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What is aliasing in DSP and how to prevent it?

Aliasing is a common undesirable phenomenon that occurs wherever digital signals are undergoing processing. You may notice it in audio signals or images. Here is a nifty video that demonstrates aliasing in a music signal.

Aliasing can also be found in digital image processing and video processing. Check out the screengrab of a video game below.

aliasing in games
Though aliasing is an option in gaming, it is usually not in full effect to save on computation power.

When does aliasing occur?

As we saw earlier in this DSP course, one of the first steps in digital signal processing is Sampling. Sampling is one of the most important steps in the long chain of processes involved in the conversion of an analog signal into a digital one. It involves multiplying a continuous-time signal with a discrete set of inputs. The values are said to be ‘sampled’ at the instants where the discrete signals exist. The contention is that these small samples of the main signal should be enough to re-create the original version.

And in theory, that is entirely possible. But, and that’s a big but. Only and only if the sampling process meets specific criteria, this criterion is Fs>=2Fm. That is, the sampling frequency should be equal to or greater than twice the maximum frequency component of the continuous-time signal. When the sampling frequency is exactly equal to twice the maximum frequency component, it is known as the Nyquist rate.

Sampling process in dsp
Sampling in DSP: In the left column, you can see the sampling process in the time domain and their frequency domain equivalents on the right.

When the Nyquist condition is met, we can represent an analog signal in the form of a discrete sequence of samples. Additionally, the original signal can be recovered accurately from the discrete sequence of samples.

When the sampling process does not meet the sampling criterion, the signal is said to be under-sampled, and aliasing is the result of under-sampling.

aliasing and the sampling process
Notice the overlapping in the time-shifted versions of the signal in the frequency domain. This overlapping is known as aliasing. (Source)

What is aliasing?

Aliasing is an unwanted case of sampling, where the minimum condition for accurate sampling is not met. Thus there is an overlap in the shifted replicas of the x(ω) signal. Consequently, the x(t) signal can neither be sampled accurately or recovered from its samples.

Alternatively, we can state that aliasing occurs when a signal undergoes sampling at an insufficient sampling rate Fs<Fm.

Physically, in aliasing, signals of different frequencies become indistinguishable from each other. The high-frequency components of the signal spectrum take the identity of the lower frequencies in the spectrum of the sampled signal.

How to prevent aliasing?

We can simply avoid aliasing by sampling the signal at a higher rate than the Nyquist rate (Fs>Fm). Or, we can use anti-aliasing filters. These are special low-pass filters that are usually found in the initial stages of any digital signal processing operation. The anti-aliasing filters attenuate the unnecessary high-frequency components of a signal. They band-limit the input signal by removing all frequencies higher than the signal frequencies. As a result, they help preserve a lot of information that is needed and remove unnecessary information.


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