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3 Frequency-domain representation of periodic signals A frequency response model of a telecommunications channel is a very useful tool, which can give an experienced engineer an immediate 'feel' for how the channel will behave in general terms, without the need for complex calculations. To be able to use such frequency domain models, however, it is necessary to characterise a digital message signal, such as the pulse trains considered above, in terms of their frequency content or spectra. Contrast, for example, the amplitude and phase distortion inherent in Fig.

Together and their amplitudes decrease, as shown in Fig. 18. As the pulse spacing is increased indefinitely, the lines become arbitrarily closely spaced, and it becomes difficult - and ultimately impossible - to distinguish between individual components. But while the amplitudes of the spectra components decrease with increasing pulse separation, the general shape of their envelope is unchanged: although the line spacing is a function of the period of the signal, the envelope (apart from its height) is determined purely by the shape of the individual pulses in the train rectangular in this example.

25. Note that the time-domain waveform corresponding to the rectangular spectrum is Frequency-domain representation of pulses 39 much more oscillatory than that corresponding to the raised-cosine spectrum; the pulse with a triangular spectrum would be somewhere in between. In fact, we have a third 'rule': Sudden changes in a spectrum imply oscillatory behaviour in the corresponding signal. 3 The engineering interpretation All the models introduced so far are mathematical abstractions. Nevertheless, they are all of profound significance for engineering.

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Andrew Johnson's Cloudy Nights [Mag-7] Star Atlas by A. Johnson

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