Octave: How can I fit a sinusoid to my data using Octave? - matlab

Question

My goal is to fit a sinusoid to data goming from a datalogger using Octave.
The datalogger logs force which is produced using an excenter, so it theoretically should be a sine wave.
I could not find any hint on how to do this elsewhere.
Currently I'm using the function "splinefit" followd by "ppval" to fit my data but I don't realy get the results I hoped from it...
Has anybody an idea how I could fit a sinusoid to my data?
Here's my current code I use to fit the data and a scrennshot of the result:
## splinefit force left
spfFL = splinefit(XAxis,forceL,50);
fitForceL=ppval(spfFL,XAxis);
##middle force left
meanForceL=mean(fitForceL);
middleedForceL=fitForceL-meanForceL;
result spline fit
on the X-Axis I have the 30'000 measurepoints or logs
on the Y-Axis I have the actual measured force values
the data comes from the datalogger in a .csv-file like this

Answer 1

You can do a simple regression using the sine and cosine of your (time) input as your regression features.
Here's an example
% Let's generate a dataset from a known sinusoid as an example
N = 1000;
Range = 100;
w = 0.25; % known frequency (e.g. from specs or from fourier analysis)
Inputs = randi(Range, [N, 1]);
Targets = 0.5 * sin( w * Inputs + pi/3 ) + 0.05 * randn( size( Inputs ) );
% Y = A + B sin(wx) + C cos(wx); <-- this is your model
Features = [ ones(N, 1), sin(w * Inputs), cos(w * Inputs) ];
Coefs = pinv(Features) * Targets;
A = Coefs(1); % your solutions
B = Coefs(2);
C = Coefs(3);
% print your nice solution against the input dataset
figure('position', [0, 0, 800, 400])
ax1 = axes()
plot(Inputs, Targets, 'o', 'markersize', 10, ...
'markeredgecolor', [0, 0.25, 0.5], ...
'markerfacecolor', [0, 0.5, 1], ...
'linewidth', 1.5)
set(ax1, 'color', [0.9, 0.9, 0.9])
ax2 = axes()
X = 1:0.1:Range;
plot( X, A + B*sin(w * X) + C*cos(w * X), 'k-', 'linewidth', 5 ); hold on
plot( X, A + B*sin(w * X) + C*cos(w * X), 'g-', 'linewidth', 2 ); hold off
set(ax2, 'xlim', get(ax1, 'xlim'), 'ylim', get(ax1, 'ylim'), 'color', 'none')

Answer 2

You could do a least squares optimization, using fminsearch
% sine to fit (in your case your data)
x = 0:0.01:50;
y = 2.6*sin(1.2*x+3.1) + 7.3 + 0.2*rand(size(x)); % create some noisy sine with known parameters
% function with parameters
fun = #(x,p) p(1)*sin(p(2)*x+p(3)) + p(4); % sine wave with 4 parameters to estimate
fcn = #(p) sum((fun(x,p)-y).^2); % cost function to minimize the sum of the squares
% initial guess for parameters
p0 = [0 0 0 0];
% parameter optimization
par = fminsearch(fcn, p0);
% see if estimated parameters match measured data
yest = fun(x, par)
plot(x,y,x,yest)
Replace x and y with your data. The par variable contains the parameters of the sine, as defined in fun.