function [t_vect, spk_vect,rho_vect] = inhom_pp2(rate1,rate2,freq)
%this function simulates an inhomogeneous Poisson process 
%with time varying rate  by the integrate method
%described in the lecture notes

%It returns a time vector, a spike vector and the rate vector  
  
  dt = 0.05;

  t_vect = 0:dt:1000;
  v_vect = zeros(size(t_vect));
  spk_vect = zeros(size(t_vect));
  
  v_thres = exprnd(1);
  v(1) = 0;
  rho_vect = (rate1/1000) + (rate2/1000)*sin(2*pi*(freq/1000)*t_vect); %in spk/msec

  %save some time
  dtrho_vect = dt*rho_vect;
  
  for i = 2:length(t_vect)
    v(i) = v(i-1) + dtrho_vect(i);
    if (v(i) > v_thres)
      v(i) = 0;
      spk_vect(i) = 1;
      v_thres = exprnd(1);
    end;
  end;