We formulate the Huffman decoding as a root-solving problem so that powerful numerical techniques such as the Newton method and the bisection method are employed for solution. The sectioning technique that narrows the searching scope for solution is further proposed for increasing the decoding speed. The numerical decoder is fast and memory efficient; it is also simple to realize and suitable for integrated circuit implementation.

We formulate the joint design of interpolation filter and frequency equalizer in DMT systems as a problem for minimization of the mean square error between the input data symbol and its output estimate. Then, an iterative algorithm is proposed for the solution. Each iteration requires only solving two quadratic minimizations; the algorithm also ensures convergence. Simulations for VDSL applications demonstrate that an increment in transmission rate can be achieved compared with the conventional design of the interpolation filter and frequency equalizer separately.

This paper presents an algorithm to design jointly interpolation filters and decision feedback equalizers in the sense of minimum mean-square error such that the joint capacity which is neglected in conventional design is explored to improve the receiver performance. The algorithm comprises an iteration of two alternating simple quadratic minimizing operations and ensures convergence. A simulation example for the raised-cosine channel demonstrates that via this approach an improvement over the conventional design can be achieved.

In this paper we present a new adaptive notch filter (ANF) using the well-known Steiglitz-McBride method (SMM) for an IIR filter with the constrained poles and zeros. The proposed ANF, termed as SMM-ANF, converges to the unbiased solution, has fast convergence speed, and requires less computational complexity than existing recursive maximum likelihood adaptive notch filters (RML-ANF). In the stationary environments, we analyze SMM-ANF convergence properties using the ordinary differential equation (ODE) technique; we derive conditions for the SMM-ANF convergence solution unbiased. Simulations further display that SMM-ANF has better resolution in identifying frequencies of multiple sine waves than RML-ANF. In the nonstationary environments, we also show that SMM-ANF and RML-ANF have approximately identical tracking performance. Simulations are also done to verify the theoretically derived results.

This paper presents a unified approach to analyze the convergence properties of Steiglitz-McBride(1966) method (SMM) in general environments. SMM is formulated as a successive substitution equation. Using results from fixed point theory enables a unified analysis of SMM in both white and colored noise, and sufficient and insufficient order cases. This analysis provides us with several new results. Specifically, for sufficient order filters in white noise environments, the convergence rate of SMM can be predicted by the signal-power to noise-power ratio (SNR) at plant output. For sufficient order filters in colored noise, SMM may diverge or converge depending on the initial estimate and SNR at plant output. If SMM converges, the convergence point is near the unbiased solution. SNR again determines the bias magnitude. For insufficient order filters, in addition to the possible multiple convergence points, we also demonstrate the existence of diverging fixed points of SMM. These diverging fixed points can be used to separate the convergence region, and identify the convergence points for each initial estimate.>

In this paper, we present a new method for adaptive IIR filtering that promises improved performance under general operating conditions, including both colored and white noise, sufficient and insufficient order filter cases. By defining the regressor in adaptive IIR filter update to be a convex combination of the regressors for the Steiglitz-McBride method (SMM) and recursive predicted error method (RPEM), we are able to tradeoff the benefits of each. RPEM minimizes mean square output error (MSOE) directly, and thus has slow convergence rate and may converge to a local minimum because of nonconvexity and multimodality of MSOE surface, SMM converges fast, but may converge to a biased solution or diverge in colored noise environments. Other composite methods (e.g., composite regressor method (CRM)) use a similar approach, but only focus on reducing bias of equation error estimates for sufficient order filters in white noise environments. Conversely, our method, CPRM, can extend applications to general environments, prevent diverging, reduce bias, and increase likelihood of convergence to the global minimum.>