Shift Variance Measures for Multirate LPSV Filter Banks With Random Input Signals

The linear periodically shift variant (LPSV) properties within critically sampled multirate FIR filter banks are generally analysed using deterministic signals. Periodic shift variance is, however, closely related to cyclostationarities introduced by the LPSV system into originally wide sense statio...

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Bibliographic Details
Published in:IEEE transactions on signal processing 2012-10, Vol.60 (10), p.5125-5134
Main Authors: Aach, T., Fuhr, H.
Format: Article
Language:English
Subjects:
Applied sciences
Atmospheric measurements
Banks
Commutator
Covariance
Covariance matrix
covariance operator
Detection, estimation, filtering, equalization, prediction
Educational institutions
Exact sciences and technology
expected shift variance
Filter banks
Fourier transforms
Hilbert space
Hilbert space norm
Hilbert-Schmidt norm
Information, signal and communications theory
linear periodically shift variant systems
multirate filter banks
Operators
Particle measurements
Radio frequency
random signals
Signal and communications theory
Signal, noise
Studies
Telecommunications and information theory
Transaction processing
Upper bounds
Variance
Vices
White noise
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Summary:The linear periodically shift variant (LPSV) properties within critically sampled multirate FIR filter banks are generally analysed using deterministic signals. Periodic shift variance is, however, closely related to cyclostationarities introduced by the LPSV system into originally wide sense stationary (WSS) random signals passing through the system. We provide first a unified framework to measure both shift variance of the LPSV system and the amount of cyclostationarity it generates. In this respect, the key concept is the covariance operator associated to a random variable. Cyclostationarity of the variable translates to LPSV properties of the operators, and vice versa. We study several related concepts for the quantification of shift variance in operators and their interpretation in the stochastic setting. We then introduce a new concept called expected shift variance. Fourier-analytic expressions for the various measures are given, and subsequently used to derive explicit formulae for the case of critically sampled two-channel filter banks, as well as sharp upper bounds for unitary two-channel filter banks. Numerical evaluations of the measures show that they provide largely consistent rankings between various critically sampled two-channel filter banks.
ISSN:1053-587X
1941-0476
DOI:10.1109/TSP.2012.2205683