Fuzzy Extreme Analysis in Time- and Frequency Domains

Abstract

Abstract-Very often, we are interested in the shape of a signal or an envelope of the signal or its spectrum. Classical extreme analysis (CEA) produces too many minor details of a signal shape. This fact, in the context of telecommunications, does not allow us to ensure a significant coefficient of a signal compression. Another option for signal analysis, based on the Delta Modulation (DM), lacks sufficient dynamic range at a relatively low sampling rate. One more "true envelope" manner is based on the cepstral analysis, and requires too many operations.Other methods are used for the definition of a signal envelope. The discrete Hilbert transform (DHT) is only expedient to capture an envelope of a narrowband signal and, moreover, requires too many mathematical operations. Other manners based on decimation, as well as the use of a signal rectifying followed by low-pass filtering do not always ensure sufficient accuracy and signal compression coefficient.Fuzzy EA (FEA) is free from similar drawbacks. Its first and second differences are compared with no zero limits, and that allows us to take into consideration only major details of the signal or spectrum shape. Consequently we obtain both an envelope of wideband signal, and a signal significant compression in real time. This article focuses on FEA features connected with the aforementioned tasks. Apart from the FEA algorithm, the article outlines some methods of signal reconstruction after FEA in both domains, and the structure of the FEA specialized processor. FEA application in both domains is demonstrated through examples.