Basic filtering related question

I'm a novice user.

I'm doing a failure test where my displacement (D) increases until a maximum value of Load (L) after which D may increase or decrease. This link shows an example (in this example D continues to increases until data collection stops): http://tiny.cc/4u1of

I use a 5 element moving average filter on both L and D, for example: D= filter(ones(1,5),5,data(:,4)

My problem is, that the filter has introduced a tail at the start of the data where D is decreasing before it increases - this should not happen. Otherwise the filter seems to work just fine - when I overlay the filtered and unfiltered data I am not losing important values as a result of the filter.

My related questions are therefore: (1) Should I use another filter? If so please recommend. OR (2) Is there a simple way of picking out the 'true' start to the data from the filtered data set - where D continually increases to the maximum value of L.

Thank you.

Answer 1

[Wayne King]

Hi Etienne, I don't think your filter is doing exactly what you think. I'm a bit confused by D = filter() since your graph has L as the output variable and D as the input. I'll assume that:

Your filter's difference equation is:

5L(n) = D(n)+D(n-1)+D(n-2)+D(n-3)+D(n-4)

A simple moving average filter is:

L = filter(1/5*ones(5,1),1,D);

As far as avoiding filter transients, have you tried filtfilt() to implement zero-phase filtering?

By the way, if you use a simple moving average filter like above, then the delay with filter() is 1/2 the filter length.

So:

    t = 0:0.001:1-0.001;
    x = cos(2*pi*100*t);
    y = filter(ones(5,1)/5,1,x);

y is delayed 2.5 samples with respect to x.

[Etienne O'Brien]

Thanks Wayne.

I'm sorry but I'm a bit lost as I'm using this filter on a recommendation and don't understand the inner workings. I filter both the D and L data and when I plot the data before and after filtering it does appear to be smoothed.

D= filter(ones(1,5),5,data(:,4).');

L= filter(ones(1,5),5,data(:,5).');

These are biomechanical failure tests. I collect Load (L) and Displacement (D) at 800 Hz.

[Wayne King]

Oh, I thought you had them as a input-output relationship, then I think you want to filter both as:

D= filter(ones(5,1)/5,1,data(:,4)');

L = filter(ones(5,1)/5,1,data(:,5)');

D and L will both be delayed 2.5 samples. You can try filtfilt()

D = filtfilt(ones(5,1)/5,1,data(:,4)');

L = filtfilt(ones(5,1)/5,1,data(:,5)');

[Etienne O'Brien]

Thanks Wayne,

D= filter(ones(5,1)/5,1,data(:,4)');

L = filter(ones(5,1)/5,1,data(:,5)'); %these made no difference

D = filtfilt(ones(5,1)/5,1,data(:,4)');

L = filtfilt(ones(5,1)/5,1,data(:,5)'); %these solved the problem