The Wigner-Ville distribution: Properties, efficient computation, and application to blosonar signal analysis

Abstract

Use of a spectrogram is the common way to perform time-frequency analysis, but it suffers from inherent trade-off of time resolution versus frequency resolution that does not provide necessary resolution in the time-frequency domain for bat pursuit signals and dolphin signals. The Wigner distribution (WD) appears ideally suited for nonstationary signal analysis. The main limitations of the WD are the interference terms, which are discussed in detail in this paper. A pair of values x(tt), x(tj) at times tt and tj produce interference oscillatory with “frequency” |tj − tt| at the position of (tt + tj)/2. The appropriate time (frequency) window length is the trade-off for the smooth and frequency (time) resolution. An efficient algorithm is proposed. This algorithm employs the fast Fourier transform (FFT) to compute two sequences of smooth pseudo-Wigner distribution; 40% of the number of arithmetic operations are saved. Twenty-one signals emitted by a Chinese Pipistrellus abramus temmink while hunting an insect over a fish pond were recorded. The 2-D time-frequency structures of bat sonar signals for searching, identification, pursuit, and capture are systematically investigated. Using the first-order moment of the WD, the instantaneous frequencies of bat signals are also obtained. As a bat is approaching an insect, the FM components are rather stationary, the CF components are shortened, and the instantaneous frequency tends to be an ideally hyperbolic one, which means the bat is keeping good range resolution, is saving energy, is providing good Doppler tolerance, and is eliminating the coupling error of Doppler delay from search to capture. In terminal phase, very short-duration and harmonic structures are significant techniques to improve range resolution. [Work supported by NSFC 1881155 of China.]