Beta encoder
A beta encoder is a analog to digital conversion (A/D) system in which a real number in the unit interval is represented by a finite representation of a sequence in base beta, with beta being a real number between 1 and 2. Beta encoders are an alternative to traditional approaches to pulse code modulation.[1][2]
As a form of non-integer representation, beta encoding contrasts with traditional approaches to binary quantization in which each value is mapped to the first N bits of its base-2 expansion. Rather than using base 2, beta encoders use base beta.[3]
In practice beta encoders have attempted to exploit the redundancy provided by the non-uniqueness of the expansion in base beta to produce more robust results. Although integrator leaks in hardware elements make some beta encoders imprecise, specific algorithms can be used to provide exponentially accurate approximations for the value of beta, despite the imprecise results provided by some circuit components.[4]
An alternative design called the negative beta encoder (called so due to the negative eigenvalue of the transition probability matrix) has been proposed to further improve the quantization error.[5]
See also
References
- ^ Du, Ke-Lin; Swamy, M. N. S. (2010), Wireless Communication Systems: From RF Subsystems to 4G Enabling Technologies, p. 483, ISBN 0521114039
- ^ Daubechies, I.; Yilmaz, O. (August 2006), "Robust and Practical Analog-to-Digital Conversion With Exponential Precision", IEEE Transactions on Information Theory, 52 (8): 3533–3545
- ^ Mathematical Reviews (3), American Mathematical Society: 2536, 2007, ISSN 0025-5629
{{citation}}: Missing or empty|title=(help) - ^ Ward, Rachel (Sept. 2008), "On Robustness Properties of Beta Encoders", IEEE Transactions on Information Theory, 54 (9): 4324–4334
{{citation}}: Check date values in:|date=(help) - ^ Tohru Kohda, Satoshi Hironaka and Kazuyuki Aihara Negative Beta Encoder Arxiv July 2009