Stability of the quantized LMS algorithm

Tamal Bose, David A. Trautman

Research output: Contribution to journalArticlepeer-review


The least mean square (LMS) algorithm is investigated for stability when implemented with two's complement quantization. The study is restricted to algorithms with periodically varying inputs. Such inputs are common in a variety of applications, and for system identification, they can always be generated as shown with an example. It is shown that the quantized LMS algorithm is just a special case of a quantized periodically shift-varying (PSV) filter. Two different sufficient conditions are obtained for the bounded input bounded output (BIBO) stability of the PSV filter. When the filter is BIBO stable, two different bounds on the filter output are also derived. These conditions and bounds are then applied to the quantized LMS algorithm. The results are illustrated with examples.

Original languageEnglish (US)
Pages (from-to)587-602
Number of pages16
JournalCircuits, Systems, and Signal Processing
Issue number5
StatePublished - Sep 1995

ASJC Scopus subject areas

  • Signal Processing
  • Applied Mathematics


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