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 a design trade-off between
reduction of aliasing and maintaining signal up to the Nyquist frequency and the frequency
content of the input signal.
Optical applications In the case of optical image sampling, as
by image sensors in digital cameras, 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 cameras 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 microlens array alone, if near 100% effective, can provide a significant
anti-aliasing effect, while in color filter array cameras, an additional filter is generally
needed to reduce aliasing to an acceptable level.
Sensor based anti-aliasing filter simulation The Pentax K-3 from Ricoh introduced a unique
sensor-based anti-aliasing filter. The filter works by micro vibrating the sensor element.
The user can turn the vibration on or off, selecting anti-aliasing or no anti-aliasing.
Audio applications 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 filters at the output of such systems, for
example in music players. In the latter case, the filter functions 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. Oversampling
A technique known as oversampling 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. Bandpass signals
Often, an anti-aliasing filter is a low-pass 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. 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, and the sampling rate would be no less than 400 kHz, but should
also satisfy other constraints to prevent aliasing.
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.
See also Spatial anti-aliasing
Sampling References