PRODUCTION OF TELEVISION SIGNALS 601 



/(/) = - dw \ fix) cos co(/ - \)d\, (2) 



where X is an auxiliary variable of integration and co is 27r times the 

 frequency. To get the effect of sending this signal through a system 

 which transmits all frequencies without phase or amplitude distortion 

 up to a cut-ofif frequency fc it is only necessary to replace the upper 

 limit of the first integral sign by N where N = lirfc. Thus: 



1 r^ c" 



F{t) = - Jco /(X) cos co(/ - \)d\. 

 Then from (1): 



F{t) = — I do: \ T7:,cos co(/ — \)d\ -\ I t/co I COS co(/ — X)^X 



T^ Jo Jq -L "^ Jo Jr 



= -^ { cos TV/ - cos N{t - T) 



+ NtlSi{Nt) - Si{Nt - NT)^ } + - I + Si{Nt - NT) • 

 If we write Nt = x, NT = z, and 7r/^(/) = y{x), then 

 3'(x) = - { cos X — cos (x — z) + x[_Si{x) — Si{x — 2)11 | 



+ - + Si{x — z), 



where 



i'^ sin X 

 Siix) = I dx. 



Jo ^ 



A series of graphs of y{x) for dififerent values of the product NT is 

 given in Fig. 15 in the body of the paper. These are generalized 

 curves, the time scale depending on the particular value of cut-off 

 frequency used. From these curves we can get the additional lag 

 in the time, r, in the rise of these curves over the original time T 



in Fig. 14. 



Appendix II 



Let /(/) be the instantaneous intensity of the picture, and let it be 

 represented by a Fourier integral : 



/(O = ( ^(w) COS [/« + $(a;)]Jaj. (1) 



Jo 



