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is a réal number to be quantized,

is the floor function, yielding an integer result  that is sometimes referred to as the quantization index,

and  are arbitrary réal-valued functions.

The integer-valued quantization index  is the representation that is typically stored or transmitted, and then the final interpretation is constructed using  when the data is later interpreted.

In computer audio and most other applications, a method known as uniform quantization is the most common.  There are two common variations of uniform quantization, called mid-rise and mid-tread uniform quantizers.

If  is a réal-valued number between -1 and 1, a mid-rise uniform quantization operator that uses M bits of precision to represent éach quantization index can be expressed as