# Parallel connected FIR filters type III

I am currently studying dsp and I have a question:

Let us assume multiple FIR filters with generalized linear phase of Type III and real IRs $$h_1[n], h_2[n], ..., h_k[n],$$ interconnected in parallel. Concerning the resulting filter, can we conclude something about its zeros, as well as whether it has generalized linear phase and of which type?

• Do the filters have the same lengths? Dec 31, 2022 at 12:46
• @MattL. Unfortunately, it is not defined, but please explain to me, how this information would be useful. Thanks for the response! :) Dec 31, 2022 at 12:54
• You would need to know how to obtain the impulse response of the total system from the individual impulse responses in order to understand what difference the lengths would make. Do you know that? Dec 31, 2022 at 13:11
• Is $k$ odd? I know it's in O&S somewhere. Whatever defines "Type III". And is the symmetry about $\omega=0$ odd? So $\sin(n\omega)$ basis functions? Jan 1, 2023 at 3:47
• @robertbristow-johnson: Type III is odd length and odd symmetry. Jan 1, 2023 at 11:10