Fourier series data fit with fixed period?

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VR 2019-3-6

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此问题的直接链接

https://ww2.mathworks.cn/matlabcentral/answers/448630-fourier-series-data-fit-with-fixed-period

编辑： Francesco Tricarico 2020-10-20

I am trying to fit a data set of one year to Fourier series and I want to fix the period to be one year. So far, it seems that functions like 'fit' gives you w (i.e.,period) as output but you can fix it as an input. I read somewhere that it is possible to fix w if you choose your lower bound and upper bound to be the same. However, they did not specify how to do it with a MWE. Any recommendations would be helpful.

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Answer 1

Francesco Tricarico 2020-10-11

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https://ww2.mathworks.cn/matlabcentral/answers/448630-fourier-series-data-fit-with-fixed-period#answer_510916

编辑：Francesco Tricarico 2020-10-11

在 MATLAB Online 中打开

Probably VR solved it but for MWE would be useful in the future, so:

% Sinusoid to sample data.
omega = 1; 
N_sp = 10;                                          % Number of sampling points.
t = linspace(0,2*pi/omega,N_sp)';
y = sin(omega*t);
% Fit Options setting. Pay attention to the bound definition.
FitOpts = fitoptions('Method','NonlinearLeastSquares',...
    'Lower',[-Inf*ones(1,5), omega],'Upper',[Inf*ones(1,5), omega]);
% Fit results.
UnboundedFit = fit(t,y,'fourier2')
BoundedFit = fit(t,y,'fourier2',FitOpts)

In UnboundedFit, the fundamental angular frequency is choosen by fit (w = 0.5). In BoundedFit, the fundamental angular frequency is that specified by the user (w = 1).

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Francesco Tricarico 2020-10-13

编辑：Francesco Tricarico 2020-10-20

在 MATLAB Online 中打开

Trying to improve flexibility of the code i posted, let's go mat-friends!

% Declaring the type of fit.
FitType = 'fourier2';
% Creating and showing a table array to specify bounds.
CoeffNames = coeffnames(fittype(FitType));
CoeffBounds = array2table([-Inf(1,length(CoeffNames));...
    Inf(1,length(CoeffNames))],'RowNames',...
    ["lower bound", "upper bound"],'VariableNames',CoeffNames);
% Sinusoid to sample data.
omega = 1; 
N_samplinpts = 10;
t = linspace(0,2*pi/omega,N_samplinpts)';
y = sin(omega*t);
% Specifying bounds according to the position shown by the table.
CoeffBounds(:,6) = [{omega}; {omega}]
% Fit Options setting.
FitOpts = fitoptions('Method','NonlinearLeastSquares','Lower',...
    table2array(CoeffBounds(1,:)),'Upper',table2array(CoeffBounds(2,:)));
% Fit results.
UnboundedFit = fit(t,y,FitType)
BoundedFit = fit(t,y,FitType,FitOpts)