1-5] 



THE MODULATION OF RADAR SIGNALS 



li 



^T 



o o o 



3 33 

 FREQUENCY *■ 



■ III 



Fig. 1-13 Amplitude Spectrum of a Pulse Train. 



19 



the latter is a cosine wave of angular frequency coi and the peak excursion 

 of the modulated transmitting angular frequency is Ao), the transmitter 

 output is 



£(/) 



.-^ cos {(joot -\ sin coi/ -j- 0) 



(1-16) 



whose envelope has a constant value. A typical frequency-modulated 

 wave is shown in Fig. 1-14. 



■Ao)- 



FREQUENCY ^ 



Fig. 1-14 Typical FM Spectrum for High-Modulation Index (Aoj/coi > 10). 



A key parameter in an FM system is the ratio 

 — = modulation index. 



(1-17) 



If this index is relatively high — say 10 or greater — the output spectrum 

 has the form shown in Fig. 1-14. As can be seen, a single modulating 

 frequency gives rise to a large number of sidebands separated from the 

 carrier frequency by harmonics of the modulating frequency coi. The 

 sidebands of primary importance lie within a bandwidth Aco centered about 

 the carrier frequency coo- 



