Just reading The Analytic Impulse, A. Duncan, 1988, I met the name "Heyser corkscrew" for the first time in my DSP life, for a 3D display of a cisoid or complex exponential $e^{i\omega }$ (often denoted $\text{cis}\, x$ for "cosine plus $i$ sine").

Heyser corkscrew spiral of the cisoid or complex exponential

The view is mentioned as Euler formula's 3D view in the context of circular polarization:

Euler formula and circular polarization

This representation is quite common for analytic signals, but this name does not seem standard. Questions are:

  1. What is the history of this Heyser name, with a precise reference?
  2. What are the (earlier) history and names for this representation (going back to the Fourier oblique view)?

After @MBaz hints, the term "Heyser spiral" seems a little more common. It is named after Richard C. Heyser, and can be interpreted as a 3D variant of Nyquist plots... Indeed, in A Matter Of Frequency: The Nyquist Plot Explained, one can read:

Dennis Gabor proposed the “analytic signal” which Richard Heyser developed into what has since been named the Heyser Spiral. The Nyquist plot is the “end view” shadow of the complex analytic signal

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    $\begingroup$ A quick search in my university's libary seems to indicate the name is common in the audio field. Even then, there are just a handful of references. $\endgroup$ – MBaz Apr 2 '16 at 22:25
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    $\begingroup$ There are a few patents: google.com/patents/US8306242 google.com/patents/US5956411 and this paper, to which I don't have access: aes.org/e-lib/browse.cfm?elib=11444 $\endgroup$ – MBaz Apr 3 '16 at 1:37
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    $\begingroup$ @MBaz "Spruce Moose: A Slightly Bent Horn", what a beautiful name for a paper $\endgroup$ – Laurent Duval Apr 3 '16 at 12:47
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    $\begingroup$ wow. i remember when that paper came out. haven't heard too much from Andrew Duncan since the 80s. Dick Heyser was a sorta visionary to some (Don Davis, SynAudCon) and, perhaps, a little controversial to others (like Stan Lipshitz and John Vanderkooy). before there were soundcards and DSP chips, Heyser pioneered using linear-swept sinusoidal (chirp) analysis of loud speakers and such because, with a tracking VCF, he could separate out reflections. he had disciples and detractors in the AES. i was sorta neutral. he died just after being elected President of the AES in the 1980s. $\endgroup$ – robert bristow-johnson Apr 4 '16 at 2:44
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    $\begingroup$ @LaurentDuval Well it's my (unanswered) question, and you seem to have found an answer :D $\endgroup$ – endolith Sep 11 '17 at 15:11

Looking at ancient geophysical papers, I have found in Truncations and phase relationships of sinusoids, Philip L. Jackson, Journal of Geophysical Research, 1967, this "Fourier transform" with "oblique view", that seems to predate Heyser corkscrew/spiral.

Fourier oblique view

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    $\begingroup$ That doesn't actually show the curve though; it shows real and imaginary parts separately $\endgroup$ – endolith Sep 7 '18 at 19:05
  • $\begingroup$ Indeed. But I provided this picture for the historical part, for others to dig deeper. I never saw the mention of "oblique" view before. I am stuck with Heyser's works which as hidden under the AES paywall for me $\endgroup$ – Laurent Duval Sep 7 '18 at 19:27
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    $\begingroup$ Yeah I don't have AES either. I've considered it. $\endgroup$ – endolith Sep 8 '18 at 20:07

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