This note presents a new approach for the robustness of Hurwitz polynomials under coefficient perturbation. The s-domain Hurwitz polynomial is transformed to the z-domain polynomial by the bilinear transformation. Then an approach based on the Rouché theorem introduced in the literature is applied to compute a crude bound for the allowable coefficient variation such that the perturbed polynomial maintains the Hurwitz stability property. Three methods to obtain improved bounds are also suggested. The results of this note are computationally more efficient than the existing direct s-domain approaches especially for polynomials of higher degree. Furthermore examples indicate that the exact bound for the coefficient variation can be obtained in some cases.

In many engineering problems it is required to convert a polynomial into another polynomial through a transformation. Due to its wide range of applications, the polynomial transformation has received much attention and many techniques have been developed to compute the coefficients of a transformed polynomial from those of an original polynomial. In this letter a new result is presented concerning the transformation matrix for arbitrary polynomial transformation. A simple algorithm is obtained which enables one to successively compute transformation matrices of various order.

This paper proposes a Mel-Wiener filter to enhance Mel-LPC spectra in the presence of additive noise. The transfer function of the proposed filter is defined by using a first-order all-pass filter instead of unit delay. The filter coefficients are estimated based on minimization of the sum of the square error on the linear frequency scale without applying the bilinear transformation and efficiently implemented in the autocorrelation domain. The proposed filter does not require any time-frequency conversion, which saves a large amount of computational load. The performance of the proposed system is comparable to that of ETSI AFE. The optimum filter order is found to be 3, and thus filtering is computationally inexpensive. The computational cost of the proposed system except VAD is 53% of ETSI AFE.

Due to its importance in engineering applications, the bilinear transformation has been studied in many literature. In this letter two new algorithms are presented to compute transformation matrix for the bilinear s-z transformation.