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Time-Intensity trading / Summing Localization

Title: Time-Intensity trading / Summing Localization
Dear colleagues,

I am looking for literature on time/intensity trading with presentation over two loudspeakers. I want to find out if anyone did a systematic study of time-intensity trading looking at what level difference between two channels is necessary for a given fixed time delay (within the summing localization range; 0<=tau<=1ms) so that a centrally positioned listener perceives the auditory event at an arbitrarily prescribed angle between the two loudspeakers. In other words is there a time-intensity panning law similar to tangent law for intensity stereophony (with no delays between leading and lagging loudspeakers)?

There seems to be many good papers on summing localization with loudspeakers. These generally look at lead/lag pairs with identical signal levels. Similarly, there seems to be many good papers on time/intensity trading but the delay between the two loudspeakers is generally higher than 1ms in these studies. Some operational curves for stereophonic systems are given in Franssen’s famed 1964 monograph “Stereophony”. However, these time-intensity trading curves are rather simplified and there doesn’t seem to be any justification as to whether these curves are applicable in practice when the time delay is in the summing localization range.

I was wondering if you know of any work on time-intensity trading in the summing localization range.

Thanks in advance,


Dr Hüseyin Hacıhabiboğlu
Centre for Digital Signal Processing Research (CDSPR)
King’s College London, Strand, London, WC2R 2LS
T: +44 (0)20 7848 1857 | F: +44 (0)20 7848 2932 | V: husshho (skype)
W: http://www.hacihabiboglu.org