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

Aach, Til; Führ, Hartmut

doi:10.1109/tsp.2012.2205683

Cited by 6 publications

(1 citation statement)

References 16 publications

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“…1) can be represented by a kernel g (m, r) satisfying the condition g (m, r)= g (m + P, r + P ) ∀m, r [25]. The output of such a system is y [m] = r∈Z g [m, r] x [r] [25], [31]. Let M P ×P be the space of P × P matrices.…”

Section: Methodsmentioning

confidence: 99%

Measures for the Degree of Time Variance: Application to Filter Banks

et al. 2022

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Quantifying a system's time-invariance deviation may reveal how it represents and processes the signals. The main objective of this paper is to quantify the departure of a time-varying system from being time-invariant. In particular, the paper quantifies the time variance of filter banks using kernel representation. We define the ℓ 2 measure for the degree of time variance (MDTV ℓ2 ) based on the discrete-time domain form of the kernel representation and the ℓ ∞ measure (MDTV ℓ∞ ) based on the matrix representation of the LPTV kernel. We show that off-diagonal matrix elements can be used to deduce the time-varying behavior of an LPTV system, proving that time-invariant and time-varying components can be separated. The matrix form of the LTI system, which is closest to an LPTV system, has been derived. This research offers a new kernel-based definition for time variance for any time-varying system and provides explicit expressions for MDTV for three distinct scenarios, namely, a single channel (SC), a uniform filter bank (UFB), and a nonuniform filter bank (NUFB). For each scenario, we determine the LPTV kernel and impulse response of the nearest LTI system to plot the MDTV versus decimation factor. Also, MDTV generated by an SC and a UFB with identical low pass filters in each channel is identical. We also observe that two-channel perfect reconstruction (PR) filter banks result in zero MDTV. Finally, we have compared the proposed approach with earlier work and demonstrated its better efficiency in terms of computational complexity.INDEX TERMS Linear periodically time-varying system, measure for degree of time variance, multirate filter bank, non-uniform filter bank, single channel, uniform filter bank.

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Section: Methodsmentioning

confidence: 99%