sine curve fitting by recursive method
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MUHAMMAD SULEMAN
on 13 Jun 2021
Commented: Mathieu NOE
on 18 Jun 2021
Find sine regression of periodic signal.
I have long period so I decomposed it in to small signals
Frequency = 50; % hertz
StopTime = 1/Frequency; % seconds
FittingTime = (0:dt:StopTime-dt)'; % seconds
%%Sine wave:
FittingVoltage = sin(2*pi*Fc*FittingTime);
Then I want to do curve fitting by recursive method. whereas
RangeOfVector= 5
for i = 0:1/Frequency:RangeOfVector
iter(i)=min(TrainTime):(1/Frequency):max(TrainTime)
end
This should process [x 0 0 0 0] then [0 x 0 0 0] then [0 0 x 0 0] and so on
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Accepted Answer
Mathieu NOE
on 16 Jun 2021
hello
this is a little demo you can adapt to your own needs ...
clc
clearvars
close all
% dummy signal (sinus + noise)
dt = 1e-4;
samples = 1000;
f = 50;
t = (0:samples-1)*dt;
s = 0.75*sin(2*pi*f*t) + 0.1 *rand(1,samples);
%%%%%%%%%%%%% main code %%%%%%%%%%%%%%%%%
ym = mean(s); % Estimate offset
yu = max(s);
yl = min(s);
yr = (yu-yl); % Range of ‘y’
yz = s-ym;
yzs = smoothdata(yz,'gaussian',25); % smooth data to remove noise artifacts (adjust factors)
zt = t(yzs(:) .* circshift(yzs(:),[1 0]) <= 0); % Find zero-crossings
per = 2*mean(diff(zt)); % Estimate period
fre = 1/per; % Estimate FREQUENCY
% stationnary sinus fit
fit = @(b,x) b(1) .* (sin(2*pi*x*b(2) + b(3))) + b(4); % Objective Function to fit
fcn = @(b) norm(fit(b,t) - s); % Least-Squares cost function
B = fminsearch(fcn, [yr/2; fre; 0; 0;]); % Minimise Least-Squares
amplitude = B(1)
frequency_Hz = B(2)
phase_rad = B(3)
DC_offset = B(4)
xp = linspace(min(t),max(t),samples);
yp = fit(B,xp);
figure(1),
plot(t, s, 'db',xp, yp, '-r')
legend('data + noise','model fit');
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