Sampling Quantization and Discrete Fourier
Francis F. Li, Trevor J. Cox · 2019
To enable digital processing, signals first need to be converted to a digital format for processing, and if necessary, processed signals are reconstructed by converting their digital representations back to an analogue form. This chapter discusses the principles of analogue to digital conversions and digital to analogue conversions, with an emphasis on sampling and quantization. The first stage of the “sampling” process is discretization, in which a function that varies continuously with respect to its independent variable is converted into a discrete sequence. The multiplication of the continuous time signal with the sampling waveform is related to the convolution of the input signal&s;s frequency domain representation with the frequency domain representation of the sampling waveform. Fourier transform divulges the relationships between the time domain and the frequency domain representations of signals sampled at even points in time and in uniform frequency bins.