Period Operator Using filtfilt

I am trying to understand the function filtfilt, but I am having difficulties wrapping my head around it. I believe it may be because I am unsure of what one of the operations is in the help document for filtfilt. The operation is: y=filtfilt(d.Numerator,1,x);

What does d.Numberator do?

Answer 1

[Wayne King]

The answer to what the period operator in your example does is the following.

filtfilt() unlike filter() does not accept a dfilt object input. The portion of the example you are showing is using a dfilt object. What you have is an FIR filter dfilt object, so the example is extracting the numerator coefficients (in the Numerator field) and providing those to filtfilt.m.

For example:

   x = randn(10000,1); % just create some noise to filter
   % Design a lowpass FIR filter with a sampling rate of 1 kHz
   D = fdesign.lowpass('Fp,Fst,Ap,Ast',100,150,1,40,1000);
   d = design(D,'equiripple'); % design FIR equiripple filter

Now you cannot filter data using filtfilt() with

   y = filtfilt(d,x);  % this will error
   % However the following works
   y = filter(d,x);

So to use filtfilt.m, you have to extract the numerator coefficients. For an FIR filter the denominator coefficient is 1.

   y = filtfilt(d.Numerator,1,x);

Answer 2

[Jan]

Do you understand the command filter? If not look at first to doc filter. You find a M-version here: Answers: Filter Constants.

Now filtfilt does the following:

1. Create some initial conditions to reduce the transitional effects on the margins. This is a kind of warm-up the filter.
2. Filter from start to end and backwards from end to start. This eliminates the delay effects: With a single filter, the values of a point depends on its predecessors, such that a peak is shifted to the right. Filtering in backward direction again shifts it to the left again.