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A common use for digital filtering is to reduce unwanted noise.
Take the example of a simple square wave. The frequency spectrum of a square wave consists of a fundamental at the square wave frequency, plus the odd harmonics decreasing in size:
If we applied a band pass filter centred around the fundamental, the signal to noise ratio would be improved because all the noise power outside the band would be suppressed:
But although the noise is suppressed, so too is significant signal power coming from the other signal frequency components. This signal power could have contributed to improving the signal to noise ratio. In fact, to make the best of all available signal power we want to include all frequency components where the signal is strong, and eliminate all frequency components where there is only noise:
The diagram shows a filter which has several bands - each centred on one of the signal frequency components. This filter will pass the maximum amount of signal power, while excluding all noise that does not coincide with a signal frequency component.
| Last updated: 9th July 1999 | http://www.bores.com/courses/advanced/matched/11_snr.htm