The fractional Fourier transform (FrFT) provides a valuable tool for the analysis of linear chirp signals. This paper develops two short-time FrFT variants which are suited to the analysis of multicomponent and nonlinear chirp signals. Outputs have similar properties to the short-time Fourier transform (STFT) but show improved time-frequency resolution. The FrFT is a parameterized transform with parameter, a, related to chirp rate. The two short-time implementations differ in how the value of a is chosen. In the first, a global optimization procedure selects one value of a with reference to the entire signal. In the second, a values are selected independently for each windowed section. Comparative variance measures based on the Gaussian function are given and are shown to be consistent with the uncertainty principle in fractional domains. For appropriately chosen FrFT orders, the derived fractional domain uncertainty relationship is minimized for Gaussian windowed linear chirp signals. The two short-time FrFT algorithms have complementary strengths demonstrated by time-frequency representations for a multicomponent bat chirp, a highly nonlinear quadratic chirp, and an output pulse from a finite-difference sonar model with dispersive change. These representations illustrate the improvements obtained in using FrFT based algorithms compared to the STFT.
This paper uses advanced time-frequency signal analysis techniques to generate new models for bio-inspired sonar signals. The inspiration comes from the analysis of bottlenose dolphin clicks. These pulses are very short duration, between 50 and 80 micros, but for certain examples we can delineate a double down-chirp structure using fractional Fourier methods. The majority of clicks have energy distributed between two main frequency bands with the higher frequencies delayed in time by 5-20 micros. Signal syntheses using a multiple chirp model based on these observations are able to reproduce much of the spectral variation seen in earlier studies on natural dolphin echolocation pulses. Six synthetic signals are generated and used to drive the dolphin based sonar (DBS) developed through the Biosonar Program office at the SPAWAR Systems Center, San Diego, CA. Analyses of the detailed echo structure for these pulses ensonifying two solid copper spherical targets indicate differences in discriminatory potential between the signals. It is suggested that target discrimination could be improved through the transmission of a signal packet in which the chirp structure is varied between pulses. Evidence that dolphins may use such a strategy themselves comes from observations of variations in the transmissions of dolphins carrying out target detection and identification tasks.
To date most sonars use narrow band pulses and often only the echo envelope is used for object detection and classification. This paper considers the advantages afforded by bio-inspired sonar for object identification and classification through the analysis and the understanding of the broadband echo structure. Using the biomimetic dolphin based sonar system in conjunction with bio-inspired pulses developed from observations of bottlenose dolphins performing object identification tasks, results are presented from experiments carried out in a wave tank and harbor. In these experiments responses of various targets to two different bio-inspired signals are measured and analyzed. The differences in response demonstrate the strong dependency between signal design and echo interpretation. In the simulations and empirical data, the resonance phenomena of these targets cause strong notches and peaks in the echo spectra. With precision in the localization of these peaks and dips of around 1 kHz, the locations are very stable for broadside insonification of the targets and they can be used as features for classification. This leads to the proposal of a broadband classifier which operates by extracting the notch positions in the target echo spectra.
scite is a Brooklyn-based organization that helps researchers better discover and understand research articles through Smart Citations–citations that display the context of the citation and describe whether the article provides supporting or contrasting evidence. scite is used by students and researchers from around the world and is funded in part by the National Science Foundation and the National Institute on Drug Abuse of the National Institutes of Health.