Generalization and Applications of Linear Chirp Stationary Processes

• Activity Number: 54
• Type: Topic Contributed
• Date/Time: Sunday, July 29, 2007 : 4:00 PM to 5:50 PM
• Sponsor: Section on Physical and Engineering Sciences
• Author(s): Stephen Robertson*+
• Companies: Southern Methodist University
• Keywords: G-Stationary Processes (GSP) ; Linear Chirp Stationary Processes (LCSP)

Abstract

Time deformation has been proposed as an alternate method to window-based approaches when analyzing time series data with time-varying frequency. Specifically, "G-Stationary Processes" (GSP) are processes which are transformed to a stationary process after a transformation of the time scale, thereby allowing use of standard approaches for analyzing stationary data. A special case of a GSP is the Linear Chirp Stationary Process (Liu, Gray, Woodward, 2004), which is a non-stationary process whose frequency changes approximately linearly in time. We generalize previous assumptions to allow analysis of LCSP for a wider range of applications. The LCSP can be classified into "generalized" and "LC(p,q)" chirp processes. We show that the relationship between generalized and LC(p,q) chirp processes is analogous to that of harmonic and ARMA models. Results are applied to simulated and actual data.