eband components at frequencies nf, + ff (where =1,2,3,...), just as do the sidebands of a sinusoidal V ( t) carrier when angle modulation is used (Fitch, 1947; Moss, 1948; Slicing level Black, 1953). It is therefore necessary to use a sampling frequency Vx(t) greater than 2F to minimise aliasing. The voltage of the d.c. component in the spectrum of an unmodu- lated train of rectangular pulses is equal to the pulse height multi- plied by the duty ratio of the pulse train (i.e. the ratio of pulse duration to pulse repetition period). If modulation causes changes in either pulse height or duty ratio, there is a corresponding modu- lation of the d.c. component. Equation 18.55 shows that the spec- trum of a PAM wave contains a voltage at the modulating frequency (f_) whose ratio to the d.c. component (1/2a is equal to the depth of modulation (m) of the pulse height. For PLM, the duty ratio varies with pulse duration, SO the baseband frequency component is 11-8+1 t2+8t2 proportional to the depth of modulation of the pulse duration. In PFM, the duty ratio increases if more pulses are generated in a given period and decreases if fewer are generated. Consequently, a low pass filter can be used for demodulating PLM and PFM, just as for Figure 18.19 Operation of a slicer in the presence of In PPM, there is no change in pulse height or pulse duration and interfering voltage (v): (a) input pulse; (b) output pulse the mean number of pulses per unit of time is constant. Conse- quently, the spectrum has only a small component at the modulating frequency. PPM is therefore demodulated by converting it to PLM (18.58) before low pass filtering. In pulse time modulation, the pulse amplitude conveys no infor- mation. It is therefore possible to use a 'slicer' at the receiver, as shown in Figure 18.18, to produce pulses from which amplitude (18.59) variations due to interference or noise have been removed. If the input pulses could have zero rise and fall times, no interference or noise would reach the output of the slicer. In practic