Why aliasing occurs

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. These effects are known as aliases, because they are higher frequency signals aliasing as lower frequency signals.

The multiple stacks of harmonics often seen in some recordings as shown here result from an artifactual effect of an overloaded recording. Combining multiple harmonics can generate flat topped waves, and unfortunately digital signal processing cannot distinguish real from artifact harmonics.

Aliasing results from a direct effect of digital sampling and adds noise to recordings. Understanding aliasing helps to interpret digital sampling and processing of bat vocalizations. However, consider what happens if our 10kHz tone is cranked up too loud and overloads the A-D converter's quantising stage.

If you clip a sine wave, you end up with something approximating a square wave, and the resulting distortion means that a chain of odd harmonics will be generated above the fundamental. 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. Note that, unlike an analogue system, in which the distortion products caused by overloads always follow a normal harmonic series, in a digital system aliasing results in the harmonic series being 'folded back' on itself to produce audible signals that are no longer harmonically related to the source.

Point process and neighbour process will be defined. Finally we will give an introduction on definition of contrast. Course Introduction Content overview 1. Introduction to image processing 2. Sampling and quantization -- Quantization and Sampling Test 3. Resizing image -- Resizing Image Test 4. Aliasing and image enhancement -- Aliasing and Image Enhancement Test 5.