A class of digital filters called Frequency Sampling Filters (FSF) has been mentioned in a side note by Richard Lyons in another related question comparing IIR digital filter design using mapping techniques. There is very little information on this technique available through a simple web-search (obscured by the "Frequency Sampling Method" which I would not recommend), but I did find details on it in chapter 7 (Specialized Lowpass FIR Filters) of Richard's great book Understanding Digital Signal Processing- but no where else. There he mentions that it predated optimized FIR design techniques (least squares and Parks-McClellan) but suggests they may have practical modern use for highly efficient linear phase filters in certain use cases.
My question is not in the details of how this filter works (Richard covers that quite well in his book), but if there are other references to this class of digital filters and who coined "Frequency Sampling Filter" (unfortunate that the terminology is so close but yet unrelated to the "Frequency Sampling Method", and if anyone can bottom line / summarize concisely with a good demonstration of a case where such a filter would be a superior choice over the optimized design techniques for linear phase filters using Parks-McClellan (PM, equiripple) or Least Squares. (A comparison of these two techniques to mapping of classic analog filters is covered in the other question referenced above.) The implementation of efficient filters structures using the PM or Least Squares techniques should consider the significant complexity optimization that can be achieved with proper decimation/interpolation structures include polyphase implementation.
Please avoid a response that only states what I would refer to as unsubstantiated opinion / rumor. I do see already how this filter structure may possibly be superior in low complexity to achieve a similar performance for smaller ratios of passband to sampling rate. I'm looking for a substantiated comparison that shows the advantage if this is the case, or if this filter structure is indeed driven to obscurity for good reason. (In case anyone has that or is interested/curious as I am enough to create a comparison...if not I will eventually post one here as my own response when time allows).