504 BELL SYSTEM TECHNICAL JOURNAL 



ample, in a 50-line system the waste bands are each about 500 cycles 

 wide. In a system using a single sideband of one million cycles width 

 the waste bands are each about 3300 cycles wide. 



These idle frequency regions naturally lead to the questions whether 

 {a) there is any way of segregating all of the relatively useless signal 

 components in one region of the frequency spectrum so that the useful 

 parts of the signal may be transmitted over a channel of about half the 

 width, or {h) whether it would be worth while placing other communica- 

 tion channels in these waste regions. It must be realized, however, 

 that even when the complete frequency space is utilized (by any one of 

 a number of possible schemes), the required frequency band for trans- 

 mitting a picture of given detail at a given rate is still only halved as 

 compared with the simple system considered above, which is not a 

 change in order of magnitude. The problems of transmitting the wide 

 band of frequencies necessary, for example, in television, while lessened, 

 therefore still remain. 



APPENDIX I 



The calculation of Yi{m, n) according to equation (20') is, for the 

 three simple apertures here considered, a straightforward mathematical 

 process which will therefore not be reproduced. The results are plotted 

 in the form of charts in the conventional manner for functions of two 

 variables, namely as a series of contours, one of the two variables being 

 icept constant for each contour. This constant value changes progres- 

 sively for each successive contour. 



The variables are taken as ni and n, multiplied by parameters depend- 

 ing on the sizes of the scanning aperture and of the picture. Because 

 of the obvious symmetry of the function, only half of each chart has 

 been drawn. In order to avoid confusion the contours have been 

 dotted when \m\ is greater than the first root of Yi{m, 0) = 0. In 

 one case the contour is shown in a dashed line when \m\ is equal to this 

 root. Constant factors in the scale of ordinates have been neglected, 

 to make Fi(0, 0) = 1. 



