Time-varying filters and filter banks: Some basic principles
Time-varying filters and filter banks: Some basic principles
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DOI：
10.1109/78.553472
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发表时间：
1996-12-01
影响因子：
5.4
通讯作者：
Vaidyanathan, PP
中科院分区：
文献类型：
--
作者：
Phoong, SM;Vaidyanathan, PP
本文研究了时变滤波器组的基本原理，用多相方法研究了时变滤波器组，得到了一些常规线性时变滤波器组所没有的特殊性质。例如，我们可以证明，对于完全重构的时变滤波器组，分析组的无损并不总是意味着合成组的无损，并且用整数L的z(-L)代替无损线性时变系统的延迟z(-1)通常会得到一个无损系统，而且，此外，我们将证明我们可以通过刻画多输入多输出(MIMO)LTV系统来刻画所有TVFB的特征。我们将详细讨论LTV系统的一个有用的子类，即无损系统，所有无损LTV系统都是可逆的，而且，如果原始无损系统是FIR，则逆是有限脉冲响应(FIR)。然而，与LTI系统不同的是，给出了逆的显式构造我们将证明逆系统不一定是唯一的或可逆的，事实上，无损LTV系统的逆也不一定是无损的，根据其逆的可逆性，无损系统可分为两组：i)可逆逆无损(i]a)系统和ii)不可逆逆无损(NIL)系统，我们将证明nIL逆TVFB只产生具有单位框界的离散时间紧框架，然而如果PR FB是IIL，我们将有L(2)的正交基。在另一篇文章中，这些结果中的一些结果被用来导出无损TVFB的更深层次的性质，包括因式分解定理。
In this paper, we study the fundamentals of time-varying filter banks (TVFB), Using a polyphase approach to TVFB's, we are able to show some unusual properties that are not exhibited by the conventional LTI filter banks, For example, we can show that for a perfect reconstruction (PR) TVFB, the losslessness of analysis bank does not always imply that of the synthesis bank, and replacing the delay z(-1) in an implementation of a lossless linear time-variant (LTV) system with z(-L) for integer L in general will result in a nonlossless system, Moreover, we show that interchanging the analysis and synthesis filters of a PR TVFB will usually destroy the PR property, and a PR TVFB in general will not generate a discrete-time basis for l(2).Furthermore, we will show that we can characterize all TVFB's by characterizing multi-input multi-output (MIMO) LTV systems, A useful subclass of LTV systems, namely the lossless systems, will be discussed in detail, All lossless LTV systems are invertible, Moreover, the inverse is finite impulse response (FIR) if the original lossless system is FIR, Explicit construction of the inverses is given, However, unlike in the LTI case, we will show that the inverse system is not necessarily unique or invertible, In fact, the inverse of a lossless LTV system is not necessarily lossless, Depending on the invertibility of their inverses, the lossless systems are divided into two groups: i) invertible inverse lossless (I]a) systems and ii) noninvertible inverse lossless (NIL) systems, We will show that an NIL PR TVFB will only generate a discrete-time tight frame with unity frame bound, However if the PR FB is IIL, we will have an orthonormal basis for l(2). In a companion paper, some of these results are used to derive deeper properties of lossless TVFB including factorization theorems.