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A LINEAR-PHASE PARAUNITARY FILTER BANK STRUCTURE

IP.com Disclosure Number: IPCOM000006248D
Original Publication Date: 1991-Jul-01
Included in the Prior Art Database: 2001-Dec-18
Document File: 5 page(s) / 252K

Publishing Venue

Motorola

Related People

Cheung Auyeung: AUTHOR [+2]

Abstract

In certain audio and image compression applica- tions, it is necessary to separate the input signal into different frequency components and then encode these components separately. Later, these components may be decoded and recombined to form a reconstruction of the original audio signal or image. Our invention consists of a set of filter bank structures which can be used to separate and recombine these frequency com- ponents efficiently.

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MOTOROLA INC. Technical Developments Volume 13 July 1991

A LINEAR-PHASE PARAUNITARY FILTER BANK STRUCTURE

by Cheung Auyeung and David Nicozisin

1. INTRODUCTION

  In certain audio and image compression applica- tions, it is necessary to separate the input signal into different frequency components and then encode these components separately. Later, these components may be decoded and recombined to form a reconstruction of the original audio signal or image. Our invention consists of a set of filter bank structures which can be used to separate and recombine these frequency com- ponents efficiently.

   As shown in Figure la, one way to separate the signal into M frequency components is to use an anal- ysis fiNer bank which consists of a set of low-pass, band-pass, and high-pass filters. At the output of the analysis filter bank, these components are then down sampled by M to preserve the same total data rate as in the input. Later, these frequency components can be up-sampled by M and recombined by a synrhesis filter bank to reconstruct the original signal. How- ever for perfect reconstruction, the analysis filter bank and the synthesis filter bank must match each other.

  One type of filter bank which can result in perfect reconstruction is the paraunitary quadrature mirror filter bank [l]. A paraunitry quadrature mirror filter bank as represented in Figure la is defined by its equivalent pofyphase representation in Figure lb. The polyphase representation is parameterized by two matrix polynomials,

N-l

EN(L) = 1 Ait-' ial

and

N-l

RN(Z) = c &,-i,

id

withMxMconstant matrices A, B, i = O,...,N- 1. In order for the filter bank to be paraunitary, the matrix polynomial E,(r) must satisfy

EN(L = 1,

where'

gN(z) Gf N2 Afz' . idI

Furthermore,

RN(z) = I-r,??f.,(Z)

for some integer r.

1.1 THE INVENTION

  The invention consists of two parts. The first is a parameteric representation which uniquely parameter- izes all pamunitary mafrices, i.e., the matrix polyno- mial of a paraunitary FIR quadrature mirror filter (QMF) bank. The second part is a set of signal flow graphs which can be used to implement all &tear- phase FIR paraunitary QMF banks with the number of channels even and with one half of the channel hav- ing symmetric impulse responses and the other half antisymmetric impulse responses.

Ad+ mm B.oL symhu. Filler E4"k

Figure la: The analysis and synthesis titter bank,

 JM z-1 IM z-1

a

 Ih( km i i z-1 IM

Ma~mrrnmk SjmlhDn mr, Bank

Figure lb: The polyphase representation of the analysis and synthesis filter bank.

'The symbol t denotes the conjugate transposition

of a vector

or a matrix.

0 Motorola. MC. 1991 161

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MOTOROLA INC. Technical Developments Volume 13 July 1991

1.1.1 A UNIQUE PARAMETERIC REPRESEN- TATION OF PARAUNITARY QMF BANK

  Vaidyanathan[2] has found a representation for all paraunitary matrices as a product of order-one parau- nitary matrices and a unitary matri...