Paraunitary Matrices
نویسندگان
چکیده
Design methods for paraunitary matrices from complete orthogonal sets of idempotents and related matrix structures are presented. These include techniques for designing non-separable multidimensional paraunitary matrices. Properties of the structures are obtained and proofs given. Paraunitary matrices play a central role in signal processing, in particular in the areas of filterbanks and wavelets.
منابع مشابه
On orthonormal wavelets and paraunitary filter banks
Binary tree-structured filter banks have been employed in the past to generate wavelet bases. While the relation between paraunitary filter banks and orthonormal bases is known to some extent, there are some extensions which are either not known, or not published so far. In particular it is known that a binary tree-structured filter bank with the same paraunitary polyphase matrix on all levels ...
متن کاملA Design of Paraunitary Polyphase Matrices of Rational Filter Banks Based on (P,Q) Shift-Invariant Systems
In this paper we present a method to design paraunitary polyphase matrices of critically sampled rational filter banks. The method is based on (P,Q) shift-invariant systems, and so any kind of rational splitting of the frequency spectrum can be achieved using this method. Ideal (P,Q) shift-invariant system with smallest P and Q that map of a band of input spectrum to the output spectrum are obt...
متن کاملCyclic LTI systems and the paraunitary interpolation problem
Cyclic signal processing refers to situations where all the time indices are interpreted modulo some integer L. Since the frequency domain is a uniform discrete grid, there is more freedom in theoretical and design aspects. The basics of cyclic(L) multirate systems and filter banks have already appeared in the literature, and important differences between the cyclic and noncyclic cases are know...
متن کاملNew Design of Orthogonal Filter Banks Using the Cayley Transform
It is a challenging task to design orthogonal filter banks, especially multidimensional (MD) ones. In the onedimensional (1D) two-channel finite impulse response (FIR) filter bank case, several design methods exist. Among them, designs based on spectral factorizations (by Smith and Barnwell) and designs based on lattice factorizations (by Vaidyanathan and Hoang) are the most effective and widel...
متن کاملOn factorization of M-channel paraunitary filterbanks
We systematically investigate the factorization of causal finite impulse response (FIR) paraunitary filterbanks with given filter length. Based on the singular value decomposition of the coefficient matrices of the polyphase representation, a fundamental order-one factorization form is first proposed for general paraunitary systems. Then, we develop a new structure for the design and implementa...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- CoRR
دوره abs/1205.0703 شماره
صفحات -
تاریخ انتشار 2012