Click here to purchase the entire book in PDF format. Masking and Critical Bands Take a noise signal with a white spectrum and band-limit it with a filter that has a centre frequency of 2 kHz. Play that noise at the same time as you play a sinusoidal tone at 2 kHz and make the tone very quiet relative to the noise. You will not be able to detect the tone because the noise signal will mask it (``mask'' is a psychoacoustician's fancy word that means ``drowns out'' in everyday speech). This is true even if you would normally be able to hear the tone if the noise wasn't there. It's because of the noise that you can't hear the tone. Now, turn up the level of the tone until you can hear it and write down its level (if there was no masking noise) in dBspl. Increase the bandwidth of the noise signal (but do not turn up its level) and repeat the experiment. You'll find that your threshold for detection of the tone will be higher. In other words, if the bandwidth of the masking signal is increased, you have to turn up the tone more in order to be able to hear it. Increase the bandwidth and do the experiment again. Then do it again. If you keep doing this, you'll notice that something interesting will happen. As you increase the bandwidth of the masker, the threshold for detection of the tone will increase up to a certain bandwidth. Then it won't increase any more. This is illustrated in Figure 5.10. Figure 5.10: Threshold of detection of a pure tone in the presence of a band-limited noise signal. Notice that the greater the bandwidth, the higher the threshold until a bandwidth is reached, after which an increase in bandwidth has no effect on the threshold. Note that these values are inaccurate and have been simplified for the sake of clarity. See [Moore, 1989] for the real version of this graph. This means that, for a given frequency, once you get far enough away in frequency, the noise does not contribute to the masking of the tone. (As an example, take an extreme case: you cannot mask a tone at 100 Hz with noise centered at 10 kHz.) The tone can only be masked by signals that are near it in frequency - anything outside that frequency range is irrelevant. The bandwidth at which the threshold for the detection of the tone stops increasing is called the critical bandwidth. So, in the case of the 2 kHz tone illustrated in Figure 5.10, the critical bandwidth is 400 Hz. If noise outside the critical bandwidth does not help to mask the tone, then we can assume that the auditory system is like a number of bandpass filters connected in parallel. If a tone and a noise are in the same filter (called an auditory filter), then the noise will contribute to the masking of the tone. If they are in different filters, then the noise cannot mask the tone. The width of these filters is measurable for any given centre frequency using the technique described above for measuring critical bandwidth. Consequently, these filters are called critical bands. So far, we have been talking about a tone being masked by a noise band where the tone has the same frequency as the centre frequency of the masking noise. Let's look at what happens if we change the frequency of the tone. Figure 5.11: Threshold of hearing curve in a quiet environment. [Zwicker and Fastl, 1999] Figure 5.11 shows your threshold of hearing contour when you're in a very quiet environment. As we saw above, if white noise is played, band limited to a critical bandwidth with a centre frequency of 1 kHz, it will mask a 1 kHz tone. In other words, we can say that the threshold of detection of the tone is raised by the masking noise. However, that noise will also be able to mask a tone at other frequencies. The further you get from the centre frequency of the masking noise, the lower the threshold of detection until, if the tone's frequency is outside the critical band, the threshold of detection is the threshold of hearing. We can therefore think of a masking noise as raising the threshold of hearing in an area around its centre frequency. Figure 5.12 shows the change in the threshold of detection caused by a masking noise with a centre frequency of 1 kHz and an level of 60 dBspl. As you can see, that threshold is not raised at only 1 kHz, but at surrounding frequencies. Figure 5.12: Threshold of detection curve in the presence of a masking noise with a bandwidth equal to the critical bandwidth, a centre frequency of 1 kHz and a level of 60 dBspl [Zwicker and Fastl, 1999]. As we discussed earlier, the amount that a masking noise will change the threshold of detection of a tone at its centre frequency depends on the bandwidth of the noise. It is also probably obvious that it will be dependent on the level of the masking noise. Figure 5.13 shows the change in the threshold of detection caused by a masking noise with a bandwidth equal to the critical bandwidth with a centre frequency of 1 kHz and various levels. Figure 5.13: The threshold of detection caused by a masking noise with a bandwidth equal to the critical bandwidth with a centre frequency of 1 kHz and various levels [Zwicker and Fastl, 1999]. Note that everything we've discussed in this chapter is known as simultaneous masking - meaning that the masking noise and the tone are presented to the listener simultaneously. You should also know that forwards masking (where the masking noise comes before the tone) and backwards masking (where the masking noise comes after the tone) exist as well. For more information on this, read [Moore, 1989] and [Zwicker and Fastl, 1999].