Implement filter that cannot be normed to a(1) = 1

Hi, I am aware of the following method of implementing a filter:

numerator = [2 1 1] ;
denominator = [1 2 2 2];
y = filter(signal, numerator, denominator);

The filter transfer function would look like this:

But how is the following filter being implemented?

ATTENTION: I DID NOT MEAN TO WRITE Z^-4 BUT Z^4 I'M VERY SORRY FOR THE CONFUSION

My take: -> The first part is essentially a delay so multiply the signal with 2 and delay it 4 counts (how do I do that?) then apply the filter as said to the signal. Is my line of thinking correct? How would you apply the delay?

Answer 1

[Honglei Chen]

You will pad 4 zeros in front of numerator.

HTH

[Joschua Kraus]

Unfortunately I do not understand your answer

[Joschua Kraus]

Now I got your point, please see the edit to my question in bold letters!