## Abstract

We propose new time-frequency (TF) symbols as the narrowband Weyl symbol (WS) smoothed by an appropriate kernel. These new symbols preserve time and frequency shifts on a random process. Choosing specific smoothing kernels, we can obtain various new symbols (e.g. Levin symbol and Page symbol). We link a quadratic form of the signal to the new symbols and Cohen's class of quadratic time-frequency representations, and we derive a simple kernel constraint for unitary symbols. We also propose an affine class of symbols in terms of the wideband Weyl symbol (P
_{0}WS). These symbols preserve scale changes and time shifts. Furthermore, we generalize the smoothed versions of the WS and P
_{0}WS to analyze random processes undergoing generalized frequency shifts or generalized time shifts.

Original language | English (US) |
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Title of host publication | ICASSP, IEEE International Conference on Acoustics, Speech and Signal Processing - Proceedings |

Publisher | IEEE |

Pages | 1345-1348 |

Number of pages | 4 |

Volume | 3 |

State | Published - 1999 |

Externally published | Yes |

Event | Proceedings of the 1999 IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP-99) - Phoenix, AZ, USA Duration: Mar 15 1999 → Mar 19 1999 |

### Other

Other | Proceedings of the 1999 IEEE International Conference on Acoustics, Speech, and Signal Processing (ICASSP-99) |
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City | Phoenix, AZ, USA |

Period | 3/15/99 → 3/19/99 |

## ASJC Scopus subject areas

- Signal Processing
- Electrical and Electronic Engineering
- Acoustics and Ultrasonics