I have this design:
Can you tell me about the type of filter and the algorithm just viewing this design, or should there be other information?
It's a bandpass filter, which is fairly obvious. FIR or IIR is hard to tell without phase. A FIR design would likely to have assumed linear phase, and omitted the phase response. and a package probably wouldn't calculate it, like in an IIR design, so I would tend towards a FIR.
The band goes to .5 which implies whoever designed the filter was taught unit sampling. A current person would most likely have the band go to pi or 1. I’m guessing who ever designed this is retired or dead.
The stop bands don't have a constant level, so I would rule out remez or linear programing.
I would guess if a FIR filter, a window technique, probably a Kaiser window. Maybe a Fejer window. The stop bands are also symmetric around the pass band, consistent with a rect function in the frequency domain, followed by a window.
The stop band is only about 55 db down, so the filter order is definitely less than 100 taps, probably more than 30. I could count the nulls but I don’t have my glasses.
This is all a lot of speculation. Can’t tell if this fixed point or floating point arithmetic.
Mastermind: How to Think like Sherlock Holmes, by Maria Konnikova
which inspired me to answer your odd question. I would put little trust in this answer. This looks like one of those situations where a legacy function is being migrated and someone thinks making it better would break something. Good luck. Windowing as a filter design method is more of a hueristic search than a direct optimization.