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So according what I have read so far notch filter (or stop-band filter) can be used to get rid of the narrowband noise when it is present in the frequency spectrum of the received signal.

For example stray sine waves may impinge on the receiver as we listen to radio.

My question is, how would the notch filter detect the particular noise frequency in first place so that it could remove it?

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  • $\begingroup$ Use an adaptive notch filter. $\endgroup$ – Peter K. Sep 6 '16 at 19:52
  • $\begingroup$ A filter as is doesn't care about what it filters. It's designed once and filters away exactly what it's designed to filter away. If you want adaptivity, you'll need to implement more, for example, adaption, as Peter linked to. Again, be a bit careful with your terminology! A filter doesn't detect anything. $\endgroup$ – Marcus Müller Sep 6 '16 at 21:39
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For a given system and application, especially wideband sytems, sometimes we can consider dominant interfering signals. So a notch filter is tuned specefically on the frequency of the interferers. In such case, we remove part of the desired signal's energy as well, however, the narrowband interference wich is usually much stronger than the desired signal (in a narrow bandwidth only) is removed and its harmful effect is prevented.

As an example, you might have heard of ultra widebsnd systems that span over a large spectrum between 3.1 Ghz to 10.6 Ghz. They may interfere with WLAN at 5.6 Ghz. Therefore, the UWB receiver can deploy a notch filter at 5.6 GHz.

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