### 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 language | English (US) |
---|---|

Pages (from-to) | 395-413 |

Number of pages | 19 |

Journal | Circuits, Systems, and Signal Processing |

Volume | 15 |

Issue number | 3 |

State | Published - 1996 |

Externally published | Yes |

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### ASJC Scopus subject areas

- Signal Processing
- Electrical and Electronic Engineering

### Cite this

*Circuits, Systems, and Signal Processing*,

*15*(3), 395-413.

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

Research output: Contribution to journal › Article

*Circuits, Systems, and Signal Processing*, vol. 15, no. 3, pp. 395-413.

}

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 -