Signals that are not band-limited usually contains all frequencies and thus do not satisfy the condition required by the sampling theorem (i.e., H(f) = 0 for |f| > 1∕(2Δ)). In this case, for any given N data, we can still calculate its DFT by using Eq. (34). However the results obtained are meaningful only when Hn approaches zero as the frequency approaches −1∕(2Δ) from above and approaches 1∕(2Δ) from below, i.e., only when the results obtained are consistent with the assumption used to obtain the results (the assumption is that H(f) = 0 for |f| > 1∕(2Δ)). When the results obtained do not satisfy the above condition, then it indicates that the “aliasing errors” have contributed to the results. We can reduce the aliasing errors by increasing the sampling frequency. The aliasing errors can be reduced but can not be completely removed for a non-band-limited signal.
In signal processing and related disciplines, aliasing is an effect that causes different signals to become indistinguishable (or aliases of one another) when sampled. It also often refers to the distortion or artifact that results when a signal reconstructed from samples is different from the original continuous signal.
An alias is a false lower frequency component that appears in sampled data acquired at too low a sampling rate.
Aliasing errors are hard to detect and almost impossible to remove using software. The solution is to use a high enough sampling rate, or if this is not possible, to use an anti-aliasing filter in front of the analog-to-digital converter (ADC) to eliminate the high frequency components before they get into the data acquisition system.
When a digital image is viewed, a reconstruction is performed by a display or printer device, and by the eyes and the brain. If the image data is processed in some way during sampling or reconstruction, the reconstructed image will differ from the original image, and an alias is seen.
Aliasing can be caused either by the sampling stage or the reconstruction stage; these may be distinguished by calling sampling aliasing (prealiasing) and reconstruction aliasing (postaliasing).
In video or cinematography, temporal aliasing results from the limited frame rate, and causes the wagon-wheel effect, whereby a spoked wheel appears to rotate too slowly or even backwards. Aliasing has changed its apparent frequency of rotation. A reversal of direction can be described as a negative frequency. Temporal aliasing frequencies in video and cinematography are determined by the frame rate of the camera, but the relative intensity of the aliased frequencies is determined by the shutter timing (exposure time) or the use of a temporal aliasing reduction filter during filming.