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I purchased a pair of noise canceling headphones today and I was just wondering how exactly they are able to cancel out background noise?

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Briefly they take the waveform of the ambient noise then produce the inverse waveform which is then generated. The two waveforms effectively cancel out leaving a much quieter ambient sound level.

The important part is to be able to separate the wanted "noise" (music or voices) from the unwanted noise.

A search will give you several results that will provide much more detail.

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