Some aspects of digital data processing vs. Analogue signal analysis

Nowadays almost all radio astronomical data is processed digitally. Digital signal process, as compared with analogue technique, has big advantages. Once the data are properly sampled and digitized and stored, the information will be kept. One could always go back to the stored data and re-process the data to obtain the desired information. But the ADC will unavoidably deteriorate the quality of the data, i.e., the sampling clock is not perfect, and only limited number of digits could be used to represent a analogue quantity. In this presentation, we will discuss two aspects. One is about total power observation. By definition, total power is proportional to the time average of the voltage squared. However, it is impractical to perform a rigorous integration of the voltage squared after ADC. The normal approach is to use the time average of the voltage squared at the sampled points to approximate the average total power. We show that the averaged sampled voltage squared could approximate the rigorous time average of voltage squared to desired accuracy by either extending the time span or increasing the sampling rate. The effect of limited number of digits in the presence of strong RFI is also mentioned.