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Re: [AUDITORY] seeking old Kaiser paper



Hello, Dick,
a derivation operation in operational calculations seems to be equivalent to integral operator with the kernel of ones triangular matrix with 1/2 as the diagonal elements. May be J.F.Kaiser treated the problem on this manner? I do not insist :)  


Вторник, 30 января 2018, 8:52 +03:00 от "Richard F. Lyon" <dicklyon@xxxxxxx>:

Does anyone have the 1963 Proceedings of the First Allerton Conference on Circuit and System Theory?  Or just "Design methods for sampled-data filters" by J. F. Kaiser? 

I'm trying to resolve a disconnect in derivations of the impulse-invariance method, which was "corrected" in several places over the years, though Kaiser had the key to the correction in his chapter "Digital Filters" in the 1966 "System Analysis by Digital Computer" book, in which he says his stuff on IIR design closely follows that missing paper as well as a BSTJ paper that does not have the key piece. 

The key observation is that using the naive impulse invariance method adds a constant (frequency independent) term to the frequency response of the digital filter proportional to the impulse response on the right side of time zero: T/2 * h(0+).  He didn't go as far as the "corrections" which said to take the impulse response h[k] at k = 0 to be (h(0-) + h(0+))/2, though it's pretty obvious from there.  It's funny that at some point he got as far as including that unwanted term yet didn't comment on the easy way to remove it.  Maybe in the missing paper...

Dick




--
alex kalinin