randomness extraction of real valued sequences of numbers I have a sequence of numbers $x_1, x_2, \dots, x_n, \dots \in \mathbb{R}$ I would like to extract fair bits from that sequence.  



My first thought was to use the Von Neumann extractor.  For a sequence of 0 and 1,


divide sequence into pairs
eliminate all occurrences of 00 and 11
apply transformation 01 &#8594; 1 and 10 &#8594; 0


This produces a sequence of fair bits from biased bits *even if you do not know the bias $p = \mathbb{P}[x_i = 1]$ as long as your sequence is


a Bernoulli trial
independently distributed
identially distributed


The sequence of numbers I have is the hourly readings from a sensor, so it exhibits cyclic behavior every 24 hours + every week.  If I compute the expected value over time, it may be possible to subtract out the daily and weekly cycles leaving sequence of loosely self-correlated real numbers.

How can I extract randomness from here in a simple way?
First, it depends how the quantization of the real values is performed.
Using 8 bits can be really different from using 16 for example.

Assuming that a fixed number of bits is chosen, hash functions are a good and simple way to extract randomness. 

Universal Hash Functions are families of hash functions that can be securely used in this context (not all hash functions are suitable for this).