Anti-aliasing filter
Encyclopedia
An anti-aliasing filter is a filter used before a signal sampler, to restrict the bandwidth of a signal to approximately satisfy the sampling theorem.
Since the theorem states that unambiguous interpretation of the signal from its samples is possible when the power of frequencies above the Nyquist frequency
is zero, a real anti-aliasing filter can generally not completely satisfy the theorem.
A realizable anti-aliasing filter will typically permit some aliasing
to occur; the amount of aliasing that does occur depends on how good the filter is and what the frequency content of the input signal is.
Anti-aliasing filters are commonly used at the input of digital signal processing
systems, for example in sound digitization systems; similar filters are used as reconstruction filter
s at the output of such systems, for example in music players. In the later case, the filter is to prevent aliasing in the conversion of samples back to a continuous signal, where again perfect stop-band rejection would be required to guarantee zero aliasing.
The theoretical impossibility of realizing perfect filters is not much an impediment in practice, though practical considerations do lead to system design choices such as oversampling to make it easier to realize "good enough" anti-aliasing filters.
In the case of optical image sampling, as by image sensor
s in digital camera
s, the anti-aliasing filter is also known as an optical lowpass filter or 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 digital camera
s is two layers of birefringent material such as lithium niobate
, which spreads each optical point into a cluster of four points.
The choice of spot separation for such a filter involves a tradeoff among sharpness, aliasing, and fill factor. In a monochrome
or three-CCD or Foveon X3
camera, the fill factor
alone, if near 100% effective with microlenses, can provide a significant anti-aliasing effect,
while in color filter array (CFA, e.g. Bayer filter
) cameras, an additional filter is generally needed to reduce aliasing to an acceptable level.
is commonly used in audio conversion, especially audio output. The idea is to use a higher intermediate digital sample rate, so that a nearly-ideal digital filter can sharply cut off aliasing near the original low Nyquist frequency
, while a much simpler analog filter can stop frequencies above the new higher Nyquist frequency.
The purpose of oversampling is to relax the requirements on the anti-aliasing filter, or to further reduce the aliasing.
Since the initial anti-aliasing filter is analog, oversampling allows for the filter to be cheaper because the requirements are not as stringent, and also allows the anti-aliasing filter to have a smoother frequency response, and thus a less complex phase response.
On input, an initial analog anti-aliasing filter is relaxed, the signal is sampled at a high rate, and then downsampled using a nearly ideal digital anti-aliasing filter.
; however, this is not a requirement. Generalizations of the Nyquist–Shannon sampling theorem
allow sampling of other band-limited passband
signals instead of baseband
signals – see undersampling
.
For signals that are bandwidth limited, but not centered at zero, a band-pass filter
can be used as an anti-aliasing filter. For example, this could be done with a single-sideband modulated
or frequency modulated signal. If one desired to sample an 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 pass-band 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
.
, 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. In digital audio
, the resulting aliased distorted signal of "digital clipping
" has a characteristic sound that can be easily recognized.
Since the theorem states that unambiguous interpretation of the signal from its samples is possible when the power of frequencies above the Nyquist frequency
Nyquist frequency
The Nyquist frequency, named after the Swedish-American engineer Harry Nyquist or the Nyquist–Shannon sampling theorem, is half the sampling frequency of a discrete signal processing system...
is zero, a real anti-aliasing filter can generally not completely satisfy the theorem.
A realizable anti-aliasing filter will typically permit some aliasing
Aliasing
In signal processing and related disciplines, aliasing refers to an effect that causes different signals to become indistinguishable when sampled...
to occur; the amount of aliasing that does occur depends on how good the filter is and what the frequency content of the input signal is.
Anti-aliasing filters are commonly used at the input of digital signal processing
Digital signal processing
Digital signal processing is concerned with the representation of discrete time signals by a sequence of numbers or symbols and the processing of these signals. Digital signal processing and analog signal processing are subfields of signal processing...
systems, for example in sound digitization systems; similar filters are used as reconstruction filter
Reconstruction filter
In a mixed-signal system , a reconstruction filter is used to construct a smooth analogue signal from a digital input, as in the case of a digital to analogue converter or other sampled data output device....
s at the output of such systems, for example in music players. In the later case, the filter is to prevent aliasing in the conversion of samples back to a continuous signal, where again perfect stop-band rejection would be required to guarantee zero aliasing.
The theoretical impossibility of realizing perfect filters is not much an impediment in practice, though practical considerations do lead to system design choices such as oversampling to make it easier to realize "good enough" anti-aliasing filters.
Optical anti-aliasing filter
Image sensor
An image sensor is a device that converts an optical image into an electronic signal. It is used mostly in digital cameras and other imaging devices...
s in digital camera
Digital camera
A digital camera is a camera that takes video or still photographs, or both, digitally by recording images via an electronic image sensor. It is the main device used in the field of digital photography...
s, the anti-aliasing filter is also known as an optical lowpass filter or 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 digital camera
Digital camera
A digital camera is a camera that takes video or still photographs, or both, digitally by recording images via an electronic image sensor. It is the main device used in the field of digital photography...
s is two layers of birefringent material such as lithium niobate
Lithium niobate
Lithium niobate is a compound of niobium, lithium, and oxygen. Its single crystals are an important material for optical waveguides, mobile phones, optical modulators and various other linear and non-linear optical applications.-Properties:...
