Accession Number:

AD0739671

Title:

A Deterministic Analysis of Limit Cycle Oscillations in Recursive Digital Filters due to Quantization.

Descriptive Note:

Doctoral thesis,

Corporate Author:

NAVAL POSTGRADUATE SCHOOL MONTEREY CALIF

Personal Author(s):

Report Date:

1970-12-01

Pagination or Media Count:

277.0

Abstract:

A deterministic analysis of the limit cycle oscillations which occur in fixed-point implementations of recursive digital filters due to roundoff and truncation quantization after multiplication operations, is performed. Amplitude bounds, based upon a correlated nonstochastic signal approach and Lyapunovs direct method, as well as an approximate expression for the frequency of zero-input limit cycles, are derived and tested for the two-pole filter. The limit cycles are represented on a successive value phase-plane diagram from which certain symmetry properties are derived. Similar results are developed for other second-order digital filter configurations, and the parallel and cascade forms. The results are extended to include limit cycles under input signal conditions. A basic design relationship between the number of significant digits required for the realization of a filter algorithm with a desired signal-to-noise limit cycle ratio is stated.

Subject Categories:

  • Statistics and Probability
  • Cybernetics

Distribution Statement:

APPROVED FOR PUBLIC RELEASE