Downloads

 

Astrapi® Brochure. Learn more about Astrapi and spiral-based signal modulation with this one-page brochure. Click to download
 
Instantaneous Spectral Analysis (ISA). Astrapi has introduced a ground-breaking technique for constructing and analyzing signals using sinusoidals with continuously-varying amplitude. Click to download See also this October 2016 ISA presentation by Henry Rodrigues of Inatel. Click to download
 
Astrapi Spiral Polynomial Division Multiplexing: Working Principle. Spiral Polynomial Division Multiplexing (SPDM) represents a significant break-through on how spiral-based modulation can be implemented. SPDM solves synchronization and channel impairment problems such as coherent interference and phase distortion. This two-page brochure introduces the technical basis for this breakthrough. Click to download
 
Astrapi Spiral Polynomial Division Multiplexing: Overview. Spiral Polynomial Division Multiplexing (SPDM) represents a significant break-through on how spiral-based modulation can be implemented. SPDM solves synchronization and channel impairment problems such as coherent interference and phase distortion. This two-page brochure provides an overview of the benefits of this technology. Click to download
 

Astrapi Engineering FAQ. This document provides brief answers to common questions about Astrapi technology for the benefit of communications engineers. Click to download
 

White Papers

 
Technical Introduction to Spiral Modulation. A unified introduction to spiral modulation, including its underlying mathematics and range of applications.
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The Astrapi Technical Value Proposition. Astrapi is the pioneer of spiral-based signal modulation, a generalization of the circle-based signal modulation that is the basis for standard techniques such as Quadrature Amplitude Modulation (QAM) and Phase-Shift Keying (PSK). Spiral-based signal modulation is a wide-open field for innovation. This technical report summarizes the benefits of this new technology and reviews the classical channel capacity literature, showing that the Shannon-Hartley law rests on an implicit assumption of signal periodicity that does not apply to spiral-based signal modulation.
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The Shannon Law for Non-Periodic Channels. Making use of new mathematical tools arising from a generalization of Euler’s formula, this technical report removes the periodic assumption implicit in the derivation of the Shannon-Hartley law and proves that non-periodic spiral-based signal modulation is in principle capable of spectral efficiencies dramatically higher than the Shannon limit.
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Euler’s Formula for Fractional Powers of i. This paper introduces a new generalization of Euler’s formula to describe spirals in the complex plane, rather than the circles which arise from the classical Euler’s formula. The paper defines an infinite family of new functions that contains and combines the traditional exponential and sinusoidal functions, and describes their geometric, analytic, and algebraic properties. It is shown that any Taylor polynomial can be easily decomposed into this new class of functions. While focused purely on mathematical topics, this paper later became the theoretical basis for Astrapi’s non-periodic spiral-based signal modulation. Click to download