[sdiy] 90-degree phase displacement network calculations

[Bernard Arthur Hutchins, Jr]

Thanks David- Outstanding

The Orchard curve (yellow) looks nearly “Equiripple” (Chebyshev error) and would be that (by the alternation theorem) if it has the right number of extremal frequencies: one more than the number of degrees of freedom in the design.  It has 16 pole choices and 17 extremals (both ends count) – so Winner!

We likely have a prejudice (looks “intentionally esthetic”) for a pretty-looking equiripple response, so keep in mind that the Orchard (like the Weaver shown) in fact shoots rapidly upward beyond the band edges.  In addition this min-max-error is achieved at the expense of increased error in other regions.

I suspect that with the tiny max error of under 0.2 degrees, this all makes little difference. Readers seeking more info on equiripple procedures for background and as applied to digital filter design might look at my “A New Simplified Equiripple Design Algorithm for FIR Filters” Electronotes 175 August 1989, pp 3-50.
-  Bernie











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