Abstract:

Pulse-Code Modulation (PCM) is the most widely used analog-to-digital (A/D) conversion technique employed in, among others, the digitization of telephony and video signals. However, though PCM is analyzed in most telecommunication textbooks, there are specific topics sufficiently addressed. Such issues have been observed to be the physical interpretation of sampling theorem, the non-linear quantization (particularly its digital format) and issues regarding the bandwidth required for the transmission of the produced PCM signal.

Regarding sampling theorem (and despite the presentation of the relevant mathematical proof), the students find it difficult to accept that the Nyquist rate can actually guarantee the reversibility of the sampling process that consider contrasting common sense. As far as the non-linear quantization is concerned, students find it difficult to comprehend the various steps of its digital implementation and realize the equivalence with its analog counterpart while regarding the bandwidth required for the transmission of a PCM signal, most students feel unable to express an answer or even a mere guess.

With the aim to encourage students’ active participation and enhance their conceptual and practical understanding, prior to the lectures on the PCM technique (delivered in the framework of the “Telecommunication Systems” course at the Electrical & Electronic Engineering Educators Dept. of the School for Pedagogical & Technological Education (ASPETE), Athens, Greece) the students are given some preliminary topics to think and comment on. More specifically, they are asked to think on the actual meaning of the original analog signal having a limited bandwidth (regarding the signal’s variation with time), as well as the spectral representation (Fourier transform) of a rectangular pulse.

Following the above, the sampling rate is presented as the necessary rate to accommodate the fastest possible temporal variation of the original analog signal (which is, in turn, dictated by its limited bandwidth).

Regarding digital implementation of non-linear quantization, the various steps are explained in detail. In this context, an essential comment is the equivalence of the analog companding characteristic (which is easier to comprehend) with the characteristic of the final number of quantization levels (16 in every signal sub-range) versus the initial number (varying from 16 for the lower signal sub-ranges to 1024 for the higher ones). At that point, the students are given specific examples for which they are asked to apply the quantization process and estimate the quantization error.

Regarding the bandwidth required for the transmission of a PCM signal, the students are asked to associate the signal’s bandwidth with the bit rate considered as the inverse of the signal’s duration. Following those preliminary comments, the students are asked to think on what the effect of a possible reduction in the transmission medium’s bandwidth would be and to what extend such a reduction would be acceptable.

With the aim to enhance students’ engineering aptitude, specific case studies are presented that is the A/D conversion of telephone and video signals. Regarding non-linear quantization (which has proved a rather difficult topic for the students to comprehend) specific examples are given in which the students are asked to form quantization tables and, optionally, to compile tables for alternative quantization processes of the A-m/n type.

Keywords:

Engineering Education, Electronic Engineering Education, Telecommunications, Digital transmission.