, which spreads each optical point into a cluster of four points.
The choice of spot separation for such a filter involves a tradeoff among sharpness, aliasing, and fill factor. In a monochrome
Monochrome
Monochrome describes paintings, drawings, design, or photographs in one color or shades of one color. A monochromatic object or image has colors in shades of limited colors or hues. Images using only shades of grey are called grayscale or black-and-white...
or three-CCD or Foveon X3
Foveon X3 sensor
The Foveon X3 sensor is a CMOSimage sensor for digital cameras, designed by Foveon, Inc. and manufactured by National Semiconductorand Dongbu Electronics....
camera, the fill factor
Fill factor
Fill factor may refer to:*Fill factor , the ratio of maximum obtainable power to the product of the open-circuit voltage and short-circuit current*In vision science, the ratio of view areas to the object visible areas....
alone, if near 100% effective with microlenses, can provide a significant anti-aliasing effect,
while in color filter array (CFA, e.g. Bayer filter
Bayer filter
A Bayer filter mosaic is a color filter array for arranging RGB color filters on a square grid of photosensors. Its particular arrangement of color filters is used in most single-chip digital image sensors used in digital cameras, camcorders, and scanners to create a color image...
) cameras, an additional filter is generally needed to reduce aliasing to an acceptable level.
Applicability of oversampling
A technique known as oversamplingOversampling
In signal processing, oversampling is the process of sampling a signal with a sampling frequency significantly higher than twice the bandwidth or highest frequency of the signal being sampled...
is commonly used in audio conversion, especially audio output. The idea is to use a higher intermediate digital sample rate, so that a nearly-ideal digital filter can sharply cut off aliasing near the original low Nyquist frequency
Nyquist frequency
The Nyquist frequency, named after the Swedish-American engineer Harry Nyquist or the Nyquist–Shannon sampling theorem, is half the sampling frequency of a discrete signal processing system...
, while a much simpler analog filter can stop frequencies above the new higher Nyquist frequency.
The purpose of oversampling is to relax the requirements on the anti-aliasing filter, or to further reduce the aliasing.
Since the initial anti-aliasing filter is analog, oversampling allows for the filter to be cheaper because the requirements are not as stringent, and also allows the anti-aliasing filter to have a smoother frequency response, and thus a less complex phase response.
On input, an initial analog anti-aliasing filter is relaxed, the signal is sampled at a high rate, and then downsampled using a nearly ideal digital anti-aliasing filter.
Bandpass signals
Often, an anti-aliasing filter is a low-pass filterLow-pass filter
A low-pass filter is an electronic filter that passes low-frequency signals but attenuates signals with frequencies higher than the cutoff frequency. The actual amount of attenuation for each frequency varies from filter to filter. It is sometimes called a high-cut filter, or treble cut filter...
; however, this is not a requirement. Generalizations of the Nyquist–Shannon sampling theorem
Nyquist–Shannon sampling theorem
The Nyquist–Shannon sampling theorem, after Harry Nyquist and Claude Shannon, is a fundamental result in the field of information theory, in particular telecommunications and signal processing. Sampling is the process of converting a signal into a numeric sequence...
allow sampling of other band-limited passband
Passband
A passband is the range of frequencies or wavelengths that can pass through a filter without being attenuated.A bandpass filtered signal , is known as a bandpass signal, as opposed to a baseband signal....
signals instead of baseband
Baseband
In telecommunications and signal processing, baseband is an adjective that describes signals and systems whose range of frequencies is measured from close to 0 hertz to a cut-off frequency, a maximum bandwidth or highest signal frequency; it is sometimes used as a noun for a band of frequencies...
signals – see undersampling
Undersampling
In signal processing, undersampling or bandpass sampling is a technique where one samples a bandpass filtered signal at a sample rate below the usual Nyquist rate In signal processing, undersampling or bandpass sampling is a technique where one samples a bandpass filtered signal at a sample rate...
.
For signals that are bandwidth limited, but not centered at zero, a band-pass filter
Band-pass filter
A band-pass filter is a device that passes frequencies within a certain range and rejects frequencies outside that range.Optical band-pass filters are of common usage....
can be used as an anti-aliasing filter. For example, this could be done with a single-sideband modulated
Single-sideband modulation
Single-sideband modulation or Single-sideband suppressed-carrier is a refinement of amplitude modulation that more efficiently uses electrical power and bandwidth....
or frequency modulated signal. If one desired to sample an 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 pass-band 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
Aliasing
In signal processing and related disciplines, aliasing refers to an effect that causes different signals to become indistinguishable when sampled...
.
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 converterAnalog-to-digital converter
An analog-to-digital converter is a device that converts a continuous quantity to a discrete time digital representation. An ADC may also provide an isolated measurement...
, 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. In digital audio
Digital audio
Digital audio is sound reproduction using pulse-code modulation and digital signals. Digital audio systems include analog-to-digital conversion , digital-to-analog conversion , digital storage, processing and transmission components...
, the resulting aliased distorted signal of "digital clipping
Clipping (audio)
Clipping is a form of waveform distortion that occurs when an amplifier is overdriven and attempts to deliver an output voltage or current beyond its maximum capability...
" has a characteristic sound that can be easily recognized.