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Ananti-aliasing filter (AAF) is afilter used before asignal sampler to restrict thebandwidth of asignal to satisfy theNyquist–Shannon sampling theorem over theband of interest. Since the theorem states that unambiguous reconstruction of the signal from its samples is possible when thepower of frequencies above theNyquist frequency is zero, abrick wall filter is an idealized but impractical AAF.[a] A practical AAF makes a trade off between reducedbandwidth and increasedaliasing. A practical anti-aliasing filter will typically permit some aliasing to occur or attenuate or otherwise distort some in-band frequencies close to the Nyquist limit. For this reason, many practical systems sample higher than would be theoretically required by a perfect AAF in order to ensure that all frequencies of interest can be reconstructed, a practice calledoversampling.
In the case ofoptical image sampling, as byimage sensors indigital cameras, the anti-aliasing filter is also known as anoptical low-pass filter (OLPF),blur filter, orAA filter. The mathematics of sampling intwo spatial dimensions is similar to the mathematics oftime-domain sampling, but the filter implementation technologies are different.
The typical implementation indigital cameras is two layers ofbirefringent material such aslithium niobate, which spreads each optical point into a cluster of four points.[1] The choice of spot separation for such a filter involves a tradeoff among sharpness, aliasing, and fill factor (the ratio of the active refracting area of amicrolens array to the total contiguous area occupied by the array). In amonochrome orthree-CCD orFoveon X3 camera, the microlens array alone, if near 100% effective, can provide a significantanti-aliasing function,[2]while in color filter array (e.g.Bayer filter) cameras, an additional filter is generally needed to reduce aliasing to an acceptable level.[3][4][5]
Alternative implementations include thePentax K-3's anti-aliasing filter, which applies smallvibrations to the sensor element.[6][promotion?]
Anti-aliasing filters are used at the input of ananalog-to-digital converter. Similar filters are used asreconstruction filters at the output of adigital-to-analog converter. In the latter case, the filter prevents imaging, the reverse process of aliasing where in-band frequencies are mirrored out of band.
Withoversampling, a higher intermediate digital sample rate is used, so that a nearly idealdigital filter cansharplycut off aliasing near the original lowNyquist frequency and give betterphase response, while a much simpleranalog filter can stop frequencies above the new higher Nyquist frequency. Because analog filters have relatively high cost and limited performance, relaxing the demands on the analog filter can greatly reduce both aliasing and cost. Furthermore, because somenoise is averaged out, the higher sampling rate can moderately improvesignal-to-noise ratio.
A signal may be intentionally sampled at a higher rate to reduce the requirements and distortion of the anti-alias filter. For example, compareCD audio withhigh-resolution audio. CD audio filters the signal to a passband edge of 20 kHz, with a stopband Nyquist frequency of 22.05 kHz and sample rate of 44.1 kHz. The narrow 2.05 kHz transition band requires a compromise between filter complexity and performance. High-resolution audio uses a higher sample rate, providing both a higher passband edge and larger transition band, which allows better filter performance with reduced aliasing, reduced attenuation of higher audio frequencies and reduced time and phase domain signal distortion.[7][8][failed verification][9][10]
Often, an anti-aliasing filter is alow-pass filter; this is not a requirement, however. Generalizations of the Nyquist–Shannon sampling theorem allow sampling of other band-limitedpassband signals instead ofbaseband signals.
For signals that are bandwidth limited, but not centered at zero, aband-pass filter can be used as an anti-aliasing filter. For example, this could be done with asingle-sideband modulated orfrequency modulated signal. If one desired to sample anFM radio broadcast centered at 87.9 MHz and bandlimited to a 200 kHz band, then an appropriate anti-alias filter would be centered on 87.9 MHz with 200 kHz bandwidth (orpassband of 87.8 MHz to 88.0 MHz), and the sampling rate would be no less than 400 kHz, but should also satisfy other constraints to preventaliasing.[specify]
It is very important to avoid input signal overload when using an anti-aliasing filter. If the signal is strong enough, it can causeclipping at theanalog-to-digital converter, even after filtering. Whendistortion due to clipping occurs after the anti-aliasing filter, it can create components outside thepassband of the anti-aliasing filter; these components can then alias, causing the reproduction of other non-harmonically related frequencies.[11]
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