A general formulation of modulated filter banks

Peter Niels Heller; Tanja Karp; Truong Q. Nguyen

doi:10.1109/78.752597

A general formulation of modulated filter banks

Peter Niels Heller, Tanja Karp, Truong Q. Nguyen

Electrical and Computer Engineering

Research output: Contribution to journal › Article › peer-review

145 Scopus citations

Abstract

This paper presents a general framework for maximally decimated modulated filter banks. The theory covers the known classes of cosine modulation and relates them to complexmodulated filter banks. The prototype filters have arbitrary lengths, and the overall delay of the filter bank is arbitrary, within fundamental limits. Necessary and sufficient conditions for perfect reconstruction (PR) are derived using the polyphase representation. It is shown that these PR conditions are identical for all types of modulation - modulation based on the discrete cosine transform (DCT), both DCT-III/DCT-IV and DCT-I/DCT-II, and modulation based on the modified discrete Fourier transform (MDFT). A quadratic-constrained design method for prototype filters yielding PR with arbitrary length and system delay is derived, and design examples are presented to illustrate the tradeoff between overall system delay and stopband attenuation (subchannelization).

Original language	English
Pages (from-to)	986-1002
Number of pages	17
Journal	IEEE Transactions on Signal Processing
Volume	47
Issue number	4
DOIs	https://doi.org/10.1109/78.752597
State	Published - 1999

Keywords

Cosine-modulated filter bank
DCT
Filter bank
MDCT
Modulated filter bank

Access to Document

10.1109/78.752597

Fingerprint Dive into the research topics of 'A general formulation of modulated filter banks'. Together they form a unique fingerprint.

Cite this

@article{28c2eda226d74d5089a4a138d2f25532,

title = "A general formulation of modulated filter banks",

abstract = "This paper presents a general framework for maximally decimated modulated filter banks. The theory covers the known classes of cosine modulation and relates them to complexmodulated filter banks. The prototype filters have arbitrary lengths, and the overall delay of the filter bank is arbitrary, within fundamental limits. Necessary and sufficient conditions for perfect reconstruction (PR) are derived using the polyphase representation. It is shown that these PR conditions are identical for all types of modulation - modulation based on the discrete cosine transform (DCT), both DCT-III/DCT-IV and DCT-I/DCT-II, and modulation based on the modified discrete Fourier transform (MDFT). A quadratic-constrained design method for prototype filters yielding PR with arbitrary length and system delay is derived, and design examples are presented to illustrate the tradeoff between overall system delay and stopband attenuation (subchannelization).",

keywords = "Cosine-modulated filter bank, DCT, Filter bank, MDCT, Modulated filter bank",

author = "Heller, {Peter Niels} and Tanja Karp and Nguyen, {Truong Q.}",

note = "Funding Information: Manuscript received April 6, 1994; revised April 17, 1997. This work was supported in part by Deutsche Forschungsgemeinschaft under Grant Fli 116/10 and the National Science Foundation under Grant MIP 9501589. The associate editor coordinating the review of this paper and approving it for publication was Prof. Roberto H. Bamberger. P. N. Heller is with Aware Inc., Bedford, MA 01730-1432 USA (e-mail: heller@aware.com). T. Karp is with Mannheim University, Mannheim, Germany (e-mail: karp@rumms.uni-mannheim.de). T. Q. Nguyen is with the Department of Electrical and Computer Engineering, Boston University, Boston, MA 02215 USA (e-mail: nguyent@bu.edu). Publisher Item Identifier S 1053-587X(99)02139-X.",

year = "1999",

doi = "10.1109/78.752597",

language = "English",

volume = "47",

pages = "986--1002",

journal = "IEEE Transactions on Signal Processing",

issn = "1053-587X",

number = "4",

}

TY - JOUR

T1 - A general formulation of modulated filter banks

AU - Heller, Peter Niels

AU - Karp, Tanja

AU - Nguyen, Truong Q.

N1 - Funding Information: Manuscript received April 6, 1994; revised April 17, 1997. This work was supported in part by Deutsche Forschungsgemeinschaft under Grant Fli 116/10 and the National Science Foundation under Grant MIP 9501589. The associate editor coordinating the review of this paper and approving it for publication was Prof. Roberto H. Bamberger. P. N. Heller is with Aware Inc., Bedford, MA 01730-1432 USA (e-mail: heller@aware.com). T. Karp is with Mannheim University, Mannheim, Germany (e-mail: karp@rumms.uni-mannheim.de). T. Q. Nguyen is with the Department of Electrical and Computer Engineering, Boston University, Boston, MA 02215 USA (e-mail: nguyent@bu.edu). Publisher Item Identifier S 1053-587X(99)02139-X.

PY - 1999

Y1 - 1999

N2 - This paper presents a general framework for maximally decimated modulated filter banks. The theory covers the known classes of cosine modulation and relates them to complexmodulated filter banks. The prototype filters have arbitrary lengths, and the overall delay of the filter bank is arbitrary, within fundamental limits. Necessary and sufficient conditions for perfect reconstruction (PR) are derived using the polyphase representation. It is shown that these PR conditions are identical for all types of modulation - modulation based on the discrete cosine transform (DCT), both DCT-III/DCT-IV and DCT-I/DCT-II, and modulation based on the modified discrete Fourier transform (MDFT). A quadratic-constrained design method for prototype filters yielding PR with arbitrary length and system delay is derived, and design examples are presented to illustrate the tradeoff between overall system delay and stopband attenuation (subchannelization).

AB - This paper presents a general framework for maximally decimated modulated filter banks. The theory covers the known classes of cosine modulation and relates them to complexmodulated filter banks. The prototype filters have arbitrary lengths, and the overall delay of the filter bank is arbitrary, within fundamental limits. Necessary and sufficient conditions for perfect reconstruction (PR) are derived using the polyphase representation. It is shown that these PR conditions are identical for all types of modulation - modulation based on the discrete cosine transform (DCT), both DCT-III/DCT-IV and DCT-I/DCT-II, and modulation based on the modified discrete Fourier transform (MDFT). A quadratic-constrained design method for prototype filters yielding PR with arbitrary length and system delay is derived, and design examples are presented to illustrate the tradeoff between overall system delay and stopband attenuation (subchannelization).

KW - Cosine-modulated filter bank

KW - DCT

KW - Filter bank

KW - MDCT

KW - Modulated filter bank

UR - http://www.scopus.com/inward/record.url?scp=0033114974&partnerID=8YFLogxK

U2 - 10.1109/78.752597

DO - 10.1109/78.752597

M3 - Article

AN - SCOPUS:0033114974

VL - 47

SP - 986

EP - 1002

JO - IEEE Transactions on Signal Processing

JF - IEEE Transactions on Signal Processing

SN - 1053-587X

IS - 4

ER -

A general formulation of modulated filter banks

Abstract

Keywords

Access to Document

Other files and links

Cite this