1218 THE BELL SYSTEM TECHNICAL JOURNAL, OCTOBER 1951 



also that this is just one of a whole family of transmission characteristics 

 with a specified symmetry about the cut-off frequency, all of which have 

 the required transient zeros. However, there is no reason to suppose that 

 any of them would prove less sensitive to variation of the transmission 

 characteristics from the ideal than the one described above. 



It is apparent that synchronization of the transmitting and receiving 

 samplers is required to insure that the receiving sampling is done at the 

 exact instant that all transient responses but the desired one are zero. 



Effect of Variations from Ideal Transmission Characteristics 



ON Distortion 



In practice of course a certain amount of distortion is tolerable. To get 

 some measure of the practicability of such reduced bandwidth transmission 

 of compressed speech, the first step is to determine how much intersymbol 

 interference can be tolerated in this type of signal, and then to translate this 

 tolerance into allowable variations in the frequency characteristics of the 

 transmission medium from the assumed ideal. However, it is hard to estimate 

 what the allowable intersymbol interference might be in this case. In a single 

 channel system, intersymbol interference produces a form of distortion, and 

 the sensitivity of such signals to distortion is primarily a matter for subjec- 

 tive determination. 



For computational purposes it will be assumed, however, that this inter- 

 symbol interference should be 20 db down in the output. It is apparent that 

 a 5% variation in the amplitude of a sample before expansion will produce 

 a 10% variation in the expanded sample. On this basis 5% intersymbol 

 interference in the medium between transmitter and receiver is the maximum 

 allowable. Using Wheeler's theory of paired echoes'*, it can readily be shown 

 that a sinusoidal variation in the phase vs. frequency characteristics of the 

 medium, with an amplitude of ^^ of a radian (5.7 degrees), will cause a 

 pair of echoes each of which will have a peak equal to 5% of the original 

 sample. Similarly a sinusoidal deviation in the attenuation vs. frequency 

 characteristic of 0.9 db from the ideal will also cause a pair of echoes with 

 an amplitude of 5%. 



In estimating the average effect of such echoes, it cannot be expected that 

 the intersymbol interference from a given echo will be appreciably less 

 than its peak amplitude would indicate. The principal reason is that, in order 

 to realize the savings in bandwidth, the pulses are 125 microseconds apart, 



which is as close together as the 4 kc band will permit. Reference to the 



*H A. Wheeler,The Interpretation of Amj)litu(ie and Phase Distortion in Terms of 

 Paired Echoes, I.R.R., June 1939. 



