An efficient method to derive explicit KLT kernel for first-order autoregressive discrete process

Mustafa U. Torun, Ali N. Akansu

Research output: Contribution to journalArticlepeer-review

18 Scopus citations


Signal dependent Karhunen-Loève transform (KLT), also called factor analysis or principal component analysis (PCA), has been of great interest in applied mathematics and various engineering disciplines due to optimal performance. However, implementation of KLT has always been the main concern. Therefore, fixed transforms like discrete Fourier (DFT) and discrete cosine (DCT) with efficient algorithms have been successfully used as good approximations to KLT for popular applications spanning from source coding to digital communications. In this paper, we propose a simple method to derive explicit KLT kernel, or to perform PCA, in closed-form for first-order autoregressive, AR (1), discrete process. It is a widely used approximation to many real world signals. The merit of the proposed technique is shown. The novel method introduced in this paper is expected to make real-time and data-intensive applications of KLT, and PCA, more feasible.

Original languageEnglish (US)
Article number6522187
Pages (from-to)3944-3953
Number of pages10
JournalIEEE Transactions on Signal Processing
Issue number15
StatePublished - 2013

All Science Journal Classification (ASJC) codes

  • Signal Processing
  • Electrical and Electronic Engineering


  • Covariance analysis
  • eigenanalysis
  • explicit Karhunen-Loève transform (KLT) kernel
  • factor analysis
  • first-order autoregressive process
  • principal component analysis (PCA)
  • signal dependent transform


Dive into the research topics of 'An efficient method to derive explicit KLT kernel for first-order autoregressive discrete process'. Together they form a unique fingerprint.

Cite this