Combine data matrices of different frequencies - matlab

Question

In MATLAB, how could I combine two matrices of data measured at different frequencies such that the result is indexed at the higher frequency? Since the data measured at the lower frequency will have many unknown values in the result, I would like to replace them with the last known value in the matrix. There is a lot of data so a vectorized solution would be preferred. I've added some sample data below.
Given:
index1 data1 index2 data2
1 2.1 2 30.5
2 3.3 6 32.0
3 3.5 9 35.0
4 3.9 13 35.5
5 4.5 17 34.5
6 5.0 20 37.0
7 5.2 ... ...
8 5.7
9 6.8
10 7.9
... ...
Result:
index1 data1 data2
1 2.1 NaN
2 3.3 30.5
3 3.5 30.5
4 3.9 30.5
5 4.5 30.5
6 5.0 32.0
7 5.2 32.0
8 5.7 32.0
9 6.8 35.0
10 7.9 35.0
... ... ...
EDIT:
I think the following post is close to what I need, but I'm not sure how to transform the solution to fit my problem.
http://www.mathworks.com/matlabcentral/newsreader/view_thread/260139
EDIT (Several Months Later):
I've recently come across this excellent little function that I think may be of use to anyone who lands on this post:
function yi = interpLast(x,y,xi)
%INTERPLAST Interpolates the input data to the last known value.
% Note the index data should be input in ASCENDING order.
inds = arrayfun(#findinds, xi);
yi = y(inds);
function ind = findinds(val)
ind = find(x<=val,1,'last');
if isempty(ind)
ind = 1;
end
end
end
Credit goes here: http://www.mathworks.com/support/solutions/en/data/1-48KETY/index.html?product=SL&solution=1-48KETY

Answer 1

The problem is one of run length decoding. See section 15.5.2 of Matlab array manipulation tips and tricks (which is an eye-opening read for any Matlab enthusiast).
Here's using the method with your example (I'm using octave but the code is identical for Matlab):
octave:33> a=[2,30.5;6,32;9,35;13,35.5;17,34.5;20,37]
a =
2.0000 30.5000
6.0000 32.0000
9.0000 35.0000
13.0000 35.5000
17.0000 34.5000
20.0000 37.0000
octave:34> i=a(:,1)-1
i =
1
5
8
12
16
19
octave:35> j=zeros(1,i(end))
j =
0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0 0
octave:36> j(i(1:end-1)+1)=1
j =
0 1 0 0 0 1 0 0 1 0 0 0 1 0 0 0 1 0 0
octave:37> j(1)=1
j =
1 1 0 0 0 1 0 0 1 0 0 0 1 0 0 0 1 0 0
octave:38> val=a(:,2)
val =
30.500
32.000
35.000
35.500
34.500
37.000
octave:39> x=val(cumsum(j))
x =
30.500
32.000
32.000
32.000
32.000
35.000
35.000
35.000
35.500
35.500
35.500
35.500
34.500
34.500
34.500
34.500
37.000
37.000
37.000
And pad the beginning with NaN as needed.

Answer 2

I recently had the same problem as you: I had data, measured by different systems, which had to be synchronized and processed.
My solution consisted of putting the measurement data and time information (frequency, time at start of measurements) in a class object. Then I implemented a multiplication, addition, etc. method for that class that automatically took care of all the necessary things, being:
upsampling the lower frequency signal (with linear interpolation (interp1)
shifting one of the signals, so the data lines up in time
cutting off the non-overlapping data set at beginning and end (with two different systems you never start or stop measuring at the same time, so there is some excess data)
actually performing the multiplication
returning the result as a new class object
Next to that there were other functions of which you can guess what they do: plot, lpf, mean, getTimeAtIndex, getIndexAtTime, ...
This allowed me to simply do
signalsLabview = importLabViewSignals(LabViewData);
signalsMatlab = importMatlabSignals(MatlabData, 100); %hz
hydrPower = signalsLabview.flow * signalsMatlab.pressure;
plot(hydrPower);
or things like that. If you have a lot of these signals on which you have to do some math, this really helps and results in clear code. Otherwise you have a lot of general code just for doing the syncing, shifting, trimming around each operation. Also for quickly checking things it's easy.
If you have to do this things a lot, I think it's definitely worth investing some time in it to build a proper framework.
Unfortunately I don't think I can disclose this code (IP and such), but it wasn't rocket science.