How to fit a sine curve with only the maximum and minimum values

Hi, I am trying to plot a sine wave through the high and low water points from a measuring station in the North Sea.

The image shows the first few data points. I've tried fitting a curve, filling the gaps etc. but I can't get Matlab to acknowledge the oscillating signal.

Help will be appreciated, thank you!

this is the goal:

[Mann Baidi]

Hi,

What type of 'fitType' are you passing in the 'fit' function?

[Sam Chak]

Hi @Patricia Hauser

It might be easier to fit a custom sinusoidal waveform if the data is converted to the unit of 'seconds'. However, it is important to note that the time step in the t vector is not uniform.

where and are the time-varying amplitude and the time-varying period of the sine wave, respectively.

T   = readtable("datapoints.xlsx", VariableNamingRule="preserve")

T = 58x2 table
         t_datetime         t_datenum
    ____________________    _________

    01-Jan-2022 03:05:00      -1.3   
    01-Jan-2022 09:02:00       1.5   
    01-Jan-2022 15:32:00      -1.4   
    01-Jan-2022 21:34:00       1.4   
    02-Jan-2022 04:08:00      -1.4   
    02-Jan-2022 10:06:00       1.5   
    02-Jan-2022 16:31:00      -1.4   
    02-Jan-2022 22:29:00       1.5   
    03-Jan-2022 05:03:00      -1.6   
    03-Jan-2022 11:04:00       1.5   
    03-Jan-2022 17:24:00      -1.4   
    03-Jan-2022 23:20:00       1.6   
    04-Jan-2022 05:56:00      -1.6   
    04-Jan-2022 11:59:00       1.5   
    04-Jan-2022 18:16:00      -1.4   
    05-Jan-2022 00:09:00       1.7   

x   = T{:,1};               % datetime data
t   = seconds(x - x(1));    % convert to seconds
A   = T{:,2};               % high and low points of the sea level
stem(t, A), grid on, xlabel('Time (sec)'), ylabel('Sea level')
title('Sea level around the North Sea from 1st to 15th, Jan 2022')

Answer 1

[Bruno Luong]

piecewise (co)sine interpolation (not fitting).

I don't think you have extra DOF to play with if you restrict data to be local extrema and model follows a sinusoidal law.

data = readtable('https://www.mathworks.com/matlabcentral/answers/uploaded_files/1662781/datapoints.xlsx');
t=datenum(data.t_datetime);
dt = t-t(1);
y = data.t_datenum;
dti = linspace(min(dt),max(dt),1025);
yi = sininterp(dt, y, dti); % function defined below

% Ploy check result
figure
subplot(2,1,1)
dtfun = @(dt) datetime(dt+t(1),'ConvertFrom','datenum');
h = plot(dtfun(dt),y,"ob",dtfun(dti),yi,"r");
% zoom plot
ax2 = subplot(2,1,2);
h = plot(dtfun(dt),y,"ob",dtfun(dti),yi,"r");
xlim(ax2,  dtfun([8 11]))

%%
function yi = sininterp(t, y, ti)
ti = ti(:);
i = discretize(ti, t);
yi = nan(size(ti));
valid = i>=1 & i<numel(ti);
i = i(valid);
y1 = y(i);
y2 = y(i+1);
ym = (y1+y2)/2;
A = (y1-y2)/2;
alpha = (ti(valid) - t(i)) .* (pi./(t(i+1)-t(i)));
yi(valid) = ym + A.*cos(alpha);
end

[Alexander]

Perfect. I'll put it in my stock for special purposes.

Answer 2

[R]

Hi Particia,

Fitting a piecewise cubic Hermite ("pchip") curve might help with this use case. Here is an example of the same

% Read data from Excel file
data = readtable('datapoints.xlsx');

% Convert first column to string array for time labels
time = string(table2array(data(:, 1)));

% Extract water level data from second column
waterLevel = table2array(data(:, 2));

% Create index array for plotting
x=(1:58)'; % Ensure x is a column vector

% Plot water level data
plot(x,waterLevel,".");
title('Water Level vs. Time');
xticklabels(time) % Set custom x-axis tick labels

% Fit a piecewise cubic Hermite interpolating polynomial
[curve,gof,output] = fit(x,waterLevel,"pchipinterp");

% Overlay fitted curve on the plot
hold on
plot(curve)
hold off

Here is the plot I get after executing the above code:

Refer to the following link to learn more about 'pchipinterp' curve fitting model:

https://in.mathworks.com/help/curvefit/list-of-library-models-for-curve-and-surface-fitting.html#btbcvnl:~:text=Curves%20only-,pchipinterp,-Shape%2Dpreserving%20piecewise

You can also find a list of curve fitting models that MATLAB supports in the following documentation:

https://in.mathworks.com/help/curvefit/list-of-library-models-for-curve-and-surface-fitting.html