Signal Detection Based On Likelihood Ratio Test And Wavelet Analysis

In the highly information-oriented society, the rapid development of in-formation technology has become the driving force of the world’s scientific and technological revolution. Signal is the loader of information, which is used to transfer and exchange information. However, in the process of transmission, inevitably there are noises. Therefore, it is very important to detect signals from noises. Signal processing includes signal detection and estimation. We can choose different criterion according to the priori information.In chapter one we introduce background knowledge of this paper. In chap-ter two, firstly we show the generalized likelihood ratio test and the optimal detection threshold for signal strength. The signal can be successfully detect-ed only if its strength is above the threshold, and no detection method can successfully detect the signal if the signal amplitude is below the threshold. Moreover, when detecting the signal there’s an algorithm that is much faster than global search. When applying the generalized likelihood ratio test in bi-ological problem, we can add some limitations to construct a faster algorithm so that we can detect and estimate the signals quickly. This is also mentioned in chapter two. After a brief introduction of wavelet, in chapter three we demonstrate a theorem which is used to find the breakpoint of a function by comparing the wavelet coefficient of different position. Chapter four is numer-ical simulation, through which we contrast the likelihood ratio procedure and wavelet procedure for signal detection. By comparison we conclude that gen-eralized likelihood ratio procedure is more sensitive to signals and can detect weak signals, however, wavelet procedure can show us more information about the signal. Especially, when the signal is not line segments but other forms of functions, wavelet procedure is more powerful.