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Noise canceling headphones use a microphone to capture noise in order to cancel it. How is it guaranteed that the microphone will not record the actual signal and attenuate it?

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The microphone will record the noise on the outside and the speaker sits on the inside with a bit of passive sound shielding in between. Outside noise will reach the microphone unattenuated, but the actual signal will be attenuated by the passive shielding. The noise that reaches the speakers attenuated by the passive sound shielding and the circuit of the active noise canceling will simulate the effect of the passive shielding to generate the right amount of anti-noise to add to the actual signal for playback on the speaker. The circuit can also simulate how much of the actual signal reaches the microphone and compensate for that or it can just ignore that issue because this effect would only cause a small attenuation of actual signal.

Example: Lets say our passive shielding reduces sound levels of signals traveling through it by 75%, so 25% reaches the other side. Actual signal on the inside without noise canceling would be 1.0, noise on the outside would be 1.0 as well. Without noise canceling noise level on the inside would 0.25 and actual signal on the outside would 0.25. So the microphone would record 1.0 noise + 0.25 noise, now when we turn on active noise canceling, as a first order model, the circuit would simulate the attenuation of the shielding and subtract 0.25 noise and 0.0625 actual signal. If the attenuation is simulated perfectly, on the inside we would get 0.9375 actual signal and no noise. SNR is significantly improved. Of course this is just a first order model, the attenuation provided by the passive shielding does not have a flat frequency response and the microphone has also some electrical noise, that will be added to the speaker signal. If the simulation of the passive attenuate is not perfect, we will also add extra noise. We also need to adjust for the frequency response and gain of microphone and speaker. Small errors can easily cause us to add more noise to the signal or subtract to much from it.

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  • $\begingroup$ Passive shielding blocks high frequency sound, but it is not effective for low frequency sound. So, the "noise" recorded by the microphone will have low frequency component of the the signal as well. This poses a danger of attenuating low frequency component of the signal to a great extent. How this is avoided? $\endgroup$
    – akm
    May 28 '16 at 5:48
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As you'll notice, they not only have one (or typically, multiple) microphone(s), but also an input to let them know what should be audible.

Simply put, they observe what they should be playing, and cancel out everything that's not that.

Now, if you know what you don't care about exactly, you can simply subtract that from the observation, i.e. the signal they give to the speakers is more or less simply subtracted from what they record with the microphones.

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  • $\begingroup$ Since the microphone is in close vicinity of the signal, it must record the signal as well, particularly low frequency components of the signal which are not blocked by foam and other materials. Then, how such components are prevented from being subtracted from the signal? $\endgroup$
    – akm
    May 28 '16 at 5:52
  • $\begingroup$ @user3357019: mathematically, using a $-$ sign, as explained. Really! The headphones have a processor that calculates what of the microphone signal is part of what was played back the speaker, and just "ignore" that, and cancel the rest. $\endgroup$ May 28 '16 at 7:02

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