Zero-crossing intervals of Gaussian and symmetric stable processes

The zero-crossing problem is the determination of the probability density function of the intervals between the successive axis crossings of a stochastic process. This thesis studies the properties of the zero-crossings of stationary processes belonging to the symmetric-stable class of Gaussian and non-Gaussian type, corresponding to the stability index nu=2 and 0<nu<2 respectively

Zero-crossing intervals of Gaussian and symmetric stable processes

The zero-crossing problem is the determination of the probability density function of the intervals between the successive axis crossings of a stochastic process. This thesis studies the properties of the zero-crossings of stationary processes belonging to the symmetric-stable class of Gaussian and non-Gaussian type, corresponding to the stability index nu=2 and 0<nu<2 respectively

A zero-crossing analyzer for distribution-free detection of a signal in noise

This thesis discusses the analysis, design, and experimental evaluation of an instrument that can be used to detect the presence or absence of a signal, not necessarily known, in a noisy background. The detection principle is based on application of the sign test of distribution-free statistics to the stochastic process defined by the zero-crossing intervals of a signal or signal plus noise process. It is shown that the detector is distribution free in the sense that the false-alarm probability can be evaluated with only a limited knowledge of the statistics of the underlying noise process. A theoretical discussion of the detection principle and false alarm probability analysis is presented in conjunction with design considerations of the circuitry used to implement the zero-crossing analyzer technique. Results of an experimental evaluation with narrow-band noise are presented along with a complete schematic diagram of the analyzer. For a noise filter center frequency of 10.3 kHz and with the signal frequency removed from the filter center frequency by at least 300 Hz, reliable detection can generally be obtained with a signal to noise power ratio of -8 dB

The application of auditory signal processing principles to the detection, tracking and association of tonal components in sonar.

A steady signal exerts two complementary effects on a noisy acoustic environment: one is to add energy, the other is to create order. The ear has evolved mechanisms to detect both effects and encodes the fine temporal detail of a stimulus in sequences of auditory nerve discharges. Taking inspiration from these ideas, this thesis investigates the use of regular timing for sonar signal detection. Algorithms that operate on the temporal structure of a received signal are developed for the detection of merchant vessels. These ideas are explored by reappraising three areas traditionally associated with power-based detection. First of all, a time-frequency display based on timing instead of power is developed. Rather than inquiring of the display, "How much energy has been measured at this frequency? ", one would ask, "How structured is the signal at this frequency? Is this consistent with a target? " The auditory-motivated zero crossings with peak amplitudes (ZCPA) algorithm forms the starting-point for this study. Next, matters related to quantitative system performance analysis are addressed, such as how often a system will fail to detect a signal in particular conditions, or how much energy is required to guarantee a certain probability of detection. A suite of optimal temporal receivers is designed and is subsequently evaluated using the same kinds of synthetic signal used to assess power-based systems: Gaussian processes and sinusoids. The final area of work considers how discrete components on a sonar signal display, such as tonals and transients, can be identified and organised according to auditory scene analysis principles. Two algorithms are presented and evaluated using synthetic signals: one is designed to track a tonal through transient events, and the other attempts to identify groups of comodulated tonals against a noise background. A demonstration of each algorithm is provided for recorded sonar signals