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U. Glaeser

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FIGURE 27.10 Critical band index in Bark according to Eq. (27.17).<br />

relative to the threshold of audibility for the curve in Fig. 27.9(a) is almost 15 dB and the threshold of<br />

audibility for the tone of frequency 1.2 kHz is about 3 dB SPL). Similarly, for 50 and 60 dB maskers<br />

the maximum PMRs are calculated to be −22.5 and −23 dB, respectively.<br />

Masking curves for tone-masking-noise are similar but smoother, because no audible bits occur in<br />

this case. In order to reduce the influence of audible bits also in the tone-masking-tone case, a tone-like<br />

narrow-band noise instead of a pure tone should be used as masker. In practical audio signals this situation<br />

is observed rather than appearance of audible bits. That is why both cases with the tone as masker can<br />

be reduced to only one: a tone-like masker. The maximum PMR can be approximated by expression [14]<br />

in decibels<br />

in which z is numerically equal to the critical band index in Bark [54] defined as<br />

© 2002 by CRC Press LLC<br />

[Bark]<br />

Critical band index , z<br />

25<br />

20<br />

15<br />

10<br />

5<br />

10 -2<br />

0<br />

10 -1<br />

Frequency, f<br />

(27.16)<br />

(27.17)<br />

where frequency f is in kilohertz. The curve determined by Eq. (27.17) is plotted in Fig. 27.10.<br />

When a wideband flat noise is used to mask a pure tone, masking is much stronger than that just<br />

considered. It should, however, be stressed that only a narrow frequency band (the critical band) of the<br />

noise centered at the tonal frequency causes masking of this tone. If the bandwidth of the previously<br />

wideband masking noise is made narrower than the respective critical bandwidth (noise with the constant<br />

power spectral density is considered) and if the previous probe tone level was just below the masking<br />

threshold, then the intensity of this tone has to be lowered before it can be masked again. On the other<br />

hand, if the noise bandwidth is wider than this critical bandwidth, no significant change in the masking<br />

effect can be observed. In this case the maximum PMR, illustrated in Fig. 27.11, can be determined in<br />

decibels by expression [23]<br />

(27.18)<br />

where frequency f is again given in kilohertz. Pessimistically, a constant value PMR n ≈ −5.5 dB can be<br />

used independently from frequency. Simultaneous noise-masking-tone effect relative to the threshold of<br />

audibility in quiet with a masker of center frequency f c = 1.2 kHz, the critical bandwidth, and 40 dB SPL,<br />

is illustrated in Fig. 27.12.<br />

10 0<br />

[kHz]<br />

PMRt = – ( 14.5 + z)<br />

10 1<br />

z 13 arctan( 0.76f ) 3.5 arctan( f/7.5)<br />

2<br />

=<br />

+<br />

PMRn – 2.0 2.05 arctan( f/4)<br />

0.75 arctan f 2 =<br />

–<br />

– ( /2.56)

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