| 1. |
- Koski, Timo, et al.
(författare)
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On quantizer distortion and the upper bound for exponential entropy
- 1991
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Ingår i: IEEE Transactions on Information Theory. - : Institute of Electrical and Electronics Engineers (IEEE). - 0018-9448 .- 1557-9654. ; 37:4, s. 1168-1172
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Tidskriftsartikel (refereegranskat)abstract
- A sharp upper bound is derived for the exponential entropy in the class of absolutely continuous distributions with specific standard deviation and an exact description of the extremal distributions. This result is interpreted as determining the least favorable cases for certain methods of quantization of analog sources. It is known that for a large class of quantizers (both zero-memory and vector) the rth power distortion, as well as some other distortion criteria, are bounded below by a constant, depending on r, multiplied by a certain integral of the source's probability density. It is pointed out that this bound can be rewritten in terms of the exponential entropy. The exponential entropy measures the quantitative extent or range of the source distribution. This fact gives a physical interpretation of the indicated limits of quantizer performance, further elucidated by the main result
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| 2. |
- Koski, Timo, et al.
(författare)
-
On the statistics of the error in predictive coding for stationary Ornstein-Uhlenbeck processes
- 1992
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Ingår i: IEEE Transactions on Information Theory. - : Institute of Electrical and Electronics Engineers (IEEE). - 0018-9448 .- 1557-9654. ; 38:3, s. 1029-1040
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Tidskriftsartikel (refereegranskat)abstract
- Explicit expression are derived for the conditional expectation and variance of the encoder in a predictive DPCM coder with an N-level quantizer, when a stationary Ornstein-Uhlenbeck process is a source. A representation of the encoder in terms of a stochastic integral is presented. These expressions yield a nonlinear stochastic difference equation for the decoding error process and a stochastic differential equation (SDE) as a weak limit for the error process. The statistical properties of the error obtained as a solution of the limiting SDE are interpreted in terms of the slope overload error
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| 3. |
- Koski, Timo
(författare)
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Statistics of the binary quantizer error in single-loop sigma-delta modulation with white Gaussian input
- 1995
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Ingår i: IEEE Transactions on Information Theory. - : Institute of Electrical and Electronics Engineers (IEEE). - 0018-9448 .- 1557-9654. ; 41:4, s. 931-943
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Tidskriftsartikel (refereegranskat)abstract
- Representations and statistical properties of the process e¯ defined by e¯n+1=λ(e¯n+ξn), are given. Here λ(u):=u-b·sign(u)+m and {ξn}n=0+∞ is Gaussian white noise. The process e¯ represents the binary quantizer error in a model for single-loop sigma-delta modulation. The innovations variables are found and the existence and uniqueness of an invariant probability measure, ergodicity properties, as well as the existence of the exponential moment with respect to the invariant probability are proved using Markov process theory. We consider also e¯ as a random perturbation, for small values of the variance of ξn, Of the orbits of sn+1=λ(sn). Here sn has the uniform invariant distribution on the interval [m-h, m+b]. Analytical approximations to the structure of the power spectrum of e¯ are obtained using a linear prediction in terms of the innovations variables and the perturbation approach
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