On The Field To Break Down Signal Sampling And Analysis

The problem how to convert analog into digital signal has been playing a major role in the signal theory. Among various analog signal,there is one kind can expressed as linear sum of existing signal. Taking a view of pure time field,this paper presents dissolvable signals and basic concepts of sampling;And also gives the very condition of discrete of signal;This paper uses linear algebra to analysis this kind of signal and then gives some results and relevant deductions;Based on these results,1 made a further step to analysis some typical band-limited signals in order to proof the coherence of my Theory of Dissolvable Signal to the typical sampling theory;I made some preliminary study about the feasibility of sampling and recovering of this kind of signal.After the scientific analysis above,we can make the following conclusion:when one of signals in one signal pool can be denoted as the linear sum of existing signals,then the signal pool can be thought as the dissolvable signal pool. The signal we named it Fundamental wave;according to the Fundamental wave,coefficients of the fundamental wave can be lined in a sequence . when the unique of the dissolve of the fundamental wave can be confirmed,the sequence of the coefficients can be regarded as one of representation forms of the signal itself;Theory of Dissolvable Signal shows that when order of the matrix of Fundamental wave sampling equals to number of fundamental waves,the sequence of the sampling values from sampling points must be matched one by one with the sequence of the coefficients of fundamental waves. The sampling composed by sequences of the sampling values must be full sampling;The relevant deductions of the Theory of Dissolvable Signal shows that when sampling the signal,sampling frequency must be lager than the ratio of the number of fundamental waves to the occupation time of the fundamental waves;To band-limited signals,when the fundamental wave is a sine signal,the results from the relevant deductions of Theory of Dissolvable Signal is coherent to the classic sampling theory.