Analog and digital worlds: Part 1. Signal sampling and Fourier Transform

Proper data sampling of a continuously varying quantity that describes the proceeding of a natural process leads to a simpler equivalent representation. This representation consists of a sequence of discrete data, which is more suitable to be mathematically handled and allows one not to lose essential information provided by the original signal. The discrete values of the sequence obtained by sampling differ from one another by finite quantities. In the ideal case, the original representation should be perfectly reconstructed by a backward procedure. The rules that should be respected in order to satisfy this basic condition are very simple, but require the decomposition of the signal into a suitable set of elementary components. This may be performed by applying to the sequence the algorithm called Discrete Fourier Transform (DFT). The direct result of the transformation consists of the spectrum of the signal, which can be analysed in many ways. The mathematics to make the FT algorithm work, eventually in an as fast as possible way (FFT – Fast Fourier Transform) is perhaps of less interest to the chemists and will not be treated here. Rather, the aim is to address the reader about what FT allows to obtain.