function [X,Y] = linear_interpolant(x,y,N)
% We're given data in the vectors x and y.  The output will be a
% linear fitting where there are N-1 new points introduced between each
% x(j) and x(j+1).  

n = length(x);

j=1;
dx = (x(j+1)-x(j))/N;
xx = x(j):dx:x(j+1)-dx;
X(1:N) = xx;
Y(1:N) = (y(j+1)-y(j))/(x(j+1)-x(j))*(xx-x(j)) + y(j);    
for j=2:n-1
  dx = (x(j+1)-x(j))/N;
  xx = x(j):dx:x(j+1)-dx;
  X((j-1)*N+1:j*N) = xx;
  Y((j-1)*N+1:j*N) = (y(j+1)-y(j))/(x(j+1)-x(j))*(xx-x(j)) + y(j); 
end
X(N*(n-1)+1) = x(n);
Y(N*(n-1)+1) = y(n);