# 1Signal Digitizing – Sampling and Coding

The conversion of an analog signal to digital form involves a twofold approximation. Firstly, in the time domain, the signal function s(t) is replaced by its values at integral time increments T and is thus converted to s(nT). This process is called sampling. Secondly, in the amplitude domain, each value of s(nT) is approximated by a whole multiple of an elementary quantity. This process is called quantization. The approximate value thus obtained is then associated with a number. This process is called coding – a term often used to describe the whole process by which the value of s(nT) is transformed into the number representing it.

The effect of these two approximations on the signal will be analyzed in this chapter. To achieve this, two basic tools will be used: Fourier analysis and distribution theory.

## 1.1 Fourier Analysis

Fourier analysis is a method of decomposing a signal into a sum of individual components which can easily be produced and observed. The importance of this decomposition is that a system’s response to the signal can be deduced from these individual components using the superposition principle. These elementary component signals are periodic and complex, so both the amplitude and phase of the systems can be studied. They are represented by a function se(t) such that:

(1.1)

where f is the inverse of the period – ...

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