Aliasing
As aliasing [ eɪliəs ] (also aliasing or shortly aliasing) are referred to in the field of signal analysis errors, which occur when the signal to be sampled occurrence frequency components that are higher than the Nyquist frequency ( half the sampling frequency ). Aliasing can on the one hand by the non-observance of the sampling theorem (insufficient sampling frequency ) occur when digital sampling signals and on the other hand if the signal to be sampled is overlaid by a noise signal. In the image processing and computer graphics, aliasing occurs in the scanning of images and lead to patterns that are not included in the original image. In audio technology, aliasing manifested as noise. Order to prevent aliasing low-pass filters are used to filter out the unwanted frequency components.
- 3.1 Example tones
Signal processing
In the signal processing aliasing effects occur when digitizing analog signals.
Thus, the original signal can be restored correctly, may occur only frequency components that are smaller than the Nyquist frequency in the signal to be sampled. Come frequency components but before that are higher than the Nyquist frequency, they will be interpreted as lower frequencies. The higher frequencies give, so to speak as a different (lower ) (see chart ), hence the name alias.
Disturbing frequency components, which can lead to aliasing, occur at a sub-sampling on (ie the sampling theorem was not met ). However, even if the sampling theorem is respected, it may also cause aliasing when the sensing signal is superimposed by a noise signal that includes frequency components that are higher than the Nyquist frequency.
To avoid such aliasing the input signal is filtered by a low pass ( anti-aliasing filter). The filtering effect of this truncation of the high frequencies can also be described by the terms of height lock, Height filter, high cut and treble cut. This filtering must be done prior to digitization - a subsequent correction of aliasing is no longer possible.
Image capture
Alias creation
In image processing and computer graphics, aliasing in the sampling of images occur, an example is the occurrence of moiré patterns.
The jaggies occurring in the screening of geometric figures is often referred to as aliasing, although this is not to "real" in the sense of aliasing signal analysis before it.
With cameras from 3 megapixels aliasing are most reliably suppressed by skillfully designing the optics. The optical resolution is deliberately set below the pixel resolution. Thus, the optics forming from a little out of focus, and thus serves as a low pass filter.
Demonstration of aliasing
30 sampling points per edge
Reconstruction of the quantized original image
As an example of an original image, which in its so-called spatial frequency has signal components above the Nyquist frequency, is the Fresnel zone plate used in the figure. It is sampled with 30 points, so only the structure in the center are shown. In the edge regions of the spatial frequency of the object exceeds the Nyquist frequency, so that here, the object can not be played back. Instead alias objects are created in the form of circles in the edge regions. Even with one sample per pixel aliasing would occur. Anti -aliasing techniques in computer graphics to try to mitigate these effects by making multiple samples per pixel.
Sample Images
Aliases are also for scanning originals on with varying spatial frequencies, then one speaks of a moiré effect; for example garments such as wool sweaters or suits with thin strips, also tile roofs etc. Moirés are often to be seen on TV when presenters wear pinstripe suits.
In the present case, the cause is a superposition of the spectra of the sample function whose output signals are periodic with fsample.
Temporal aliasing
In films aliasing can occur which are due to the composition of the film of the still images. As a well known example of the apparent backward running of the cart wheels is called in Western. It occurs as soon as the wheel continues to rotate from image to image more than about half the angle between two spokes.
If one observes the acceleration of a car in the movie, the wheel initially rotating in the correct direction. From a certain speed on but the wheel seems to be turning backward to be seemingly slower again with further increasing speed of the carriage. Then it seems to stand still in order right after that to move unnaturally low speed back in the right direction. The apparent forward and reverse running is repeated for further acceleration.
Considered signal Theoretically, each frame one scan represents the sampling frequency equal to the refresh rate (typically 24 frames per second). The signal frequency corresponds to the frequency with which the spokes through a certain angle. Changes a part of the image with a higher frequency than the refresh rate, then aliasing occurs.
- If the wheel turns between two successive images by a half spoke on, can not be distinguished whether it rotates forward or backward (signal frequency = Nyquist frequency). Of the velocity at the aliasing begins.
- If the signal frequency is between the Nyquist frequency and the sampling frequency, the phase is inverted; cartwheel seems to be going backwards.
- The wheel moves per image by exactly one spoke or an integral multiple of further, it seems to have stopped (signal frequency = n × sampling frequency ).