### Abstract

Abstract-A matched filter is the optimal linear filter for
maximizing the signal to noise ratio (SNR) in the presence of additive noise. Matched filters are commonly used in radar systems where the transmitted signal is known and may be used as a replica to be correlated with the received signal which can be carried out by multiplication in the frequency domain by applying Fourier Transform (FT). Fractional Fourier transform (FrFT) is the general case for the FT and is superior in chirp pulse compression using the optimum FrFT order. In this paper a matched filter is implemented for a chirp radar signal in the optimum FrFT domain. Mathematical formula for a received chirp signal in the frequency domain and a generalized formula in the fractional Fourier domain are presented in this paper using the Principle of Stationary Phase (PSP). These mathematical expressions are used to show the limitations of the matched filter in the fractional Fourier domain. The parameters that affect the chirp signal in the optimum fractional Fourier domain are described. The performance enhancement by using the matched filter in the fractional Fourier domain for special cases is presented.

Original language | English |
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Number of pages | 5 |

Publication status | Published - 29 Sep 2010 |

Event | Sensor Signal Processing for Defence 2010 (SSPD 2010) - London, UK Duration: 29 Sep 2010 → 30 Sep 2010 |

### Conference

Conference | Sensor Signal Processing for Defence 2010 (SSPD 2010) |
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City | London, UK |

Period | 29/09/10 → 30/09/10 |

### Keywords

- radar
- radar matched filtering
- fractional fourier transform
- fourier transform

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## Cite this

Elgamel, S. A. E. H., Clemente, C., & Soraghan, J. J. (2010).

*Radar matched filtering using the fractional fourier transform*. Paper presented at Sensor Signal Processing for Defence 2010 (SSPD 2010), London, UK, .