Normalization of a given filter to have unity gain at DC

Hello everyone,

As the title says, I should find a general way to normalize some filters to have unity gain at DC. My filters are an Hanning window (note that b/d and a/c are the vectors in which are reported the coefficients of, respectively, numerator and denominator of the transfer function of the filters)

b = [0.25 0.5 0.25];
a = [1 0 0];

And a derivative-based filter:

d = [1 -1];
c = [1 -0.95]

Any help will be greatly appreciated.

Answer 1

[Honglei Chen]

I don't quite understand your question. For example, in your filter formed by d and c, it has a null at DC, how do you expect it to have a unit gain at DC?

In general, if you have filter coefficients b and a, the DC gain is given by sum(b)/sum(a). You can just scale the filter response accordingly.

[Vittorio]

Yes, what you said is correct. In fact, I resolved my issue by just scaling:

[h,w] = freqz(b,a,500,1000);    %frequency response of the filter H = b/a
scale = 1/max(abs(h));          %scaling factor
b = b*scale;                    %scale*H

Thank you for your answer!