### 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) |
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Pages (from-to) | 2998-3001 |

Number of pages | 4 |

Journal | Proceedings - IEEE International Symposium on Circuits and Systems |

Volume | 4 |

State | Published - Dec 1 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 |

### ASJC Scopus subject areas

- Electrical and Electronic Engineering

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## Cite this

Bose, T., & Sarvate, D. (1990). Periodic and nonperiodic modes in two-dimensional digital filters.

*Proceedings - IEEE International Symposium on Circuits and Systems*,*4*, 2998-3001.