### Abstract

The relationship between the periodicity of a two-dimensional sequence and its energy state diagram is investigated. Some examples are given which illustrate that if the initial conditions are not finite then the trajectory of the energy state diagram does not necessarily terminate on a closed curve, and conversely if the trajectory terminates on a closed curve then the sequence is not necessarily periodic. It is proven that if a two-dimensional sequence is periodic and finite initial conditions are used, then the trajectory of its energy state diagram terminates on a closed curve consisting of a finite number of points.

Original language | English (US) |
---|---|

Title of host publication | Proceedings - IEEE International Symposium on Circuits and Systems |

Publisher | Publ by IEEE |

Pages | 2998-3001 |

Number of pages | 4 |

Volume | 4 |

State | Published - 1990 |

Externally published | Yes |

Event | 1990 IEEE International Symposium on Circuits and Systems Part 4 (of 4) - New Orleans, LA, USA Duration: May 1 1990 → May 3 1990 |

### Other

Other | 1990 IEEE International Symposium on Circuits and Systems Part 4 (of 4) |
---|---|

City | New Orleans, LA, USA |

Period | 5/1/90 → 5/3/90 |

### Fingerprint

### ASJC Scopus subject areas

- Electrical and Electronic Engineering
- Electronic, Optical and Magnetic Materials

### Cite this

*Proceedings - IEEE International Symposium on Circuits and Systems*(Vol. 4, pp. 2998-3001). Publ by IEEE.

**Periodic and nonperiodic modes in two-dimensional digital filters.** / Bose, Tamal; Sarvate, Dinesh.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution

*Proceedings - IEEE International Symposium on Circuits and Systems.*vol. 4, Publ by IEEE, pp. 2998-3001, 1990 IEEE International Symposium on Circuits and Systems Part 4 (of 4), New Orleans, LA, USA, 5/1/90.

}

TY - GEN

T1 - Periodic and nonperiodic modes in two-dimensional digital filters

AU - Bose, Tamal

AU - Sarvate, Dinesh

PY - 1990

Y1 - 1990

N2 - The relationship between the periodicity of a two-dimensional sequence and its energy state diagram is investigated. Some examples are given which illustrate that if the initial conditions are not finite then the trajectory of the energy state diagram does not necessarily terminate on a closed curve, and conversely if the trajectory terminates on a closed curve then the sequence is not necessarily periodic. It is proven that if a two-dimensional sequence is periodic and finite initial conditions are used, then the trajectory of its energy state diagram terminates on a closed curve consisting of a finite number of points.

AB - The relationship between the periodicity of a two-dimensional sequence and its energy state diagram is investigated. Some examples are given which illustrate that if the initial conditions are not finite then the trajectory of the energy state diagram does not necessarily terminate on a closed curve, and conversely if the trajectory terminates on a closed curve then the sequence is not necessarily periodic. It is proven that if a two-dimensional sequence is periodic and finite initial conditions are used, then the trajectory of its energy state diagram terminates on a closed curve consisting of a finite number of points.

UR - http://www.scopus.com/inward/record.url?scp=0025628832&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=0025628832&partnerID=8YFLogxK

M3 - Conference contribution

AN - SCOPUS:0025628832

VL - 4

SP - 2998

EP - 3001

BT - Proceedings - IEEE International Symposium on Circuits and Systems

PB - Publ by IEEE

ER -