EFFECTS OF PHASE DISTORTION 553 



As will be seen later, it is convenient to regard these two operations 

 as occurring in sequence. The second term of the expression introduces 

 a definite time delay of Bi, sometimes called the envelope delay, and no 

 distortion in the form of the original wave. Following this operation, 

 the phases of all of the sinusoidal components of the delayed original 

 are shifted by the constant amount Bq the resulting wave being the 

 received wave. 



If Bo equals zero or even multiples of it, the amplitude factor sin Bq 

 equals zero, so that, the received and original waves are identical in 

 form. If Bo is an odd multiple of t the received wave is reversed in 

 sign only. In both cases the received wave is delayed by an amount 

 (IBjdw, and the wave cannot appear until this time has elapsed. 



For all other values of Bq the form of the received wave differs from 

 that of the original to a greater or less degree depending upon the 

 original wave form and the value of Bq. In this case the delay in the 

 received wave as a whole cannot be spoken of precisely for no point 

 on the received wave can be said to correspond to a point on the original 

 wave. Theoretically the received wave may begin to appear at some 

 earlier time than dB/doj, as has been shown by Mr. T. C. Fry in some 

 unpublished work for the case of a wave having the form of a tele- 

 graph dot. 



When the phase characteristics are curved over appreciable portions 

 of the frequency range, as is usually the case in actual systems, exact 

 statements of the above nature are difficult to make. It seems best, 

 therefore, to confine the discussion to particular characteristics and to 

 the case of speech waves. 



A qualitative picture of what happens for the type of characteristic 

 shown in Fig. 2 may be seen by regarding it as the limiting case of a 

 characteristic made up of a number of straight lines of different slopes, 

 each line approximating the curved characteristic for a frequency 

 range A/. As discussed above, the wave of a speech sound may be 

 regarded as made up of steady state component waves of different 

 frequency. The resultants of the component waves in various fre- 

 quency ranges A/ are subject to the phase distortion discussed in the 

 preceding paragraphs, that is, the original forms of the resultants are 

 delayed by times dB/doo, and then undergo a distortion that depends 

 upon the terms Bo or the intercepts of the straight lines with the 

 vertical axis. 



As mentioned above it is convenient to regard these operations as 

 taking place in sequence, the first introducing definite delays and no 

 distortion in portions of the original signal corresponding to frequency 

 ranges A/, the second introducing a constant amount of phase shift in 



