Use of trapezoidal function and resampling of time series?

Consider the following data set / timeseries (ts):

time   val
0      1
5      1
5      4
10     4
10     3
15     3

The timeseries is continuing step/stair-wise. In this case, I want to resample the time series into values sectioned into a 3-minute interval, such as:

resample(ts,0:3:15)

I want matlab to find the new values at [0,3,6,9,12,15], representing a new stair/step-graph with a value valid for three minutes, until the next point appears. Whereas the point 0 should be equal (1*3)/3 = 1 based on the first time interval (0-5), the point 3 is computed as (2*1+4*1)/3 and should thus be 2.

I have thought of using the trapezoidal rule to get the results, but I don't know how to implement it in resample, or synchronization with a new ts. Any hints?

[Titus Edelhofer]

Hmm, I'm not sure what the result should be: if the value is 1 from t=0 until t=5, why should for the resampled signal the value at t=3 should be different from 1? Please give (again) an example what you expect at t=0, 3, 6, 9, 12.

Titus

[Titus Edelhofer]

Forget the comment, I now see what you mean. The value at three is the mean value of the signal on the interval [3 6]. Therefore you mentioned the trapezoidal rule. I admit right now I have no easy solution that would not require looping over the vector 0:3:15 ...

Titus