Quasicyclic Principal Component Analysis

TL;DR

This paper introduces quasicyclic PCA (QPCA), a novel method for analyzing cyclostationary data by exploiting cyclic structures, formulated as an optimization problem and demonstrated through signal processing applications.

Contribution

QPCA extends PCA to handle cyclostationary data by incorporating shift-orthogonal vectors, with an explicit algorithm and analysis for efficient computation.

Findings

Effective in recovering carrier pulses from cyclostationary signals

Provides methods for estimating unknown oversampling rates

Improves data preprocessing for non-integer oversampling in QPCA

Abstract

We present quasicyclic principal component analysis (QPCA), a generalization of principal component analysis (PCA), that determines an optimized basis for a dataset in terms of families of shift-orthogonal principal vectors. This is of particular interest when analyzing cyclostationary data, whose cyclic structure is not exploited by the standard PCA algorithm. We first formulate QPCA as an optimization problem, which we show may be decomposed into a series of PCA problems in the frequency domain. We then formalize our solution as an explicit algorithm and analyze its computational complexity. Finally, we provide some examples of applications of QPCA to cyclostationary signal processing data, including an investigation of carrier pulse recovery, a presentation of methods for estimating an unknown oversampling rate, and a discussion of an appropriate approach for pre-processing data with a non-integer oversampling rate in order to better apply the QPCA algorithm.