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BELL SYSTEM TECHNICAL JOURNAL 



ferent both in character and in location. For the cisoidal oscillation 

 the singularity is always located at / = « ; for the impulse the singu- 

 larity is at / = g. 



The fundamental differences between the two elementary time 

 functions adapt them for different uses. It is desirable to be in a 

 position to employ first one and then the other, shifting from one to 

 the other without any trouble or delay, so that at each step of a 

 problem the elementary function best suited for use may be employed. 



Fig. 1 — Wire models of cisoidal oscillations cis {2-Kfi) (above) and of unit impulses 

 ^o(^ — g) (below) for the particular values 0, ± 1/2, ± 3/2, of the parameters/ and g. 



For this we require only an adequate table of pairs and a certain 



familiarity in the use of the pairs. It is desirable to acquire the habit 



of thinking of the coefficients of a pair as alternative representations 



of a curve. 



The Use of Table I for Obtaining Coefficient Pairs ^ 



The table is divided into nine parts. In Part 1 are given the general 



processes for deriving any coefficient mate; but such processes are to 



^ Five other closely related uses may be made of Table I as explained in the 

 first footnote to that table. Operational expressions are brought within the scope 

 of the table by substituting for the operator p = d/dg the particular value i2irf, 

 other possible interpretations of the operator, if any, being ignored. 



