Vectorized or Optimized Finite Low Pass Filter

Let me start out with I do not have the signal processing toolbox. A simple low pass filter function should be easy. Indeed, "brute force" it is, I have the following code for filtering a timeseries:

function tsy = dlpf( tsx, lpff )
%dlpf - discrete low pass filter
%   Outputs a low pass filtered timeseries when a timeseries and frequency
%   are entered

      tslen = length(tsx.time);

      tau = 1/(2*pi*lpff);   

      %Line by line version
      %This is more accurate, but much slower
      disp = '';
      tsy = tsx; 
      for n = 2:tslen
         dt = tsx.time(n) - tsx.time(n-1);
         alpha = dt/(tau+dt);
         tsy.data(n,:) = alpha*tsx.data(n,:) + (1-alpha)*tsy.data(n-1,:);
      end

end

But, I feel like I've given up whenever I use a for loop in MATLAB. I have timeseries data with over 400000 entries and as with any for loop in MATLAB, this is VERY slow. I want to make a "fast" version that's vectorized, or at least optimized in some way. The problem is, I don't think the equation:

y[i] = a*x[i] + (1-a) * y[i-1]

can be vectorized since the series y appears on both sides of the equation. If I did vectorize, it would look something like this:

      %Vectorized version
      %For speed, this takes an average dt, which will work if the timeseries
      %is more or less uniform.
      %For a very nonuniform timeseries, a line by line version would be
      %needed

      dt = mean(tsx.time(2:tslen)-tsx.time(1:tslen-1));
      alpha = dt/(tau+dt);
      tsy = tsx
      tsy.data(2:tslen) = (1-alpha)*tsy.data(1:tslen-1,:) + alpha*tsx.data(2:tslen)

I fear that the tsy.data series on the right will not contain the correct values, as they would be updated with each iteration through the series. I don't know how MATLAB would handle this in the background. Would this do what I want, or does anyone know of a better way to do this?

[Alan]

I just ran both sets of code. The vectorized version ran much faster (seconds), of course, but I believe my suspicions that it won't work were true. The result is not the same and does not appear to be an effective filter. It has much more noise than the for loop version. I suspect it's essentially the same as if I used (1-alpha)*tsx.data(1:tslen-1,:) which is not the same as the equation I'm trying to achieve.

Answer 1

[Honglei Chen]

If your signal is uniformly spaced, and if I understand correctly, your alpha can be pre-determined, then this can be done via

y = filter([1 alpha-1],alpha,x)

[Alan]

Thank you for the response. I've tried exactly that formula, but I'm getting weird results. For one, though it filters and works quite fast, it does not appear to filter as well as the for loop version I posted (though it should, in theory, be almost the same). Second, my signal appears to be getting multiplied 5X when I use it. (Peak is about 400 in original and for loop filtered version, 2000 in the filter() version)

[Honglei Chen]

Don't know why the difference but I did make a mistake in my answer, it should be

y = filter([1 alpha-1],alpha,x)

Sorry about that and I've corrected the original answer too.

[Alan]

Correcting from 1-alpha to alpha-1 got rid of the 5X magnitude issue. However, this filter is actually increasing the noise in my signal, not decreasing. Perhaps I'm calculating my "alpha" wrong? Of course, I'm calculating "alpha" almost the same way in my for loop version - which actually filters it quite well but is just really slow. The one difference is I used an average value for dt (which is used to calculate alpha) across all for the filter() version and I update it each iteration in the for loop version. I wouldn't suspect the difference would be that great, though.

[Alan]

It works. Sorry, I was not comparing the right graphs. Thank You very much! I marked it as accepted.