ver, it is also possible to modulate carriers having other waveforms. For example, it is possible to modulate trains of pulses to produce pulse amplitude modulation (PAM), Its spectrum thus contains a d.c. component, the PRF and its pulse frequency modulation (PFM) or pulse phase modulation harmonics, as shown in Figure 18.17(d). If the pulses are of short (PPM), which is sometimes called pulse position modulation. It is duration, the amplitudes a of the harmonics are approximately also possible to produce pulse length modulation, which is some- equal up to large values of n. times called pulse duration modulation (PDM) or pulse width If the pulse train is amplitude modulated by a sinusoidal baseband modulation (PWM). signal, the resulting PAM signal is given by Equation 18.55. Pulse modulation 18/13 m (1) 1/f r Frequency Frequency 2fr-Fm 2fr+Fm 31,Fm 31r+Fm Frequency Figure 18.17 Pulse amplitude modulation waveforms: (a) baseband signal; (b) unmodulated pulse train; (c) modulated pulse train; (d) spectrum of unmodulated pulse train; (e) spectrum of baseband signal; (f) spectrum of modulated pulse train and all higher frequencies. For this to be possible, Equation 18.56 must hold, where F m is the maximum frequency of the baseband signal and fo is the cut off frequency of the filter. Thus Equation 18.57 must hold. (18.56) (18.55) f 2 2 Fm (18.57) Thus, the spectrum of the PAM signal contains all the components Equation 18.57 is a statement of the sampling theorem. This may of the original pulse train, together with the baseband frequency f be expressed as follows: if a signal is to be sampled and the original and upper and lower side frequencies (nf, f f m about the PRF and signal is to be recovered from the samples without error, the samp- its harmonics. If the modulating signal consists of a band of frequen- ling frequency must be at least twice the highest frequency in the cies, as shown in Figure 18.17(e), the spectrum of the PAM signal original signal. The sampling theorem is due to Nyquist and the contains 