Isaac Scientific Publishing

Frontiers in Signal Processing

The Extended Golden Section and Time Series Analysis

Download PDF (727.2 KB) PP. 67 - 80 Pub. Date: October 10, 2017

DOI: 10.22606/fsp.2017.12003

Author(s)

  • Sarkis Agaian*
    Department of Electrical Engineering, Stanford University, Stanford, United States
  • John T. Gill III
    Department of Electrical Engineering, Stanford University, Stanford, United States

Abstract

The Golden ratio has played an important role in musical composition, architecture, visual art, science, and increasingly in signal processing [1,2,3]. Underlying many of these applications are several extensions of the golden proportions including the Golden p-Section by Stakhov, the generalized Golden section by Bradley, and others [4,5]. In this paper we review and introduce generalizations of the Golden ratio. We show that there exists a fundamental connection between the limit of two consecutive terms of recursive sequences, the generalized (p, q)-Golden ratio and the Golden ratio generated by the characteristic equation. We apply these generalizations to forecasting financial time series to illustrate one of their applications in signal processing.

Keywords

Golden Ratio, Euclid, Fibonacci, Aesthetic Ratio, Time Series, Signal Processing

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