Any continuous-time analogue signal can be converted into a digital signal by making discrete both the time and the amplitude axes. The process of making the time axis discrete is called sampling and consists of substituting the whole continuous-time analogue signal with a series of its analogue values (samples) taken at particular instants. This process is reversible only if the original signal has limited bandwidth. A well-known result, the fundamental Sampling Theorem [2.1]–[2.3], commonly attributed to Shannon orNyquist1, assures that the series of (analogue) samples taken with sampling frequency fs is perfectly equivalent to the original signal if
where B (bandwidth) is the maximum Fourier frequency in the signal spectrum.
The process of making the amplitude axis discrete is called quantization. It consists of dividing the amplitude axis in contiguous intervals and in associating to all the amplitudes within any interval a single amplitude value chosen among them. In practical applications, the number of intervals is finite and the quantized amplitude values can be thus expressed in a numerical form, with a fixed number of digits depending on the total number of intervals chosen.
Through the joint processes of sampling and quantization, therefore, any continuous-time analogue signal is converted to a sequence of numbers or binary ...