signal processing – How to make a curve smoothing in matlab?

signal processing – How to make a curve smoothing in matlab?

Lets define a wavy function:

x = 0:.1:20;
y1 = 5*sin(x) + 2*x - x.^2 +.3*x.^3 - .2*(x-15).^4 - 10*x.^2.*cos(x./3+12).^3 + .5*(x-12).^4;

And add lots of noise:

r = randi(1000,1,201) - 500;
y2 = y1+r;

Now make a 1D Gaussian filter, normalize it and convolve it with our function:

g = gausswin(20); % <-- this value determines the width of the smoothing window
g = g/sum(g);
y3 = conv(y2, g, same)

Lets see the result

figure;
hold on; 
plot(y1, r, linewidth, 3); 
plot(y2, b); 
plot(y3, g, linewidth, 3);

Red the original function, blue the noisy version, green the smoothed, recovered function.

another option is to use smooth. I like to use it because it is a single line function. Using the code of the previous answer by @Junuxx:

x = 0:.1:20;
y1 = 5*sin(x) + 2*x - x.^2 +.3*x.^3 - .2*(x-15).^4 - 10*x.^2.*cos(x./3+12).^3 + .5*(x-12).^4;
r = randi(1000,1,201) - 500;
y2 = y1+r;

Now apply smooth:

ys = smooth(x,y2,0.25,rloess);
plot(x,y2,x,ys)

For more info:

doc smooth

signal processing – How to make a curve smoothing in matlab?

gausswin() requires the Signal Processing Toolbox

smooth() requires the Curve Fitting Toolbox

If you dont have these toolboxes, here is a simple smooth() implementation:

smooth.m:

function yy = smooth(y, span)
    yy = y;
    l = length(y);

    for i = 1 : l
        if i < span
            d = i;
        else
            d = span;
        end

        w = d - 1;
        p2 = floor(w / 2);

        if i > (l - p2)
           p2 = l - i; 
        end

        p1 = w - p2;

        yy(i) = sum(y(i - p1 : i + p2)) / d;
    end
end

result for y3 = smooth(y2, 15), using @Junuxx code: