Non-parametric linear time-invariant system identification by discrete wavelet transforms

Wing Pong Robert Luk, R. I. Damper

Research output: Journal article publicationJournal articleAcademic researchpeer-review

18 Citations (Scopus)


We describe the use of the discrete wavelet transform (DWT) for non-parametric linear time-invariant system identification. Identification is achieved by using a test excitation to the system under test (SUT) that also acts as the analyzing function for the DWT of the SUT's output, so as to recover the impulse response. The method uses as excitation any signal that gives an orthogonal inner product in the DWT at some step size (that cannot be 1). We favor wavelet scaling coefficients as excitations, with a step size of 2. However, the system impulse or frequency response can then only be estimated at half the available number of points of the sampled output sequence, introducing a multirate problem that means we have to 'oversample' the SUT output. The method has several advantages over existing techniques, e.g., it uses a simple, easy to generate excitation, and avoids the singularity problems and the (unbounded) accumulation of round-off errors that can occur with standard techniques. In extensive simulations, identification of a variety of finite and infinite impulse response systems is shown to be considerably better than with conventional system identification methods.
Original languageEnglish
Pages (from-to)303-319
Number of pages17
JournalDigital Signal Processing: A Review Journal
Issue number3
Publication statusPublished - 1 May 2006


  • Discrete wavelet transform
  • Linear-time invariant systems
  • System identification

ASJC Scopus subject areas

  • Signal Processing
  • Electrical and Electronic Engineering


Dive into the research topics of 'Non-parametric linear time-invariant system identification by discrete wavelet transforms'. Together they form a unique fingerprint.

Cite this