Editing Quantization (signal processing) (section)

==Mathematical properties==
Because quantization is a many-to-few mapping, it is an inherently [[non-linear]] and irreversible process (i.e., because the same output value is shared by multiple input values, it is impossible, in general, to recover the exact input value when given only the output value).

The set of possible input values may be infinitely large, and may possibly be continuous and therefore [[uncountable]] (such as the set of all real numbers, or all real numbers within some limited range). The set of possible output values may be [[finite set|finite]] or [[countably infinite]].<ref name=GrayNeuhoff/> The input and output sets involved in quantization can be defined in a rather general way. For example, vector quantization is the application of quantization to multi-dimensional (vector-valued) input data.<ref>{{cite book |author1=Allen Gersho |author-link=Allen Gersho |author2=Robert M. Gray |author-link2=Robert M. Gray |url=https://books.google.com/books?id=DwcDm6xgItUC |title=Vector Quantization and Signal Compression |publisher=[[Springer Science+Business Media|Springer]] |isbn=978-0-7923-9181-4 |date=1991}}</ref>