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