weighted average time series
in [Matlab]
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From: dormant on 7 Mar 2010 13:52 I am sure that what I want to do is simple in MATLAB, but my maths has totally failed me and Help is driving me round in circles. Can anyone help? I have ten time series', all sampled over the same time interval, all trying to measure the same thing. All ten share a similar shape, but all of them show departures from it. All ten have a very different amplitude range, but they all start from 0. In case my description isn't enough, the time series' look like this (ignore the red one): http://www.pbase.com/dormant/image/122549911 I want to combine them together to construct a weighted-average time series. So I need to determine one average time series and ten weights. I thought this would be a least-squares problem, but I can't seem to get it in the right form.
From: Sadik on 7 Mar 2010 20:17 How about normalizing all of them to have a maximum value of 1? You can obtain a set of weights this way, but I don't know if this simple solution would work for you. Best. "dormant" <rod.stewart(a)uwiseismic.com> wrote in message <hn0skl$ppc$1(a)fred.mathworks.com>... > I am sure that what I want to do is simple in MATLAB, but my maths has totally failed me and Help is driving me round in circles. Can anyone help? > > I have ten time series', all sampled over the same time interval, all trying to measure the same thing. All ten share a similar shape, but all of them show departures from it. All ten have a very different amplitude range, but they all start from 0. > > In case my description isn't enough, the time series' look like this (ignore the red one): > http://www.pbase.com/dormant/image/122549911 > > I want to combine them together to construct a weighted-average time series. So I need to determine one average time series and ten weights. > > I thought this would be a least-squares problem, but I can't seem to get it in the right form.
From: ImageAnalyst on 7 Mar 2010 20:54 Or, instead of normalizing to the max value, you could normalize them by the area under the curve. Depends on what you want to do. The normalization method you select might depend on what gave rise to the different amplitudes, plus the noise spectrum. If it's just a gain difference, then you should normalize to the max but the problem is the max could be a noise spike, so you might have to do some noise reduction and then divide by the max.
From: dormant on 9 Mar 2010 13:06 Thanks for the suggestions, some of which I tried already. To answer one question. The signals I am discussing are not the same signal plus different noise in each time series. The signal is subtly different in each time series, and I am trying to quantify these differences. There is also noise present, but that can't be removed by any processing.
From: ImageAnalyst on 9 Mar 2010 21:37
On Mar 9, 1:06 pm, "dormant" <rod.stew...(a)uwiseismic.com> wrote: > Thanks for the suggestions, some of which I tried already. > > To answer one question. The signals I am discussing are not the same signal plus different noise in each time series. The signal is subtly different in each time series, and I am trying to quantify these differences. There is also noise present, but that can't be removed by any processing. ----------------------------------------------------------------------------- So you have no noise and the signals are different because they really are different. And you are "trying to quantify the differences." So, in the absence of any other information, I'd say that you just simply subtract the signals to get the differences. If that's not right, then say why. |