1216 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 



signal, and Fig. 1(b) shows a 10 kc portion of this signal after instantaneous 

 compression. Now the minimum sampling rate required to handle a 4 kc 

 signal band is 8 kc. It is also the sampling rate that will allow the maxi- 

 mum band reduction in this case, as further analysis will show. The fre- 

 quency spectrum of a sampling function with an 8 kc repetition rate has a 

 d-c. component, an 8 kc fundamental, and all the harmonics of this repetition 

 rate as shown in Fig. 1(c). These harmonics are all of equal ampHtude and 

 all are phased so as to add up every 125 microseconds to form the charac- 

 teristic sampling waveform. Figure 1(d) shows the frequency spectrum 

 formed by sampling the 10 kc portion of the compressed speech signal. It 



4 8 12 16 



FREQUENCY IN KILOCYCLES PER SECOND 



Fig. 2 — Frequency analysis of instantaneous sampling and expanding of transmitted 

 signal. 



represents the product of the spectra of Fig. 1(b) and 1(c). As such, it is 

 composed of the various component frequencies in the sampling spectrum 

 as carrier frequencies, with the 10 kc portion of the compressed speech 

 signals as amplitude modulated sidebands about these carriers. 



Figure 2(a) shows the resulting spectrum that falls in the 4 kc baseband 

 of Fig. 1(d). It represents that part of the compressed and sampled spectrum 

 that would be received over an ideal 4 kc baseband channel. This spectrum is 

 worth examining because it illustrates how the addition of instantaneous 

 sampling makes it possible to transmit all the components in the compressed 

 speech over a 4 kc channel. The effect may be described as a linear "folding" 

 of the broadband spectrum back and forth over the 4 kc band. However, 



