Abstract
Wavelet/wavelet packet decomposition has become a very useful tool in describing nonstationary processes. Important examples of nonstationary processes encountered in practice are cyclostationary processes or almost-cyclostationary processes. In this paper, we study the statistical properties of the wavelet packet decomposition of a large class of nonstationary processes, including in particular cyclostationary and almost-cyclostationary processes. We first investigate in a general framework, the existence and some properties of the cumulants of wavelet packet coefficients. We then study more precisely the almost-cyclostationary case, and determine the asymptotic distributions of wavelet packet coefficients. Finally, we particularize some of our results in the cyclostationary case before providing some illustrative simulations.
Highlights
Nonstationary processes have recently received an increasing attention in the signal processing community, due to their wide applicability in modeling natural phenomena generated by physical systems with time-varying parameters
Cyclostationary and almost-cyclostationary processes are very useful for modeling many real signals which appear in communication, telemetry, radar, sonar, and economics [4]
We are interested in higher-order statistics of the wavelet coefficients of nonstationary processes, and especially cyclostationary/almost-cyclostationary processes
Summary
Nonstationary processes have recently received an increasing attention in the signal processing community, due to their wide applicability in modeling natural phenomena generated by physical systems with time-varying parameters. X(tn + u)) depend in general on the lag u When these functions in u are uniformly almost periodic (UAP) [1], we say that the process is nth-order almost-cyclostationary. This means that the cumulants have generalized Fourier series s∈Ω Ans (t)e 2πηsu, with Ω countable [2, 3] and. The nth-order translated cumulants may be assumed to have (n − 1)th-order finite energy, that is, to belong to L2(Rn−1)
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