Frequency response adaptation in binaural hearing . David Griesinger Cambridge MA USA www.DavidGriesinger.com. Introduction. This paper proposes fundamental questions about the properties of human hearing.
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Cambridge MA USA
To answer these questions the author constructed an accurate physical model of his own hearing, including the ear canal and eardrum. The eardrum impedance is modeled with a resistance tube. The pinna compliance is modeled by cutting away the inside of the pinna casting.
Tiny probe microphones were also built with a very soft tip. This allows binaural recording of performances at the author’s eardrums, correct headphone calibration, and verification of the accuracy of the dummy head model.
Over a long period of time the brain builds spectral maps of the features in HRTFs that define up/down and back/front information. When a sound is heard these features are compared to the maps, and a localization is found.
When a match has been found, the perceptible features of the particular HRTF are removed, again from a fixed spectral map.
But this spectrum is altered by an adaptive equalizer, which acts to make all frequency bands equally perceived. The time constant of this mechanism for the author is about 5 minutes. It may be shorter for some individuals.
This equalizer can correct for gross errors in timbre if given sufficient time.
When we listen to binaural recordings with headphones the whole process is broken. Headphones match individuals very poorly (as we will see). None of the spectral features match the fixed HRTF maps. The brain is confused, and the subject perceives the sound inside the head.
But the adaptive equalizer is still active – and after a time period the sound is perceived as frequency balanced.
Sound enters basilar membrane at the oval window. High frequencies excite the membrane near the entrance, passing through it and exiting through the second window below.
Low frequencies travel further down the spiral, until they excite the membrane and pass through.
Strong low frequencies disturb the high frequency portion of the membrane, causing the well know phenomenon of upward masking.
Upward masking is a purely mechanical effect, and it cannot be compensated by adaptive equalization. The high frequencies are simply not detected.
Intelligibility is frequently low in acoustic spaces because there is little low frequency absorption, and the LF acoustic power is boosted.
We adapt to the frequency imbalance, and say the sound is OK – but unintelligible
If safe, comfortable probe microphones are available, it is possible to make accurate binaural recordings. First we measure the headphone response at the eardrum – response H. We can then record with the same probe microphones. If we equalize the recording with the inverse of H, H’, the recording will play back with perfect fidelity. (Note that measuring the headphone at the eardrum eliminates the second instance of the ear canal.)
If we want to play back the binaural recording over speakers, or if we want to play loudspeaker music over headphones, we need to measure the spectrum of a carefully equalized loudspeaker at the eardrums of the listener. This is the spectrum S. We then equalize the binaural recording with S’, and we can play it over speakers. Equalizing the phones with H’S allows playback of both binaural and loudspeaker mixed music. H’S is the inverse of the free-field earphone response
This graph shows the frequency response and time response of the digital inverse of the two probes as measured against a B&K 4133 microphone.
Matlab is used to construct the precise digital inverse of the probe response, both in frequency and in time. The resulting probe response is flat from ~25Hz to 17kHz. In general, I prefer NOT to use a mathematical inverse response, as these frequently contain audible artifacts. I minimized these artifacts here by carefully truncating the measured response as a function of frequency.
Here are pictures of a partially blocked canal and a fully blocked canal. The following data applies to the fully blocked measurements, but the partially blocked measurements are similar.
Twenty different HRTFs were measured with a blocked canal, equalized by the above EQ, and the difference between them and the open ear canal are plotted. This data supports Hammershoi and Muller’s contention that that the directional properties of the measured HRTFs are preserved by the blocked measurement, at least to a frequency of ~7kHz.
Note the vertical scale is +-30dB. The errors at 7-10k are significant.
Using the same method, I measured three headphones. Blue is the AKG 701, red is the AKG 240, and Cyan is the Sennheiser 250 The curves plot the difference between the blocked and unblocked measurement, with the measured HRTF at azimuth 15, elevation 0 as a reference. The vertical scale is +-30dB. Errors of at least 10dB exist at midband.
Blue – and old but excellent noise protection earphone by Sharp. Red – Ipod earbuds. The error in the blocked measurements are large enough to prevent accurate localization of binaural recordings.
Top – ISO equal loudness curves for 80dB and 60dB SPL. These are the average from many individuals, so features in them are broadened.
Bottom – (blue/red) averaged frontal response over a +-5 degree cone in front of the author, measured at the eardrums. The loudspeaker was equalized to 200Hz.
Bottom - black/cyan – the same measurement for the author’s dummy head with no equalization. The difference in eardrum impedance above 8kHz boosts the response of the dummy – but this can be removed by equalization.
About 10 students from Helsinki University participated in the test.
The top left graph shows the equal loudness contours from the loudspeaker for each subject.
The other curves show the difference between this curve and the equal loudness curves for four different headphones.
It was hoped that the Stax 303 phones would show less individual variation. This was not the case.
(blue = left ear, red = right cyan = author’s left ear)
The Philips phones were an insert type. These also showed large variation among individuals.