552 BELL SYSTEM TECHNICAL JOURNAL 



little if any change in the character of the sound. A possible exception 

 may arise for complex waves of large amplitude because of non- 

 linearity in the hearing mechanism. It would be expected then that 

 the observable effects of phase shift would arise from the intervals 

 preceding and following the steady state intervals of the sound waves. 

 For this reason the wave of a speech sound is regarded as non-periodic 

 and when an amplitude frequency distribution is spoken of a Fourier 

 Integral is implied. 



Types of Phase Characteristics 

 The determination of the effects of phase distortion on quality 

 involved the characteristics of the experimental system as a whole 

 although, for convenience, the distortion usually originated in a spe- 

 cific network in the system. The procedure that was followed was to 

 make the system, except for the network, as distortionless as possi- 

 ble. In most cases the characteristic of the system from the view- 

 point of distortion, was the insertion characteristic of the network. 



Before taking up experimental results on phase distortion it will be 

 helpful to briefly review certain conclusions bearing on the relation 

 between phase shift and wave distortion that have been obtained by 

 analytical methods.^ A phase characteristic of interest is one of 

 form B = Bq -\- Bioi, where B — phase shift in radians and co = 1-kj. 

 If the original wave be represented by a Fourier Integral, the expression 

 for the received wave may be obtained by shifting the phases of all 

 of the sinusoidal components in the original in accordance with the 

 above expression, assuming negligible attenuation distortion. For 

 convenience the two terms in the above expression may be considered 

 separately. If this is done, it can be shown by inspection that a 

 constant shift of B^ in the phases of all of the sinusoidal components 

 gives a wave which is the sum of two waves, one the original wave 

 multiplied by an amplitude factor cos 5o, the other a wave obtained 

 from the original by shifting all of its components by 7r/2 radians and 

 multiplying by an amplitude factor sin B^. 



If the phases of the sinusoidal components in the original are shifted 

 by the amounts Bxw, where co = 27r times the frequency of the com- 

 ponent, it can be shown that the resulting wave differs from the original 

 only in that the origin of time is displaced by an amount Bx or the slope 

 dBldw of the above expression. 



^ Transient Oscillations in Electrical Wave Filters, Carson and Zobel, Bell Sys. Tech. 

 Jour., July 1923. Building Up of Currents in Long Periodically Loaded Lines, Carson, 

 Bell Sys. Tech. Jour., Oct. 1924. Phase Distortion and Phase Distortion Correction, 

 Mead, Bell Sys. Tech. Jour., Apr. 1928. Phase Compensation, .Sandeman, Electrical 

 Communication, 1929. Transient Solutions of Electrical Networks, Mason, Bell Sys. 

 Tech. Jour., Jan. 1929. Phase Distortion in Telephone Apparatus, Loc. cit. 



