Maximal limits, waveform amplitude derivatives, and responses in individual neurons.
An important determinant of spike timing in individual spatially-selective neurons may not be amplitude, per se, but changes in amplitude. The figures below therefore consider the derivatives of amplitude envelopes.
Envelope derivative weights contributing to the firing of individual spatially-selective neurons. The demonstration below is for a pair of 150 ms ‘lead/lag’ noise-bursts, passed through a 500 Hz auditory filter, when the ‘leading’ signal is spatialized to the right with an ITD of 0.25 ms and the ‘lagging’ signal is spatialized, after a 2.5 ms delay, to the left with an ITD of -0.25 ms.
The weights are generally strong when the amplitudes of both signals are rising and ITD is positive, reflecting the ‘leading’ signal’s positive ITD (0.25 ms). In contrast, weights are generally weak when the amplitudes of the signals are declining and ITDs are negative, reflecting the ‘lagging’ signal’s negative ITD (-0.25 ms).
To understand how weights are computed, consider the amplitude modulated waveform (gray lines) and its amplitude envelope (dark circles) shown below in panel A. Principal outputs are envelope weights (panel B) ascribed incrementally to envelope derivative values (A’t) using the logistic function shown in panel C.
For further explanation, see analogous figures and descriptions where envelope amplitude weights are modeled.
Envelope weights and other measures derived from amplitude envelope derivatives when the upper weight limit = 5
Envelope weights and other measures derived from amplitude envelope derivatives when the upper weight limit = 2
Envelope weights and other measures derived from amplitude envelope derivatives when the upper weight limit = 10
Notes:
- • ‘Lead/lag’ noise-pairs are typically associated with the ‘precedence effect.’ I hesitate to mention this, even in these notes, because the term carries an enormous amount of academic baggage. Another example of ‘persuasive writing’ leading to presumptuous dogma…
Igor Pro experiment file used to generate figures:
This experiment require the SpatialHearing XOP:
