Envelope Detection Algorithm for an Amplitude-Modulated Random Signal

Determining the characteristics of underwater sound is an urgent task in marine acoustics. In the course of radiation or propagation, a sound wave is subjected to perturbations by various factors. In particular, it may be amplitude modulated in accordance with the characteristic features of the radiating system as well as the temporal variability of the thermodynamic properties of the propagation medium. Usually, the modulating effects of parameters are in the low-frequency range; as a consequence, one of the practical problems of processing acoustic information is the detection of the low-frequency envelope of the audio signal. Currently, the best known means of obtaining such information is a software package developed by the methods DEMON and LOFAR [1, 2]. The method of DEMON is a kind of narrowband analysis aimed at identifying the modulation characteristics of the acoustic noise from the multiple blades of a screw. The LOFAR method of analysis is carried out to determine the broadband modulation characteristics of the acoustic noise due to the vibration of machinery. Both methods are based on the repeated application of the Fourier transform, which leads to a significant computational cost. Unfortunately, further modifications of these methods have not been able to reduce the amount of computation [3, 4]. In this paper, we propose a new computational algorithm that enables the direct detection (without the use of the Fourier transform) of the proper envelope of regular and pseudorandom signals. The essence of the algorithm will be considered using a pseudorandom signal which requires a more complex analysis. The origin of this type of signal is given by a physical model of the following form. Some marine object (surface or underwater) in quiet mode (all mechanisms and items immobile) emits an acoustic noise signal entering the measuring circuit in the form of s(t) + r(t), where s(t) is the intrinsic noise of the object, r(t) is background noise (marine aquatic noise). After the activation of some periodic operating mechanism, the measuring path receives the signal F(t) = M(t)s(t) + r(t), where the function M(t) describes the amplitude modulation of the noise signal s(t), and its mathematical model is defined by the relation