Inversion of linear periodically time-varying digital filters

Kazlauskas, Kazys

doi:10.1109/82.281852

Cited by 16 publications

(12 citation statements)

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“…We note that the leading zero entries in the row vectors given in (13) result from the fact that filter (1) is FIR with order M; the tailing zero entries are due to the causality of filter (1). In terms of block input u n in (8), it can be checked that the vector U in (14), for each 0 m N 2 1, is equal to…”

Section: Matrix Impulse Response Of Fir Periodic Filtersmentioning

confidence: 99%

“…The inverse, or approximate inverse, of a periodic filter is used for recovering scrambled signals [7] and for equalisation of periodically modulated communication channels [12]. Inversion of periodic filters has been discussed by Kazlauskas [13], Lin and King [14] and Vetterli [15] for the noiseless case and by Wu and Lin [16], Wang et al [17] and Zhou et al [18] when measurement noise is present. There are many different descriptions of single-input single-output (SISO) linear periodic digital filters [2,19,20], either in the time domain via periodic state equation and periodic difference equation or in the frequency domain using the poly-phase model.…”

Section: Introductionmentioning

confidence: 99%

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Optimal finite impulse response approximate inverse of linear periodic filters

Lin

2006

IEE Proc., Vis. Image Process.

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A method to construct an optimal finite impulse response (FIR) approximate inverse for discrete-time causal FIR periodic filters in the presence of measurement noise is proposed. The objective function to be minimised is the sum-of-mean-square errors over one period. On the basis of the matrix impulse response of the multi-input multi-output time-invariant representation of periodic filters, the optimisation problem is formulated as one that minimises the summed equation errors of a set of over-determined linear equations. It is shown that the problem is equivalent to a set of least-squares problems from which a simple, closed-form solution is obtained. Numerical examples are used to illustrate the performance of the proposed FIR approximate inverse.

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Section: Matrix Impulse Response Of Fir Periodic Filtersmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

Optimal finite impulse response approximate inverse of linear periodic filters

Lin

2006

IEE Proc., Vis. Image Process.

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“…The inverse LPTV system is also well studied, e.g. [3]- [10]. Theoretically, the inverse LPTV system can perfectly reconstruct the input sequence.…”

Section: Introductionmentioning

confidence: 99%

Error modeling and reduction of inverse LPTV systems

Chen

Zhang

2011

2011 6th IEEE Conference on Industrial Electronics and Applications

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In this paper, we study the system error of an inverse LPTV system, which is the difference between the reconstructed input sequence and the actual input sequence. The inverse LPTV system is computed by outer-inner factorization approach, and is realized mixed causal-anticausally. It is shown that the system error is exponential stable and can be modeled. By appending a number of zeros before and after the actual input sequence, a number of redundant system errors are introduced. The actual system error can be reduced by discarding the redundant errors.

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“…The inverse of a standard linear time-invariant (LTI) system can be easily achieved by inverting the corresponding transfer function. The procedure for inverting a linear time-varying (LTV) system is much more complex and has attracted considerable attentions, see for example, [3], [4], [5], [6], [7]. The anti-causal inverse in multi-rate filter banks and its implementation are studied in [8] and [9], where a state space representation is employed to induce the anti-causal inverse.…”

Section: Introductionmentioning

confidence: 99%