Smoothing measured data in MATLAB?

Question

I have measured data from MATLAB and I'm wondering how to best smooth the data? Example data (1st colum=x-data / second-colum=y-data):

    33400       209.11
    34066       210.07
    34732        212.3
    35398       214.07
    36064       215.61
    36730       216.95
    37396       218.27
    38062       219.52
    38728       220.11
    39394       221.13
    40060        221.4
    40726       222.5
    41392       222.16
    42058       223.29
    42724       222.77
    43390       223.97
    44056       224.42
    44722        225.4
    45388       225.32
    46054       225.98
    46720       226.7
    47386       226.53
    48052       226.61
    48718       227.43
    49384       227.84
    50050       228.41
    50716       228.57
    51382       228.92
    52048       229.67
    52714       230.02
    53380       229.54
    54046       231.19
    54712       231.00
    55378        231.5
    56044        231.5
    56710       231.79
    57376       232.26
    58042       233.12
    58708       232.65
    59374       233.51
    60040       234.16
    60706       234.21

The data in the second column should be monoton but it isn't. How to make it smooth? I could probably invent a short algorithm myself but I think it's a better way to use an established and proven one... do you know a good way to somehow integrate the outliners to make it a monoton curve!?

Thanks in advance

Answer 1

Monotone in your case is always increasing!

See the options below (1. Cobb-Douglas; 2. Quadratic; 3. Cubic)

    clear all
    close all

    load needSmooth.dat % Your data

    x=needSmooth(:,1);
    y=needSmooth(:,2);
    n=length(x);

    % Figure 1
    logX=log(x);
    logY=log(y);
    Y=logY;
    X=[ones(n,1),logX];
    B=regress(Y,X);
    a=exp(B(1,1));
    b=B(2,1);
    figure(1)
    plot(x,y,'k*')
    hold
    for i=1:n-1
      plot([x(i,1);x(i+1,1)],[a*x(i,1)^b;a*x(i+1,1)^b],'k-')
    end    


    %Figure 2

    X=[ones(n,1),x,x.*x];
    Y=y;
    B=regress(Y,X);
    c=B(1,1);
    b=B(2,1);
    a=B(3,1);
    figure(2)
    plot(x,y,'k*')
    hold
    for i=1:n-1
      plot([x(i,1);x(i+1,1)],[c+b*x(i,1)+a*x(i,1)^2; c+b*x(i+1,1)+a*x(i+1,1)^2],'k-')
    end    

%Figure 3

X=[ones(n,1),x,x.*x,x.*x.*x];
Y=y;
B=regress(Y,X);
d=B(1,1);
c=B(2,1);
b=B(3,1);
a=B(4,1);
figure(3)
plot(x,y,'k*')
hold
for i=1:n-1
  plot([x(i,1);x(i+1,1)],[d+c*x(i,1)+b*x(i,1)^2+a*x(i,1)^3; d+c*x(i+1,1)+b*x(i+1,1)^2+a*x(i+1,1)^3],'k-')
end    

There are also some cooked functions in Matlab such as "smooth" and "spline" that should also work in your case since your data is almost monotone.