Why aliasing occur

According to digital sampling theory, this detector can only resolve real, i. This limiting frequency is called the Nyquist frequency. Alias harmonics represent real frequency content misinterpreted by too low a sampling frequency, or artifacts of signal content too loud for the microphone or recording hardware to interpret, analogous to overexposure in photography. The frequency scale for this sonogram ends at the Nyquist frequency of kHz and you would find no displayed frequency content above that.

Any real frequency content above kHz will render alias harmonics, as will artifactual frequency content interpreted from overloaded signals. Aliasing occurs when a signal is sampled at a less than twice the highest frequency present in the signal. Signals at frequencies above half the sampling rate must be filtered out to avoid the creation of signals at frequencies not present in the original sound.

Thus digital sound recording equipment contains low-pass filters that remove any signals above half the sampling frequency. Since a sampler is a linear system, then if an input is a sum of sinusoids, the output will be a sum of sampled sinusoids. This suggests that if the input contains no frequencies above the Nyquist frequency, then it will be possible to reconstruct each of the sinusoidal components from the samples.

So our original 10kHz sine wave has now acquired an unwanted series of strong harmonics at 30kHz, 50kHz and so on. Note that these harmonics were generated in the overloaded quantiser and after the input anti-aliasing filter that was put there to stop anything above half the sample rate getting in to the system.

By overloading the converter, we have generated 'illegal' high-frequency signals inside the system itself and, clearly, overloading the quantiser breaks the Nyquist rule of not allowing anything over half the sample rate into the system. Figure 2: When the 10kHz signal overloads the A-D converter, the resulting third harmonic at 30kHz creates an alias at 18kHz which will be allowed through by the low-pass filter.

The 18kHz product is clearly below half the sample rate, and so will be allowed through by the reconstruction filter. This is the 'alias'. We started with a 10kHz signal, and have ended up with both 10kHz and 18kHz see Figure 2, above. Similarly, the 50kHz harmonic will produce a 2kHz frequency, resulting in another alias. Aliasing occurs when a system is measured at an insufficient sampling rate.

It is perhaps best explained through example. Imagine a disk or paper plate with a dot near the edge. If the disk began rotating at one revolution per minute, you could observe the angular velocity by looking at it. Now close your eyes. If you open your eyes every 15 seconds and observe the dot, you can still measure direction of rotation and speed.

Look every 75 seconds and the plate appears to be rotating opposite to its true rotation. This is aliasing. The same thing happens when a digital measurement device does not sample a signal often enough. The most common example comes from old westerns. If you watch a movie with a stage coach, the wagon wheels appear to move backwards once a certain speed is reached.