A Qualitative Interpretation of the Sampling Theorem in the Time Domain

The signals coming from the real world around us are analog and, in order to treat these quantities with a computer, it is necessary to perform a conversion from analog to digital signals. In this paper we show how the analog signals can be processed digitally. In order to achieve such result we introduce the main definitions necessary for a more comfortable reading of the paper and then we present the process of signal conversion from analog to digital. The conversion of signals from analog to digital is proposed giving a qualitative interpretation of the sampling theorem in the time domain instead of, as happens more often, in the frequency domain. The reason behind the choice of presenting the qualitative analysis in the time domain, is twofold: on one side this approach does not require the introduction of the concept of Fourier Transform and spectrum of a signal and, on the other hand, it allows us to give a more intuitive interpretation of the sampling theorem. At the end of the paper we present some of the best known digital formats, both compressed and uncompressed, highlighting the necessity of compression to reduce the size of a file containing audio and digital video. Finally we present some examples of compression techniques such as the RLE (Run Length Encoding) and Huffman coding.