whenever one converts a signal to a digital form, a process of sampling is used to read parts of the analog signal at regular time or space intervals, all other parts of the analog signal is discarded (eg. occurs between the time when the signal is being read or, as in camera sensors, misses the photosite sensor).
in audio, we sample the sound at regular time intervals to capture instantaneous values, the higher the sampling rate, the closer the digital signal is to the original analog signal.
in imaging, we sample light using sensors arranged in an array, the distance between these sensors is the spatial sampling frequency in cycles per millimetre.
the famous Nyquest-Shannon sampling theorem says that we need to sample at twice the highest frequency contained in the analog signal to be able to perfectly reconstruct the original signal from the series of sampled values alone.
thus if we sample at a rate of R per second (the sampling rate), we will completely capture any signal containing frequencies up to R/2 per second (the Nyquist frequency for the system). Unfortunately, if the signal contains frequencies above this, it is not just discarded, but creates an artefact by becoming part of the sampled value at a value the same amount below the Nyquest frequency as the original value was above it - this maverick component of the sample is called aliasing distortion and the phenomenon is called aliasing.
to prevent such aliasing distortion, we use an anti-aliasing low pass filter which attempts to remove all parts of the signal which are at or above the Nyquest frequency before we sample the signal.
in digital photography, the anti-aliasing filter needs to work best at frequencies at or just above the Nyquest frequency, as frequencies much higher than that tend to be removed by the optical system's aberrations (incl. diffraction limits) and inexact focusing. In addition, as sensors are not perfect, they can usually only resolve up to 70-80% of Nyquist frequency, and thus the anti-aliasing filter may need to block frequencies in this range as well to minimise digital sampling artefacts.
thus in digital cameras, the anti-aliasing “filter” is actually provided by a combination of factors:
lens blur
image-shifting anti-aliasing filter - usually with a cos(pi * x) response
integration over the area of the sensor pixels
lenslets if the sensor is so equipped, with its sin(pi*x)/(pi+x) response
it is thus possible that for optimum anti-aliasing levels, the degree of anti-aliasing needed depends to some extent on the lens system used, and thus the importance of matching the lens to the camera, which may explain the often sub-optimal results digital SLR's have when used with lenses designed for film cameras.