0.3 Signal processing in processing: sampling and quantization  (Page 4/4)

We note how aliasing can be produced by down-sampling (or decimating) a sampled image. Starting from a discrete-spaceimage, we can select only a subset of samples arranged in a regular grid. This will determine the periodic repetition ofthe spectral images, that will end up overlapping.

In order to explore the concepts of sampling, down-sampling, and aliasing, run the applet drawing ellipses . With the keyboard arrow you can double or halve the horizontal and vertical sampling steps.

A simple introduction to the first elements of image processing is found in Digital Image Processing Basics .

Quantization

With the adjective "digital" we indicate those systems that work on signals that are represented by numbers, with the(finite) precision that computing systems allow. Up to now we have considered discrete-time and discrete-space signals as ifthey were collections of infinite-precision numbers, or real numbers. Unfortunately, computers only allow to representfinite subsets of rational numbers. This means that our signals are subject to quantization.

For our purposes, the most interesting quantization is the linear one, which is usually occurring in the process ofconversion of an analog signal into the digital domain. If the memory word dedicated to storing a number is made of $b$ bits, then the range of such number is discretized into $2^b$ quantization levels. Any value that is found between two quantization levels can be approximated by truncation orrounding to the closest value. The [link] shows an example of quantization with representation on $3$ bits in two's complement .

Sampling and quantization of an analog signal

The approximation introduced by quantization manifests itself as a noise, called quantization noise . Often, for the analysis of sound-processing circuits, such noise isassumed to be white and de-correlated with the signal, but in reality it is perceptually tied to the signal itself, in such anextent that quantization can be perceived as an effect.

To have a visual and intuitive exploration of the phenomenon of quantization, consider the applet that allows to vary between $1$ and $8$ the number of bits dedicated to the representation of each of the RGB channels representing color. The same number of bitsis dedicated to the representation of an audio signal coupled to the image. The visual effect that is obtained by reducingthe number of bits is similar to a solarization .