THEORETICAL FUNDAMENTALS OF PULSE TRANSMISSION 



729 



where \po(u) is the phase characteristic of- the original ampUtude charac- 

 teristic Ao(co). 



Thus, for any consine modification in the attenuation characteristic 

 there is a corresponding sine modification in the phase characteristic, 

 and for any sine modification in the phase characteristic a corresponding 

 cosine modification in the attenuation characteristic. In general any 

 modification in the attenuation characteristic may be represented by a 

 Fourier cosine series, in which case the modification in the phase charac- 

 teristic will be the correspondhig Fourier .sine series. 



With a cosine modification in the amplitude rather than in the at- 



LOW-PASS (a) 



HIGH-PASS (b) 



BANDPASS (a-b) 



ATTENUATION 



PHASE/' 





FREQUENCY, CJ — *- 



Fig. 4 — Attenuation and phase shift for various types of transmission fre- 

 quency characteristics. 



