By J. J. O’Reilly (auth.)
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Ii) Express x(t) as an exponential form Fourier series and calculate non-zero coefficients up to Inl = 5. Hence sketch the signal spectrum, X(f), over a corresponding frequency range. Spectrum of a Train of Narrow Pulses Consider now a periodic rectangular wave described by x(t) Use is made of this result when sampling is studied in Chapter 5. 48) Note in this instance the individual pulses have unit area whatever value of 7 < Tis adopted. Consider the spectrum as 7-t0; the sequence illustrated in Fig.
Some Examples of Signals in the Frequency Domain (i) Sum of Cosine Waves. 22) positive frequency term at +F2 negative frequency term at -F2 For example, if F2 = 3Fj and B = AI2 this signal has a frequency spectrum of the form shown in Fig. 12. (ii) Square wave signal. A square wave can be viewed as a sum of harmonically related co sinusoidal components. This is illustrated graphically in Fig. 13. Starting with a term cos(27rtlT) as the fundamental component, we then add a third harmonic component, -1I3cos(27r3tlT).
57 -------, r-----I I I I I I I I I I .. f o Fig. 8 A single sideband signal obtained by filtering a DSB-SC signal. If this signal is passed through a high pass filter which rejects all components IfI < Fe and passes all components IfI > Fe a signal is obtained with spectrum as shown in Fig. 8. This signal corresponds to two contra-rotating phasors atf = ± (Fc + Fm) and may be expressed analytically as y(t) = Ac~m [ exp[-j(wc + wm)t] negative frequency part This is the simplest and perhaps the most widely used of three basic methods for generating SS8-SC signals.