Moving Average with timestep

I have an array M=[1,4,7,6,4.5,7.5,8.5,4.5] and for time t=[1,2,3,4,5,6,7,8]. I have to find the average of M w.r.t t, with a window size of 2 and step size of window should be 1 or 2. How can I do that?

I am using movmean function to calculate the average, how can I used the window and the step size in this function?

[Enrico Gambini]

v=movmean(M,2); %mean over a sliding window of length 2 across neighboring elements of M

Is this the answer?

[MakM]

Yes but I want the sliding window of length 2 to move with the displacement of 1.

[Jan]

This is exactly what the shown code does. If you want to omit each second output:

v = v(1:2:end)

[MakM]

I dont want to omit it. I want to calculate the average by using the windows of size 2 and this window should move with the displacement of 1.

[DGM]

It does move with a displacement of 1.

M = [1,4,7,6,4.5,7.5,8.5,4.5];
v = movmean(M,2) % this

v = 1×8

1.0000 2.5000 5.5000 6.5000 5.2500 6.0000 8.0000 6.5000

[M(1) mean(M(1:2)) mean(M(2:3)) mean(M(3:4)) mean(M(4:5)) ...
      mean(M(5:6)) mean(M(6:7)) mean(M(7:8))] % is the same

ans = 1×8

1.0000 2.5000 5.5000 6.5000 5.2500 6.0000 8.0000 6.5000

Note that the first element represents the filter window being truncated. See the documentation for other options.

You also said you want it to move with a displacement of 2. Jan described that as well.

v = v(2:2:8) % assumed alignment

v = 1×4

2.5000 6.5000 6.0000 6.5000

[mean(M(1:2)) mean(M(3:4)) mean(M(5:6)) mean(M(7:8))] % same thing

ans = 1×4

2.5000 6.5000 6.0000 6.5000

If this isn't what you want, you need to explain why. If you have specific requirements for the window span or alignment, you need to communicate that information.

[MakM]

Thanks DGM for the information. But as I mentioned I need to average the M w.r.t time, lets say, I have time having values I mentioned in the question and M, then I have to enter the window size with displacement value, which should take average of M and T. I hope I have made the question a bit clear. :)

[DGM]

Provide an example of what the expected output should be for the given vectors.

[MakM]

Does this image make my question clear?

[Jan]

In the original question M was a vector. Is it a matrix now? The sketch does not clarify, what you want to achieve. Please post some code, which defines the procedure exactly, e.g.:

WindowsSize  = 2;
Displacement = 1;
Data         = rand(1, 10);
Output       = [mean(Data(1:1+WindowSize-1)), ...
                mean(Data((1:1+WindowSize-1)) + 1*Displacement), ...
                mean(Data((1:1+WindowSize-1)) + 2*Displacement), ...
                ]

It is not clear what "with timestep" means.

[DGM]

The figure only raises more questions. Therein, the sample window is shown as a 2x2 area between the t and M axes.

What exactly does this area represent? Are you trying to find the local average value of some function of M and t? Their union? sum? product? Are you trying to find some blockwise mean of the Toeplitz matrix formed from M and t?

Furthermore, what happens when the filter is moved? Where is it moved? Since we've established that 1 might equal 2 and 2 now means 2x2, will it still be a 2x2 square?

The clearest explanation is a simple concrete example.

P.S. If it is just the union of M and t, just do movmean((M+t)/2,2).

[MakM]

Timestep is actually the displacement with which the window should move. Now what I did is,

v=movmean(M,2); %taking window size 2
v=v(1:2:end);   %taking the time step or displacement 2 
t=t(1:2:end)    %As omitted values for v, t values need to be omitted to plot them together 
plot(t,v)       %plot them together

Is thi correct?

[Jan]

Yes, this is what was suggested yesterday.

If the length of M is a multiple of 2, an equivalent code is:

v = (M(1:2:end) + M(2:2:end)) * 0.5;
t = t(1:2:end)

[MakM]

Thank you Jan, Kindly paste your answer, so I can accept :)

Answer 1

[Jan]

A simple average over 2 elements (length of M can be even or odd):

Len = numel(M);
v   = (M(1:2:Len - rem(Len, 2)) + M(2:2:Len)) * 0.5;
t   = t(1:2:end)