MATLAB: Choosing middle points in discrete function

Question

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

Answer 1

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