Researches On Fractional Hartley Analysis

Many signals, such as communication signals, some radar signals, seismic waves and sonar, are all nonstationary signals. Because the traditional Hartley analysis is done in either time domain or frequency domain separately, it can't describe the joint time-frequency characteristics of a nonstationary signal, namely it can't tell how the frequencies of the signal evolve over time. However, the characteristics are just the most important and critical properties of the nonstationary signal. Fractional Hartley transform (FRHT) is a kind of improved method of the classic Hartley analysis. It is based on the rotation of coordinate axis in time-frequency plane. It can show the joint time-frequency properties of signals and overcome the limitation of the traditional Hartley analysis.In this dissertation, the definition and the properties of fractional Hartley transform (FRHT) are firstly introduced and the relationship between fractional Hartley transform and Hartley transform (HT) as well as the other fractional transforms are discussed. Based on the fractional Hartley transform, we present a new fractional Hartley analysis method: fractional Hartley series (FRHS) expansion. Moreover, we improve the fractional Hartley series to obtain a modified fractional Hartley series (MFRHS). The MFRHS can be applied to chirp signals with arbitrary central frequency and overcome the defect that the fractional Hartley series is limited to those with central frequency equal to a multiple of a particular value. Then, an algorithm for efficient and accurate computation of the fractional Hartley transform is developed and applied to signal filters to remove interference. Finally, a simplified fractional Hartley transform (SFRHT) is introduced, which has the property of real-input-real-output to deal with real signals.