"Levelling" out a signal with moving average

I'm doing studies on stress-relaxation with a dynamic displacement. The result I have is a almost sinusoidal signal with a moving average (decreasing due to stress-relaxation).

I'm wondering what is the best way to shift all the waves so that instead of having a moving average, I can have a constant average?

Thanks!

[Sean de Wolski]

Huh? Could you elaborate a little more, perhaps with an image of a plot to help explain? If you want a more constant average - expand your window length.

[Tom]

If it is fairly sinusoidal, you could do an FFT (or several over different 'windows' of data) to determine the time period of one oscillation, and work out an average over this period?

[Sandy]

Here is a sample of the signal I have:

http://dl.dropbox.com/u/22993792/signal.jpg

I was initially thinking of doing it your way, Tom, but thought maybe there was a quick function in MATLAB that may do it for me quickly! I think if all else fails, manually averaging it will have to do.

Answer 1

[Sean de Wolski]

What about using medfilt1 in the signal processing toolbox?

doc medfilt1

Edit: more

pictures really are worth thousands of words

Use the median filter, medfilt1 to create a new vector and then subtract this from your original.

[Sandy]

I'm a beginner at signal processing so I'm not entirely sure what the capabilities of each function are but from what I can tell, both the medfilt1 and smooth functions are used to remove noise, if I'm correct?

The noise of the signal is fine, what I need right now is to have all the sine waves in straight line, so to speak. Kind of like this:

http://dl.dropbox.com/u/22993792/signal.jpg

[Sandy]

Apologies, I mean like this:

http://dl.dropbox.com/u/22993792/signal2.jpg

[Tom]

I had a very quick look-I think you could use the medfilt1 function, but you'd have to know how many points to smooth over, which kind of comes back to the frequency of it- unless you take a bit of a stab with a large number. But someone may know a cleverer way than this.

[Honglei Chen]

@Sandy, I think you may want to find out first whether your original data is a power function or an exponential function. Then you do either polyfit or expfit like suggested by Gurudatha there. You can then try to subtract the fitted trend from the data. medfilt1 might work too but you then need to play with different window length. IMHO, the other approach is easier. I don't think smooth apply here. Also, smooth is not from Signal Processing Toolbox, it is from curve fitting toolbox.

[Sandy]

Thank you all so much! The medfilt1 idea seems to have worked quite well. As suggested, I used medfilt1 to smooth the data as much as possible so it was practically just a single non-linear line and subtracted that from my original result:

http://dl.dropbox.com/u/22993792/medfilt1result.jpg

Unfortunately, it looks like there may be a problem with the initial value as it looks like it starts at 1.4 and immediately falls to 0. Anyhow, I will have a closer look at the problem.

Once again, all the help was very much appreciated!

[Honglei Chen]

You will have to drop the edge if you use medfilt1 because that is your transient response.

Answer 2

[Honglei Chen]

Maybe you want to try detrend?

doc detrend

[Sandy]

Thanks,

I've had a look at the detrend function and it seems that it's for linear trends. I tried using the function on my results and unfortunately it didn't make a difference.

The trend I have decreases non-linearly, kind of like the results here:

http://www.sensorprod.com/research-articles/white-papers/2005_nop/Representative-data-of-Pressure01.jpg

[Honglei Chen]

Then what I can think of is to do a polyfit on your data and then subtract the resulting fit from your data. But I don't know how good it can work out.

Answer 3

[Gurudatha Pai]

I would recommend fitting an exponential curve rather than a poly fit. e.g see example 8.10 in Steven M. Kay, "Fundamentals of Statistical Signal Processing: Estimation Theory." pp 257.