412 BELL SYSTEM TECHNICAL JOURNAL 



uniformity in modulation and average transmission, and accuracy in 

 wave-length. In the present instrument it was found possible to keep 

 the harmonic content of the screens down to 5 per cent. The modula- 

 tion varied from 79 per cent to 94 per cent in different screens, and the 

 average transmission from 20 per cent to 24 per cent. Variations in 

 the wave-length of the screens amounted to about 1 per cent.'' 



It is convenient though not necessary to have good wave form in 

 the screens. When readings are made in pairs as described above, 

 the effects of even order harmonics in the cosine screens cancel out. 

 Moreover, G. R. Stibitz has shown ^ that the cosine screens may have 

 practically any wave form (not even necessarily periodic), and cor- 

 rection factors can be derived for them. The process of correction is 

 rather cumbersome, however, since the correction for each harmonic is 

 not a constant, but depends on other harmonics present in the function. 



Uses of the Analyzer 



This instrument was designed particularly to accommodate sound 

 records on film as used in commercial motion picture work. How- 

 ever, functions from any other source can be analyzed equally well 

 if they are reproduced with the proper dimensions on film. Provision 

 is made for measurement of the first 30 harmonics. As stated above, 

 the function must be between 1/16 and 5/16 inch in length and no 

 higher than its length. At the speeds customarily used for recording 

 sound on film this corresponds to a fundamental frequency of from 

 65 to 310 cycles per second, or 1950 to 9300 cycles per second for the 

 30th harmonic. 



The smallest harmonic which the instrument will indicate is about 

 2 per cent of the peak which it can accommodate. In connection with 

 this statement, it should be remembered, however, that for many 

 functions the largest harmonic in the analysis is considerably less than 

 the peak amplitude of the function, which reduces the effective ampli- 

 tude range. 



An interesting check on the operation of the analyzer can be ob- 

 tained by making an analysis of a simple geometric wave form. 

 For example, a single cycle of a saw-toothed wave can easily be 

 formed by placing a straight edge obliquely across the sound track 

 slot of the analyzer. Such a wave form is shown at the top of Fig. 4. 

 It is known that this wave form can be resolved into a series of har- 



' Since a 1 per cent error in wave-length amounts to an error of about one-third 

 of a wave in the total length of a screen of the 30th order, errors of this magnitude are 

 quite objectionable in the higher order screens, although unimportant in the low 

 orders. 



8 Unpublished work. 



