560 



BELL SYSTEM TECHNICAL JOURNAL 



column C emerges with smooth transitions as shown m 2, 3 and 4. These 

 pulses rise and fall in a nearly sinusoidal manner. The width between half- 

 amplitude points is To . Shortening the rectangular pulse ("curbing") 

 and narrowing the shaping filter can be made to result in pulses 5 and 6 

 which have the same width between, say, 3% points (at /i) as pulse 4. 



(A) PULSE (B) SPECTRUM 



(C) FILTER 



-To To 2To TIME— *• 



Fig. 26 — Typical pulses and their spectra. 



Pulses 5 and 6 are then shorter than 4 between half-amplitude points. If 

 the half-amplitude width is made the same as in pulse 4 the width between 

 lower amplitude points is greater than in pulse 4. This is illustrated in 

 pulse 7. 



Gaussian filters^^ as defined here are naturally linear phase networks 



* Gaussian filters are networks whose transfer admittance follows the error law as a 

 function of frequency. A decibel plot of a bandpass Gaussian filter is accordingly a para- 

 bola in shape. 



