Is there a way to linearly interpolate dates and times?

I am trying to interpolate discharge data using gage information. The time that corresponds to the discharge data is listed in Excel as:

1/10/08 15:33 (for example)

In MATLAB I've used the datestr command on the data and the dates are now listed as:

11-Jan-0108 15:33:42 (for example)

The data is generally given in 10 minute increments, so my question is as follows: is there a way to linearly interpolate the discharge data so it returns data for every 2 minutes, for example? I've tried using interp1 but I'm not sure exactly how to input the date so it reads properly.

Answer 1

[Kye Taylor]

If you convert the dates to serial date numbers as the cyclist suggests, then you might be able to benefit from this example...

% Create a dataset that resembles yours
dates = today:10:today+100; % dates as serial date numbers
data  = sin(linspace(0,2*pi,length(dates))); % create some fake data

disp('The dates include')
for i = 1:length(dates)
  disp(datestr(dates(i)))
end

finerDates = dates(1):2:dates(end); % get a finer grid

% map x-data to 0,1
scaledDates = (dates - min(dates))/(max(dates)-min(dates));
scaledFinerDates = (finerDates - min(finerDates))/(max(finerDates)-min(finerDates));

% get interpolated data -- spline is an option, could be 'linear'
interpolatedData = interp1(scaledDates, data, scaledFinerDates,'spline');

% visualize it
figure,hold on
plot(dates,data,'ro')
plot(finerDates, interpolatedData,'b.-')
legend('original data','interpolated data')
datetick('x');

[Matt]

I understand the concept of converting the dates to numbers. Could you explain what is happening with scaledDates and scaledFinerDates? Are the serial numbers for the dates being divided? I'm a little confused there. Thanks!

[Kye Taylor]

The serial date numbers are on the order of 10^5. The interpolant that I use is comprised of polynomials (like p(x) = a*x + b*x^2 + c*x^3 -- a cubic spline). One needs to scale the data so that you don't end up squaring or cubing 10^5. as this will result in too wide a range of values to get a meaningful interpolant. If you use 'linear' as the option to interp1, the scaling should make no difference, but if you want a more sophisticated interpolant, you should scale.

[Nahid Atashi]

thank you so much Kye. your code was great for me too

Answer 2

[the cyclist]

One method would be to use the datenum() command to convert the dates to pure numbers, which can be consumed by interp1.

[Walter Roberson]

"consumed" ?