Journal of the Society of Motion Picture and Television Engineers (1950-1954)

not available for the more close-up echoes, the general indications are that the advantage for the differentiation becomes very much smaller. For the present considerations the advantage will be taken to become substantially negligible. Consequently the tolerance on the long sweeping excursions is taken as constant over the frequency range. Other classes of echo distortion than differentiation can be considered. That discussed, however, is generally typical, and others will not be explored here. Cumulation of Echoes The discussion so far has included only the very simple cases of a single echo, or two echoes quite far apart. In practice such a situation is likely to be rare, and the numbers of echoes from different sources and having various delays may be expected to be found. The simplest method of dealing with them is to assume that they add at random, both as signal amplitudes and as sinusoidal ripples in the amplitude and response characteristics. If this is the case, both signal amplitudes and ripple amplitudes cumulate on a root sum square basis. The tolerances then can logically be set in the same manner as before, but on the cumulated instead of the individual amplitudes. In practice, however, the tolerances are usually set on maximum rather than on rms (root mean square) excursions. The ratio of peak to rms amplitudes tends to increase as a number of sinusoidal ripples of different periodicities are added together. Hence there is some tendency for the maximum excursion to cumulate faster than the rss (root sum square) echo amplitude. An examination of possible systematic factors in the cumulation of echoes has been made by Fowler and Christopher.8 The first case comes when the echoes occur closely together. In the extreme situation the signal amplitudes add arithmetically instead of on a rss basis. It is similarly found that the subjective per ceptibility also adds faster than on the rss basis. Where the echoes which come close together are each close up to the original picture the ripple amplitudes in the transmission characteristics follow closefy the same shape regardless of the echo spacing, as was indicated in Figs. 9 and 10. They tend therefore also to add arithmetically rather than on the rss basis. Thus tolerances set on the cumulated excursions continue consistent, whether for single or multiple echoes. Where the echoes coming close together are all far from the original picture, the tendency for the ripple amplitudes in the transmission characteristics to add arithmetically continues, but not so markedly as for the closer-in echoes. Thus the excursions may cumulate somewhat more slowly than the subjective effect. The second case of a systematic factor comes when the echoes are well separated from each other. In the extreme situation the echoes tend to become independent. Complete independence would mean that the insertion of the additional echoes would not degrade the picture beyond the effect of the echoes already existing. Here the excursions cumulate somewhat faster than the subjective effect. This influence becomes less pronounced as the echo level is raised and as more echoes are cumulated. For general engineering purposes the law of random cumulation and use of the peak excursions probably represent the most useful simple guide to the tolerances to be applied. Where there is opportunity for a more detailed analysis of the echoes this evaluation may be found conservative or liberal according to the specific situation and may be revised to suit. A specific case of multiple echoes comes about when all the excursions come in only the amplitude-response or phase-shift characteristic and the other is smooth and flat. As was developed in Ref. 3, and indicated in the Appendix, 592 May 1953 Journal of the SMPTE VoL 60