Contains reports on one research project.Joint Services Electronics Programs (U.S. Army, U. S. Navy, and U. S. Air Force) under Contract DAAB07-71-C-030

Milder, F. L.

Searle, Campbell L.

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XII. SIGNAL PROCESSINGAcademic and Research StaffProf. A. G. Bose Prof. D. E. Nelsen Prof. H. J. ZimmermannProf. J. D. Bruce Prof. A. V. Oppenheim Dr. M. V. CerrilloProf. C. L. SearleGraduate StudentsJ. B. Bourne M. F. Davis T. L. RhyneM. Bruce-Lockhart D. A. Feldman J. R. Samson, Jr.R. M. MersereauA. A QUANTITATIVE DEFINITION OF PERCUSSIVENESSThis is a report on a preliminary study of the subjective definition of percussiveness.Sinusoidal tone bursts at 1000 Hz of the shapes shown in Figs. XII-1 and XII-2 were pre-sented to a subject at a repetition rate of one per three seconds. The subject was allowedto listen to each burst as many times as he deemed necessary and was asked torespond to the leading edge by identifying the burst with percussive onset, smoothonset, borderline between percussive and smooth, near borderline but percussive,or near borderline but smooth. For data processing these responses were givennumerical values respectively of 0, 10, 5, 2. 5, and 7. 5. The subject was testedon approximately 20 different bursts of variable rise time (tr), fall time (tf), andoverall length (T) on each day of testing, and on about 100 different bursts altogether.The testing on subsequent days overlapped so as to permit us to evaluate consis-tency of the judgments. The shape of the bursts was achieved by sending a sinewave through two consecutive electronic switches; one controlled tr, one controlledtf, and the timing of the switches controlled T. The tests were performed at 65 dBSPL, a level chosen by the subject for clear distinguishability without discomfort.Stimuli were delivered through headphones in a quiet room.The results were classified according to two types of tone bursts: Class I,where T was essentially equal to tr + tf; and Class II, where T > tr + tf + 20 msand tf _ 10 ms. We noticed that for Class I, if we place the averaged responseson a plot of tr versus T (see Fig. XII-1) the plane of the graph can be broken upinto three areas: an area of precisely the value 10, an area of precisely the value 0,and a solid band in between these two which includes all values between 0 and 10.We analyze the data as follows. Since an average response of 5 can be obtainedin various ways (for example, one judgment of borderline, or one judgment of smoothonset and one of percussive, etc.) and since there were, in actuality, very fewThis work is supported by the Joint Services Electronics Programs (U. S. Army,U.S. Navy, and U. S. Air Force) under Contract DAAB07-71-C-0300.QPR No. 103 177(XII. SIGNAL PROCESSING)ENVELOPE SHAPEK t rJ L10 10I0 10O O10 10 10 10 10JUDGMENT SCALEI I I0 5 10PERCUSSIVE BORDERLINE SMOOTH10 10 10SMOOTH ONSET10 10S 10D---.e.o __S 0 7.5BAND OFCONFUSION50 100 150 200T (ms)Fig. XII-1. Class I tone bursts.responses of borderline during the tests, we may choose the center line of the bandas the true border. In addition, we noticed that for a given value of T the bandis 10 ms wide, and we therefore define this as a band of confusion. Near the cen-ter of the band the judgments are difficult to make and not necessarily consistent;near the edges of the band the judgments are difficult but consistent.In Class II, the results plotted in Fig. XII-2 are more erratic. If we chooseto maintain the same true border, the band of confusion must be widened on thepercussive side to at least 15 ms. Possibly we could change the border slightlyand increase the band somewhat less. It is evident, however, that any modifica-tion of Class II is strictly conjectural because of the sparsity of the data.Our conclusions are:1. There exists a borderline tb as a function of T for basically triangular tonebursts.t b =-.175 T + 45 ms for T - 200 msFor tr > tb we have smooth onset; for tr < tb we have percussive onset,2. There is a band of confusion of ±5 ms for any value of t b.QPR No. 103 178(XII. SIGNAL PROCESSING)3. For a given T, either t b, or the width of the band of confusion, or both, arefunctions of the burst's shape.ENVELOPE SHAPET10BORDERLINEMODIFIDED BOSMOOTH ONSET10)RDERLINE10 1050 100 150T(ms)WIDENEDBAND OFCONFUSION200Fig. XII-2. Class II tone bursts.Although an explanation of the dependence of tb on T may require more investi-gation, one possibility is that the subjective judgment of percussiveness may beproportional to the energy concentrations outside of the area of the exact frequencypresented. If this is so, shortening the burst length T increases these outsideenergy concentrations and hence increases percussiveness. This explanation agreesqualitatively with the results. Experiments are planned to see if the agreement isquantitative as well.F. L. Milder, C. L. SearleQPR No. 103 179- 7.5

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