# Systems-Analysis Techniques

Having identified and discussed the main subsystems in a communication system and certain characteristics of transmission media, let us now look at the techniques at our disposal for systems analysis and design.

#### 1. Time and Frequency-Domain Analyses

The electrical engineer lives in the two worlds of time and frequency. Also, dual time-frequency analysis techniques are especially valuable for linear systems for which the principle of superposition holds. Although many of the subsystems and operations encountered in communication systems are for the most part linear, many are not. Nevertheless, frequency-domain analysis is an extremely valuable tool to the communications engineer, more so perhaps than to other systems analysts. Since the communications engineer is concerned primarily with signal bandwidths and signal locations in the frequency domain, rather than the transient analysis, the essentially steady-state approach of the Fourier series and transforms is used.

#### 2. Modulation and Communication Theories

Modulation theory employs time and frequency-domain analyses to analyze and design systems for modulation and demodulation of information-bearing signals. To be specific consider the message signal m(t), which is to be transmitted through a channel using the method of double-sideband modulation. The modulated carrier for double-sideband modulation is of the form xc(t) = Acm(t)cosωct, where ωc is the carrier frequency in radians per second and Ac is the carrier amplitude. Not only must a modulator be built that can multiply two signals, but amplifiers are required to provide the proper power level of the transmitted signal. The exact design of such amplifiers is not of concern in a systems approach. However, the frequency content of the modulated carrier, for example, is important to their design and therefore must be specified. The dual time-frequency analysis approach is especially helpful in providing such information.

At the other end of the channel, there must be a receiver configuration capable of extracting a replica of m(t) From the modulated signal, and one can again apply time and frequency-domain techniques to good effect.

The analysis of the effects of interfering signals on system performance and the subsequent modifications in design to improve performance in the face of such interfering signals are part of communication theory, which, in turn, makes use of modulation theory.

This discussion, although mentioning interfering signals, has not explicitly emphasized the uncertainty aspect of the information-transfer problem. Indeed, much can be done without applying probabilistic methods. However, as pointed out previously, the application of probabilistic methods, coupled with optimization procedures, has been one of the key ingredients of the modern communications era and led to the development during the latter half of the twentieth century of new techniques and systems totally different in concept from those that existed before World War II.

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