Unitary PUMA Algorithm for Estimating the Frequency of a Complex Sinusoid

Cheng Qian, Lei Huang, Hing Cheung So, Nicholas D. Sidiropoulos, Junhao Xie

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24 Scopus citations


One-dimensional (1-D) and two-dimensional (2-D) frequency estimation for a single complex sinusoid in white Gaussian noise is a classic signal processing problem with numerous applications. It is revisited here through a new unitary principal-singular-vector utilization modal analysis (PUMA) approach, which is realized in terms of real-valued computations. The 2-D unitary PUMA is first formulated as an iteratively weighted least squares optimization problem. Recognizing that only one iteration is sufficient when 2-D unitary PUMA is initialized using least squares, a computationally attractive closed-form solution is then obtained. A variant of 2-D unitary PUMA is also developed for the 1-D case. Due to the real-valued computations and closed-form expression for the frequency estimate, the unitary PUMA is more computationally efficient than a number of state-of-The-Art methods. Furthermore, the asymptotic variances of 1-D and 2-D unitary PUMA estimators are theoretically derived, and numerical results are included to demonstrate the effectiveness of the proposed methods.

Original languageEnglish (US)
Article number7152983
Pages (from-to)5358-5368
Number of pages11
JournalIEEE Transactions on Signal Processing
Issue number20
StatePublished - Oct 15 2015

Bibliographical note

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  • Complex sinusoid
  • frequency estimation
  • subspace method
  • weighted least squares


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