# Aliasing

**aliasedaliastemporal aliasingaliasesaliasing artifactsaliasing distortionanti-aliasingare physically equivalent to vectors inside itdigital aliasingfolding frequency**

In signal processing and related disciplines, aliasing is an effect that causes different signals to become indistinguishable (or aliases of one another) when sampled.wikipedia

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### Spatial anti-aliasing

**anti-aliasinganti-aliasedantialiasing**

Spatial anti-aliasing techniques avoid such poor pixelizations.

In digital signal processing, spatial anti-aliasing is a technique for minimizing the distortion artifacts known as aliasing when representing a high-resolution image at a lower resolution.

### Anti-aliasing filter

**anti-aliasinganti-aliasing (AA) filteroptical low-pass filter**

Aliasing is generally avoided by applying low pass filters or anti-aliasing filters to the input signal before sampling.

Since the theorem states that, unambiguous reconstruction of the signal from its samples is possible when the power of frequencies above the Nyquist frequency is zero, a real anti-aliasing filter trades off between bandwidth and aliasing.

### Moiré pattern

**moirémoiremoire pattern**

Aliasing can also occur in spatially sampled signals, for instance moiré patterns in digital images.

Moiré patterns are often an artifact of images produced by various digital imaging and computer graphics techniques, for example when scanning a halftone picture or ray tracing a checkered plane (the latter being a special case of aliasing, due to undersampling a fine regular pattern).

### Reconstruction filter

**filteringmultivariate interpolation kernelsreconstruction**

Suitable reconstruction filters should then be used when restoring the sampled signal to the continuous domain.

The sampling theorem describes why the input of an ADC requires a low-pass analog electronic filter, called the anti-aliasing filter: the sampled input signal must be bandlimited to prevent aliasing (here meaning waves of higher frequency being recorded as a lower frequency).

### Digital audio

**digital musicaudiodigital**

Aliasing can occur in signals sampled in time, for instance digital audio, and is referred to as temporal aliasing.

Analog signals that have not already been bandlimited must be passed through an anti-aliasing filter before conversion, to prevent the aliasing distortion that is caused by audio signals with frequencies higher than the Nyquist frequency (half the sampling rate).

### Sampling (signal processing)

**sampling ratesamplingsample rate**

In signal processing and related disciplines, aliasing is an effect that causes different signals to become indistinguishable (or aliases of one another) when sampled. If a piece of music is sampled at 32000 samples per second (Hz), any frequency components above 16000 Hz (the Nyquist frequency for this sampling rate) will cause aliasing when the music is reproduced by a digital to analog converter (DAC). See Sampling (signal processing), Nyquist rate (relative to sampling), and Filter bank.

That fidelity is reduced when s(t) contains frequency components whose periodicity is smaller than two samples; or equivalently the ratio of cycles to samples exceeds ½ (see Aliasing).

### Nyquist frequency

**NyquistN/2 different frequenciesNyquist component**

If a piece of music is sampled at 32000 samples per second (Hz), any frequency components above 16000 Hz (the Nyquist frequency for this sampling rate) will cause aliasing when the music is reproduced by a digital to analog converter (DAC).

It is sometimes known as the folding frequency of a sampling system.

### Wagon-wheel effect

**wagon wheel effect**

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.

In these recorded media, the effect is a result of temporal aliasing.

### Analog-to-digital converter

**ADCanalog to digital converteranalog-to-digital conversion**

Audio signals are sampled (digitized) with an analog-to-digital converter, which produces a constant number of samples per second.

The SNR of an ADC is influenced by many factors, including the resolution, linearity and accuracy (how well the quantization levels match the true analog signal), aliasing and jitter.

### Nyquist rate

**Nyquist limitNyquist sampling rateNyquist**

See Sampling (signal processing), Nyquist rate (relative to sampling), and Filter bank.

1) as a lower bound for the sample rate for alias-free signal sampling (not to be confused with the Nyquist frequency, which is half the sampling rate of a discrete-time system) and

### Distortion

**distortedharmonic distortiondistort**

It also refers to the distortion or artifact that results when the signal reconstructed from samples is different from the original continuous signal.

Other forms of audio distortion that may be referred to are non-flat frequency response, compression, modulation, aliasing, quantization noise, wow and flutter from analog media such as vinyl records and magnetic tape.

### Undersampling

**bandpass samplingundersampled**

Undersampling, which creates low-frequency aliases, can produce the same result, with less effort, as frequency-shifting the signal to lower frequencies before sampling at the lower rate.

When one undersamples a bandpass signal, the samples are indistinguishable from the samples of a low-frequency alias of the high-frequency signal.

### Nyquist–Shannon sampling theorem

**sampling theoremsampling theoryNyquist**

is met for the highest frequency component of the original signal, then it is met for all the frequency components, a condition called the Nyquist criterion.

When the bandlimit is too high (or there is no bandlimit), the reconstruction exhibits imperfections known as aliasing.

### Signal reconstruction

**reconstructreconstructionPixel filtering**

When a digital image is viewed, a reconstruction is performed by a display or printer device, and by the eyes and the brain.

Aliasing

### Whittaker–Shannon interpolation formula

**interpolation/sampling theoryreconstructingsinc interpolation**

But the fidelity of a theoretical reconstruction (via the Whittaker–Shannon interpolation formula) is a customary measure of the effectiveness of sampling.

(See Aliasing.)

### Jaggies

**jaggednessjagginessjaggyness**

Jaggies

"Jaggies" is the informal name for artifacts in raster images, most frequently from aliasing, which in turn is often caused by non-linear mixing effects producing high-frequency components or missing or poor anti-aliasing filtering prior to sampling.

### Wave field synthesis

**wave fieldWFS**

Spatial aliasing, particular of angular frequency, can occur when reproducing a light field or sound field with discrete elements, as in 3D displays or wave field synthesis of sound.

There are undesirable spatial distortions caused by position-dependent narrow-band break-downs in the frequency response within the rendition range – in a word, aliasing.

### Stroboscopic effect

**stroboscopicstrobe effectstroboscopically**

Stroboscopic effect

The stroboscopic effect is a visual phenomenon caused by aliasing that occurs when continuous motion is represented by a series of short or instantaneous samples.

### Sawtooth wave

**sawtoothsawsaw wave**

Six sawtooth waves are played in succession, with the first two sawtooths having a fundamental frequency of 440 Hz (A4), the second two having fundamental frequency of 880 Hz (A5), and the final two at 1760 Hz (A6).

If the waveform is digitally created directly in the time domain using a non-bandlimited form, such as y = x - floor(x), infinite harmonics are sampled and the resulting tone contains aliasing distortion.

### Wavelength

**wavelengthsperiodsubwavelength**

Waves must be sampled at more than two points per wavelength, or the wave arrival direction becomes ambiguous.

This produces aliasing because the same vibration can be considered to have a variety of different wavelengths, as shown in the figure.

### Sinc filter

**brick-wallbrick-wall filterbrickwall filter**

Sinc filter

Aliasing

### Signal processing

**signal analysissignalsignal processor**

In signal processing and related disciplines, aliasing is an effect that causes different signals to become indistinguishable (or aliases of one another) when sampled.

### Artifact (error)

**artifactartifactsartefacts**

It also refers to the distortion or artifact that results when the signal reconstructed from samples is different from the original continuous signal.

### Digital image

**digital imagesimagesimage**

Aliasing can also occur in spatially sampled signals, for instance moiré patterns in digital images.

### Low-pass filter

**low-passlow pass filterlow pass**

Aliasing is generally avoided by applying low pass filters or anti-aliasing filters to the input signal before sampling.