Anti-aliasing filter

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An anti-aliasing filter (AAF) is a

brick wall filter is an idealized but impractical AAF.[a] A practical AAF makes a trade off between reduced bandwidth and increased aliasing. 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 called oversampling
.

Optical applications

See also: Spatial anti-aliasing
Simulated photographs of a brick wall without (left) and with (right) an optical low-pass filter
Lowpassfilter
Optical low-pass filter (OLPF)

In the case of optical image sampling, as by image sensors in digital cameras, the anti-aliasing filter is also known as an optical low-pass filter (OLPF), blur filter, or AA filter. The mathematics of sampling in two spatial dimensions is similar to the mathematics of time-domain sampling, but the filter implementation technologies are different.

The typical implementation in

three-CCD or Foveon X3 camera, the microlens array alone, if near 100% effective, can provide a significant anti-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 the

promotion?
]

Audio applications

Anti-aliasing filters are used at the input of an analog-to-digital converter. Similar filters are used as reconstruction filters at the output of a digital-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.

Oversampling

Main article: Oversampling

With

analog 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 some noise is averaged out, the higher sampling rate can moderately improve signal-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, compare

CD audio with high-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]

Bandpass signals

See also: Undersampling

Often, an anti-aliasing filter is a low-pass filter; this is not a requirement, however. Generalizations of the Nyquist–Shannon sampling theorem allow sampling of other band-limited passband signals instead of baseband signals.

For signals that are bandwidth limited, but not centered at zero, a

FM 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 (or passband 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 prevent aliasing.[specify
]

Signal overload

It is very important to avoid input signal overload when using an anti-aliasing filter. If the signal is strong enough, it can cause clipping at the analog-to-digital converter, even after filtering. When distortion due to clipping occurs after the anti-aliasing filter, it can create components outside the passband of the anti-aliasing filter; these components can then alias, causing the reproduction of other non-harmonically related frequencies.[11]

Notes

  1. order
    .

References

  1. ISBN 0-240-51590-0
    .
  2. Bibcode:1974eosd.conf....1C. {{cite book}}: |journal= ignored (help
    )
  3. ^ Brian W. Keelan (2004). Handbook of Image Quality: Characterization and Prediction. Marcel–Dekker.
    ISBN 0-8247-0770-2
    .
  4. ^ Sidney F. Ray (1999). Scientific photography and applied imaging. Focal Press. p. 61.
    ISBN 978-0-240-51323-2
    .
  5. ^ Michael Goesele (2004). New Acquisition Techniques for Real Objects and Light Sources in Computer Graphics. Books on Demand. p. 34.
    ISBN 978-3-8334-1489-3
    .
  6. ^ "Pentax K-3". Retrieved November 29, 2013.
  7. ^ Kester, Walt. "Oversampling Interpolating DACs" (PDF). Analog Devices. Retrieved January 17, 2015.
  8. ^ Nauman Uppal (August 30, 2004). "Upsampling vs. Oversampling for Digital Audio". Audioholics. Retrieved October 6, 2012.
  9. ^ Story, Mike (September 1997). "A Suggested Explanation For (Some Of) The Audible Differences Between High Sample Rate And Conventional Sample Rate Audio Material" (PDF). dCS Ltd. Archived (PDF) from the original on November 28, 2009.
  10. ^ Lavry, Dan (1997). "Sampling, Oversampling, Imaging and Aliasing - a basic tutorial" (PDF). Lavry Engineering. Archived (PDF) from the original on June 21, 2015.
  11. ^ Level and distortion in digital broadcasting (PDF), retrieved May 11, 2021
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