Linear Periodically Time-varying Filters Research Articles

Relationship between an LPTV system and the equivalent LTI MIMO structure

It is understood how to transform a linear periodically time-varying (LPTV) filter/ difference equation into an equivalent multiple-input/multiple-output (MIMO) structure, or transfer matrix, with linear time-invariant (LTI) elements, but no published method exists for the reverse operation. The paper presents a technique to transform from the LTI MIMO structure to the original single-input/single-output LPTV difference equation and discusses its implications. In addition, it is shown how this new result is then used to represent parallel and cascade connections of LPTV systems as single LPTV filters, implement order reduction of an LPTV difference equation, and finally obtain an LPTV difference equation representation that is equivalent to an LPTV state-space structure.

Representations of linear periodically time-varying and multirate systems

The linear switched time-varying (LSTV), polyphase (blocked), and alias-component representations of linear periodically time-varying (LPTV) systems are studied. In particular, alias-components are related to the time-shifted versions of the system. It is shown that in general, a filterbank is equivalent to the cascade connection of two LPTV systems. By generalizing some of the results of the LSTV representation of LPTV systems, it is shown that for relatively coprime integers p and m, a p-channel filterbank that has LPTV filters with period m is equivalent to an mp-channel filterbank with LTI filters. The representation of multirate systems that have LPTV kernels is discussed next. Due to the presence of the upsampler and downsampler, there are some degrees of freedom in the choice of the kernel. This redundancy is dealt with by choosing from various subclasses so that there is a one-to-one relationship between a multirate system and its kernel. Then, we find the LPTV kernel that has the least period.

On the Periodic Realisation of Transfer Matrices

It is understood how to transform a linear periodically time-varying (LPTV) filter/difference equation into an equivalent multiple-inputlmultiple-output (MIMO) structure, or transfer matrix, but no published method exists for the reverse operation. This paper now presents a technique to return from the MIMO structure to the original LPTV difference equation. This new result is then used to 'approximate' a MIMO structure with a single LPTV filter, represent parallel and cascade connections of LPTV systems as single LPTV filters, implement order reduction of a LPTV difference equation, and finally obtain a LPTV difference equation representation that is equivalent to a LPTV state-space structure.

Inversion of linear periodically time-varying digital filters

This paper discusses the inversion of linear periodically time-varying (LPTV) digital filters using the idea of converting the LPTV filter to the block time-invariant filter. Explicit expressions are given to determine the inversion of LPTV filters. Controllability and observability of the inversion of LPTV filters are discussed.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Invertibility of linear periodically time-varying filters

The invertibility of linear periodically time-varying (LPTV) filters is addressed. A necessary and sufficient condition under which a LPTV filter can be inverted is shown using a LPTV postfilter. Such techniques find application, for example, in aliasing cancellation in multirate systems. >