Good answer. But, dang, I now have to peruse those.
DaveD
KC0WJN
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All spelling mistakes are the responsibilty of the reader (Rick Renz, STK, ca. 1994)
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> On Jul 6, 2024, at 12:37, Reginald Beardsley via groups.io <pulaskite@...> wrote:
>
> ? This is a general reply to Jeff, Mike and Dave. I initially looked at:
>
> Digital Design Handbook
> Fred J. Taylor
> Marcel Dekker 1983
>
> Digital Signal Processing
> Oppenheim and Shafer
> Prentice-Hall 1975
>
> Theory and Application of Digital Signal Processing
> Rabiner and Gold
> Prentice-Hall 1975
>
> Digital Signal Processing with Kernel Method
> Rojo-Alvarez et al
> Wiley/IEEE 2018
>
> Advanced Digital Signal Processing
> and Noise Reduction
> Vaseghi
> Wiley 4th ed 2008
>
>? Subsequent to the responses I checked:
>
> Spectral Analysis and Time Series
> Priestly
> Academic Press 1981
>
> Continuous a Signals and System Analysis and Discrete
> McGillem and Cooper
> Holt, Reinhart and Winston 1974
>
> None of them properly discuss the issue of causality.
>
> I did NOT look at any of the many monographs by Enders Robinson, Robinson & Treitel or John H. Karl as I know they have the matter stated very clearly. Robinson and Treitel were members of Norbert Weiner's Geophysical Analysis Group at MIT and founded the entire basis of DSP. I spent 4 years at UT Austin under another member of the GAG, Milo Backus. Robinson performed the first digital deconvolution problem in 1952 using pencil, paper and a desk calculator.? Robinson has pride of place as the first person to apply DSP to data.
>
> Causality requires that the real and imaginary parts be a Hilbert transform pair. This is well stated in:
>
> The Fourier Integral and Some of Its Applications
> Ronald Bracewell
> McGraw-Hill 2nd ed 1978
>
> Causality simply states that there is no output prior to the input. If a filter is not causal it produces output before the event. The EE community appears to consistently label a zero phase signal as linear phase with a phase delay. As Bracewell provides a proof and I spent 2 semesters studying Churchill's "Operational Mathematics" under Bill Guy in "Integral Transforms" at Austin in addition to the semester I spent with Bracewell in "Linear Systems", if the EE community wants to redefine the math they may. I shall stick to what the mathematicians wrote.
>
> Have Fun!
> Reg
>
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