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The just audible tonality of short exponential and Gaussian pure tone bursts
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Image of FIG. 1.
FIG. 1.

Test signal examples. The solid line shows a 500 Hz pure tone that has exponential attack and decay functions. The dashed line is also a 500 Hz pure tone, but it has Gaussian attack and decay functions. T A = 15 ms and T D = 50 ms.

Image of FIG. 2.
FIG. 2.

Example of a Gaussian (dashed) and an exponential (solid) envelope. Both signal envelopes have the same total energy and T D = T A = 5 ms for both envelope functions.

Image of FIG. 3.
FIG. 3.

Frequency spectra of three different 2000 Hz tone bursts. The dashed curve is the DFT of a single (decay) slope signal, the solid curve is an exponential signal, and the dash-dot curve a Gaussian-shaped signal. All signals have the same total energy. The Gaussian and exponential signals have T D = T A = 5 ms and the single slope signal has T D = 5 ms and T A = 0.

Image of FIG. 4.
FIG. 4.

(Color online) Reassigned spectrogram of one headphone impulse response. RMS filtering was applied along the time-domain to make the spectrogram more readable. Computational parameters: Window type = Bartlett window, window length = 111 samples, NFFT = 211, window overlap = maximum = minimum time increments = one sample.

Image of FIG. 5.
FIG. 5.

Illustration of loudness compensation. The solid curve shows the value that the signal must be multiplied by to obtain equal loudness as a function of total signal duration (i.e., T A + T D for the test signals used in this paper), irrespective of frequency. The dashed curve represents the loudness level decrement in phon (Ref. 21).

Image of FIG. 6.
FIG. 6.

The structure of the main listening test based on the method of limits.

Image of FIG. 7.
FIG. 7.

The averaged (over all valid listeners) results for test 1 (top)–test 4 (bottom). The subscript D denotes decay; A, attack; ASC, ascending; DESC, descending (refer to Fig. 6); JAT, just audible tonality; and IRconv, convolution with headphone impulse response. The error bars for ASC and DESC represent one standard deviation.

Image of FIG. 8.
FIG. 8.

Signal Q-values corresponding to all T JAT.

Image of FIG. 9.
FIG. 9.

T JAT as a function of signal Q-values.

Image of FIG. 10.
FIG. 10.

Reassigned spectrogram of an exponential 2500 Hz tone burst with T A= T D = 3 ms.

Image of FIG. 11.
FIG. 11.

Reassigned spectrogram of a 2500 Hz Gaussian tone burst with T A = T D= 3 ms.

Image of FIG. 12.
FIG. 12.

Reassigned spectrogram of an exponential 2500 Hz tone burst with T A = 0 and T D = 3 ms.

Image of FIG. 13.
FIG. 13.

Reassigned spectrogram of a 8 ms long 2500 Hz pure tone burst (rectangular window).


Generic image for table

An overview of the stimuli envelopes and loudness levels used during the different listening tests.


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752b84549af89a08dbdd7fdb8b9568b5 journal.articlezxybnytfddd
Scitation: The just audible tonality of short exponential and Gaussian pure tone bursts