In receiving systems in which the analog signal voltage is sampled and quantized to allow further processing in digital form, the difference between the analog samples and their digital representation gives rise to a component of random quantization noise. The power spectrum of the quantization noise is close to being uniformly level across the receiver passband, even for large variation in the...

We present a new Trellis Coded Vector Residual Quantizer (TCVRQ) that combines trellis coding and vector residual quantization. We introduce new methods for computing quantization levels and experimentally analyze the performances of our TCVRQ in the case of speech coding at very low bit rates. The results obtained show that transparent quantization of Linear Prediction (LP) parameters can be p...

We present a constructive approach to the functional quantization problem of stochastic processes, with an emphasis on Gaussian processes. The approach is constructive, since we reduce the infinite-dimensional functional quantization problem to a finite-dimensional quantization problem that can be solved numerically. Our approach achieves the sharp rate of the minimal quantization error and can...

We derive high-resolution upper bounds for optimal product quantization of pathwise contionuous Gaussian processes respective to the supremum norm on [0, T ]. Moreover, we describe a product quantization design which attains this bound. This is achieved under very general assumptions on random series expansions of the process. It turns out that product quantization is asymptotically only slight...

In this paper, the problem of optimal quantization is solved for uniform distributions on some higher dimensional, not necessarily self-similar N−adic Cantor-like sets. The optimal codebooks are determined and the optimal quantization error is calculated. The existence of the quantization dimension is characterized and it is shown that the quantization coefficient does not exist. The special ca...

A simple approach is proposed for the quantization of the electromagnetic field in nonlinear and inhomogeneous media. Given the dielectric function and nonlinear susceptibilities, the Hamiltonian of the electromagnetic field is determined completely by this quantization method. From Heisenberg’s equations we derive Maxwell’s equations for the field operators. When the nonlinearity goes to zero,...

We show an equivalence between Dirac quantization and the reduced phase space quantization. The equivalence of the both quantization methods determines the operator ordering of the Hamiltonian. Some examples of the operator ordering are shown in simple models.

We consider optimal scalar quantization with rth power distortion and constrained Rényi entropy of order α. For sources with absolutely continuous distributions the high rate asymptotics of the quantizer distortion has long been known for α = 0 (fixed-rate quantization) and α = 1 (entropyconstrained quantization). These results have recently been extended to quantization with Rényi entropy cons...

In this paper, we study probabilistic numerical methods based on optimal quantization algorithms for computing the solution to optimal multiple switching problems with regime-dependent state process. We first consider a discrete-time approximation of the optimal switching problem, and analyze its rate of convergence. The error is of order 1 2 − ε, ε > 0, and of order 12 when the switching costs...