By J. J. O’Reilly (auth.)
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Note its close relationship with the frequency domain representation: the amplitudes An give the heights of the various spectral lines. c. ) = C *n c_ n = TexP assuming An is real. 19) -co This, the exponential form of the Fourier series, is particularly useful in signal analysis. The Cn values are complex numbers with Icnl corresponding to the magnitudes and arg(cn) to the phases of the constituent spectral components. In this representation, however, n takes both positive and negative values and it is convenient to consider a two-sided spectrum of the form shown in Fig.
5 Demodulated DSB-SC signal. 3) = -tAmcoswmt + Amcoswmt-tcos(2wct) The first term corresponds with the message m(t) = Amcoswmt scaled in amplitude by AH2 and the second to a DBS-SC signal centred on f = 2Fc. Hence the spectrum of y(t) , denoted as Y(f), has the form shown in Fig. 5. The output spectrum is the product of Y(f) and the filter transfer function H(f). 4) Once again, this result holds also for a general message spectrum, as illustrated in Fig. 6. 1 An audio signal occupies the frequency range 30 Hz < IfI < 15 kHz.
It is not necessary to be concerned with the physical mechanisms giving rise to these random waveforms but it is necessary to assess their implications for the performance of communication systems. In order to do this both the message or signal waveform and the unwanted noise/interference components must be represented mathematically. In this chapter the various ways in which signals may be represented are examined. Before doing this, however, it is appropriate to note that it is neither necessary nor practicable to assess the performance of a system by examining how it will process all possible message waveforms.