nx,ny ] = nrp( xdata,ydata)

%UNTITLED Summary of this function goes here % Detailed explanation goes here

imax=length(xdata);

count=1;

j=1;

for i=1:imax-1

    if ydata(i)==ydata(i+1)

        count=count+1;

    else

        midcount=int16(count/2);

        nx(j)=xdata(i-midcount+1);

        ny(j)=ydata(i-midcount+1);

        count=1;

        j=j+1;

    end

end

nx=[nx xdata(length(xdata))];

ny=[ny ydata(length(ydata))];

end