Polynomial curve fitting
12 visualizzazioni (ultimi 30 giorni)
Mostra commenti meno recenti
Hi,
I am trying to make polynomial curve fitting in sine wave. First I have created the wave and I took 10 samples, on which I add noise from a gaussian distribution.Now, I am trying to make curve fitting with a polynomial of 9th degree.I think that my results are wrong as the green curve is linear between the points.Does anybody know if am I correct?If there is a mistake I would like to inform me.
Thanks in advance
%%%%%%% code %%%%%%%%% t=0:0.001:1; k=sin(2*pi*t); plot(t,k); x=linspace(0,1,10);
for i=1:1:10 y(i)=sin(2*pi*x(i)); end;
r = randn(10,1);
for i=1:1:10 y_noise(i)=y(i)+r(i); end;
p = polyfit(x,y,9);
x2 = x; y2 = polyval(p,x2); plot(x,y,'o',x2,y2,t,k) grid on
disp(p)
RMSE=sqrt(mean((y-y2).^2+(x-x2).^2));
0 Commenti
Risposta accettata
Matt Fig
il 5 Apr 2011
You did it correctly. The curve is linear between the points because that is how MATLAB plots these things. If you zoom in high enough, there are lines connecting the points even on the curves that look smooth.
If you want your polynomial to look smooth, make the spacing smaller:
t = 0:0.001:1;
k = sin(2*pi*t);
x = linspace(0,1,10);
y = sin(2*pi*x);
r = randn(1,10); % Some noise
y_noise = y + r; % y with the noise added.
p = polyfit(x,y,9);
x2 = x; % For error comparison.
y2 = polyval(p,x2);
x3 = linspace(0,1,100); % For plotting.
y3 = polyval(p,x3);
plot(x,y,'ob',x3,y3,'r',t,k,'k')
grid on
RMSE = sqrt(mean((y-y2).^2+(x-x2).^2));
.
.
.
EDIT
Notice that what you probably meant to do was something like this, which shows why higher order polynomial fitting is not always a good idea. As N gets larger, the fit gets better:
N = 10;
t = 0:0.001:1;
k = sin(2*pi*t);
x = linspace(0,1,10);
y = sin(2*pi*x);
r = randn(1,10)/N; % Some noise, adjustable!!!
y_noise = y + r; % y with the noise added.
p = polyfit(x,y_noise,9);
x2 = x; % For error comparison.
y2 = polyval(p,x2);
x3 = linspace(0,1,100); % For plotting.
y3 = polyval(p,x3);
plot(x,y_noise,'ob',t,k,'k',x3,y3,'r')
legend({'Noisy Sin(2\pix)';'six(2\pix)';'Polyfit'})
grid on
RMSE = sqrt(mean((y-y2).^2+(x-x2).^2));
3 Commenti
Matt Fig
il 5 Apr 2011
Yes, if you want a better error estimate, look at more points:
N = 20;
t = 0:0.001:1;
k = sin(2*pi*t);
x = linspace(0,1,10);
y = sin(2*pi*x);
r = randn(1,10)/N; % Some noise
y_noise = y + r; % y with the noise added.
p = polyfit(x,y_noise,9);
x2 = x; % For error comparison.
y2 = polyval(p,x2);
x3 = t; % For plotting.
y3 = polyval(p,x3);
plot(x,y_noise,'ob',t,k,'k',x3,y3,'r')
legend({'Noisy Sin(2\pix)';'six(2\pix)';'Polyfit'})
grid on
RMSE = sqrt(mean((y-y2).^2+(x-x2).^2));
Più risposte (0)
Vedere anche
Categorie
Scopri di più su Get Started with Curve Fitting Toolbox in Help Center e File Exchange
Community Treasure Hunt
Find the treasures in MATLAB Central and discover how the community can help you!
Start Hunting!