### Abstract

Time-frequency distributions (TFDs) are computationally costly to compute. We address this problem by presenting algorithms to reduce the computational load for computing TFDs. Before we can compute the TFDs, however, we first must define a discrete version of the TFD. Defining a discrete TFD (DTFD) is, unfortunately, not a straightforward process - for example, a popular DTFD definition does not satisfy all desirable mathematical properties that are inherent to the continuous TFD. In this paper, we define a new DTFD definition, the DTFDC. This definition is closely related to another DTFD definition which we recently proposed, the DTFD-B. The DTFD-B and DTFD-C satisfy all desirable properties. We provide algorithms for both these definitions and show that the DTFD-C requires only 50% of the computational complexity and memory required to compute the DTFD-B.

Original language | English |
---|---|

Pages (from-to) | 320-329 |

Number of pages | 10 |

Journal | WSEAS Transactions on Signal Processing |

Volume | 4 |

Issue number | 5 |

Publication status | Published - May 2008 |

### Fingerprint

### Keywords

- Algorithms
- Computational load
- Discrete time-frequency distributions (DTFD)
- Discrete Wigner-Ville distributions (DWVD)
- Discrete-time signal processing (DSP)
- Fast Fourier transforms (FFTs)
- Time-frequency signal analysis

### ASJC Scopus subject areas

- Software
- Signal Processing
- Computer Vision and Pattern Recognition
- Computer Networks and Communications

### Cite this

*WSEAS Transactions on Signal Processing*,

*4*(5), 320-329.

**Algorithms for discrete quadratic time-frequency distributions.** / O'Toole, John M.; Mesbah, Mostefa; Boashash, Boualem.

Research output: Contribution to journal › Article

*WSEAS Transactions on Signal Processing*, vol. 4, no. 5, pp. 320-329.

}

TY - JOUR

T1 - Algorithms for discrete quadratic time-frequency distributions

AU - O'Toole, John M.

AU - Mesbah, Mostefa

AU - Boashash, Boualem

PY - 2008/5

Y1 - 2008/5

N2 - Time-frequency distributions (TFDs) are computationally costly to compute. We address this problem by presenting algorithms to reduce the computational load for computing TFDs. Before we can compute the TFDs, however, we first must define a discrete version of the TFD. Defining a discrete TFD (DTFD) is, unfortunately, not a straightforward process - for example, a popular DTFD definition does not satisfy all desirable mathematical properties that are inherent to the continuous TFD. In this paper, we define a new DTFD definition, the DTFDC. This definition is closely related to another DTFD definition which we recently proposed, the DTFD-B. The DTFD-B and DTFD-C satisfy all desirable properties. We provide algorithms for both these definitions and show that the DTFD-C requires only 50% of the computational complexity and memory required to compute the DTFD-B.

AB - Time-frequency distributions (TFDs) are computationally costly to compute. We address this problem by presenting algorithms to reduce the computational load for computing TFDs. Before we can compute the TFDs, however, we first must define a discrete version of the TFD. Defining a discrete TFD (DTFD) is, unfortunately, not a straightforward process - for example, a popular DTFD definition does not satisfy all desirable mathematical properties that are inherent to the continuous TFD. In this paper, we define a new DTFD definition, the DTFDC. This definition is closely related to another DTFD definition which we recently proposed, the DTFD-B. The DTFD-B and DTFD-C satisfy all desirable properties. We provide algorithms for both these definitions and show that the DTFD-C requires only 50% of the computational complexity and memory required to compute the DTFD-B.

KW - Algorithms

KW - Computational load

KW - Discrete time-frequency distributions (DTFD)

KW - Discrete Wigner-Ville distributions (DWVD)

KW - Discrete-time signal processing (DSP)

KW - Fast Fourier transforms (FFTs)

KW - Time-frequency signal analysis

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UR - http://www.scopus.com/inward/citedby.url?scp=48849092001&partnerID=8YFLogxK

M3 - Article

VL - 4

SP - 320

EP - 329

JO - WSEAS Transactions on Signal Processing

JF - WSEAS Transactions on Signal Processing

SN - 1790-5022

IS - 5

ER -