Analysis of 2-D state-space periodically shift-variant discrete systems

Sreeraman Rajan, Kyung Sub Joo, Tamal Bose

Research output: Contribution to journalArticle

9 Citations (Scopus)

Abstract

Two-dimensional (2-D) periodically shift-variant (PSV) digital filters are considered. These filters have applications in processing video signals with cyclostationary noise, scrambling digital images, and 2-D multirate signal processing. The filters are formulated in the form of a Givone-Roesser (GR) state-space model with periodic coefficients. This PSV model is then presented in block form as a shift-invariant system that also has the same GR state-space form. This block form has reduced computations and ease of analysis. An algorithm is developed that transforms any given 2-D PSV GR system to its equivalent shift-invariant model. Invertibility of this model is an important consideration, especially in image scrambling applications. A condition is established for the invertibility of the shift-invariant model of the 2-D PSV system. Also, the inverse system can be easily computed from the original. The established results are illustrated with an example.

Original languageEnglish (US)
Pages (from-to)395-413
Number of pages19
JournalCircuits, Systems, and Signal Processing
Volume15
Issue number3
StatePublished - 1996
Externally publishedYes

Fingerprint

Discrete Systems
State Space
Invertibility
Invariant
Filter
Inverse System
Video Processing
Video signal processing
Digital Filter
Periodic Coefficients
Space Form
State-space Model
Digital Image
Model
Signal Processing
Digital filters
Transform
Signal processing
Form

ASJC Scopus subject areas

  • Signal Processing
  • Electrical and Electronic Engineering

Cite this

Analysis of 2-D state-space periodically shift-variant discrete systems. / Rajan, Sreeraman; Joo, Kyung Sub; Bose, Tamal.

In: Circuits, Systems, and Signal Processing, Vol. 15, No. 3, 1996, p. 395-413.

Research output: Contribution to journalArticle

@article{99fba2981686497388d568fec8bbefb1,
title = "Analysis of 2-D state-space periodically shift-variant discrete systems",
abstract = "Two-dimensional (2-D) periodically shift-variant (PSV) digital filters are considered. These filters have applications in processing video signals with cyclostationary noise, scrambling digital images, and 2-D multirate signal processing. The filters are formulated in the form of a Givone-Roesser (GR) state-space model with periodic coefficients. This PSV model is then presented in block form as a shift-invariant system that also has the same GR state-space form. This block form has reduced computations and ease of analysis. An algorithm is developed that transforms any given 2-D PSV GR system to its equivalent shift-invariant model. Invertibility of this model is an important consideration, especially in image scrambling applications. A condition is established for the invertibility of the shift-invariant model of the 2-D PSV system. Also, the inverse system can be easily computed from the original. The established results are illustrated with an example.",
author = "Sreeraman Rajan and Joo, {Kyung Sub} and Tamal Bose",
year = "1996",
language = "English (US)",
volume = "15",
pages = "395--413",
journal = "Circuits, Systems, and Signal Processing",
issn = "0278-081X",
publisher = "Birkhause Boston",
number = "3",

}

TY - JOUR

T1 - Analysis of 2-D state-space periodically shift-variant discrete systems

AU - Rajan, Sreeraman

AU - Joo, Kyung Sub

AU - Bose, Tamal

PY - 1996

Y1 - 1996

N2 - Two-dimensional (2-D) periodically shift-variant (PSV) digital filters are considered. These filters have applications in processing video signals with cyclostationary noise, scrambling digital images, and 2-D multirate signal processing. The filters are formulated in the form of a Givone-Roesser (GR) state-space model with periodic coefficients. This PSV model is then presented in block form as a shift-invariant system that also has the same GR state-space form. This block form has reduced computations and ease of analysis. An algorithm is developed that transforms any given 2-D PSV GR system to its equivalent shift-invariant model. Invertibility of this model is an important consideration, especially in image scrambling applications. A condition is established for the invertibility of the shift-invariant model of the 2-D PSV system. Also, the inverse system can be easily computed from the original. The established results are illustrated with an example.

AB - Two-dimensional (2-D) periodically shift-variant (PSV) digital filters are considered. These filters have applications in processing video signals with cyclostationary noise, scrambling digital images, and 2-D multirate signal processing. The filters are formulated in the form of a Givone-Roesser (GR) state-space model with periodic coefficients. This PSV model is then presented in block form as a shift-invariant system that also has the same GR state-space form. This block form has reduced computations and ease of analysis. An algorithm is developed that transforms any given 2-D PSV GR system to its equivalent shift-invariant model. Invertibility of this model is an important consideration, especially in image scrambling applications. A condition is established for the invertibility of the shift-invariant model of the 2-D PSV system. Also, the inverse system can be easily computed from the original. The established results are illustrated with an example.

UR - http://www.scopus.com/inward/record.url?scp=0029700147&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0029700147&partnerID=8YFLogxK

M3 - Article

VL - 15

SP - 395

EP - 413

JO - Circuits, Systems, and Signal Processing

JF - Circuits, Systems, and Signal Processing

SN - 0278-081X

IS - 3

ER -