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

Question

Patricia Hauser 2024-4-8

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评论： Alexander 2024-4-9

datapoints.xlsx

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:

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Mann Baidi 2024-4-8

Hi,

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

Sam Chak 2024-4-8

在 MATLAB Online 中打开

datapoints.xlsx

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')

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Answer 1

Bruno Luong 2024-4-8

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https://ww2.mathworks.cn/matlabcentral/answers/2104206-how-to-fit-a-sine-curve-with-only-the-maximum-and-minimum-values#answer_1438206

编辑：Bruno Luong 2024-4-8

在 MATLAB Online 中打开

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

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Alexander 2024-4-9

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

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Answer 2

R 2024-4-8

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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