In this paper, the relationship between the recursive least square (RLS) method with a U-D decomposition algorithm and ARMA lattice filter realization algorithm is presented. Both the RLS method and the lattice filter realization algorithm are used for the same applications, such as model identification, etc., therefore, it is expected that the lattice filter algorithm is in some ways related to the RLS. Though some of the proposed lattice filter algorithms have been derived by the RLS method, they do not express the relationship between RLS snd ARMA lattice filter realization algorithm. In order to describe the relation clearly, a new structure of ARMA lattice filter is proposed. Further, based on the relationship, a method of model identification with frequency weighting (MIFW), which is different from a previous method, is derived. The new MIFW method modifies the lattice parameters which are acquired without a frequency weighting and obtain the parameters of an ARMA model, which is identified with frequency weighting. The proposed MIFW method has the following restrictions: (1) The used frequency weighting is FIR filter with a low order. (2) By using the parameters of the ARMA lattice filter with ARMA (N,M) order and the frequency weighting with L order, the new ARMA parameter with the frequency weignting is with ARMA(N-L,M-L) order. By using the proposed MIFW method, the ARMA parameters estimated with the frequency weighting can be obtained without starting the computation again.

We discuss estimation error as a basic problem in formant estimation in the analysis of speech of very short-time duration in the glottal closure of the vowel. We also show in our simulation that good estimation of the first formant is almost impossible with the ordinary method using a waveform cutting. We propose a new method in which the cut waveform, as a discontinuous function of finite time, is mapped to a continuous function defined in the whole time domain; and we show that using this method, the estimation accuracy for low frequency formants can be greatly improved.

Wave digital filters are a class of digital filters. They are equivalent to commensurate transmission line circuits synthesized with uniform, lossless, and commensurated transmission lines. In order to extend their applications to physical wave phenomena including quantum electronics, it is necessary to consider a generalized distributed line whose velocity of energy flow has frequency characteristics. This paper discusses a generalized distributed circuit, and we obtain two types of lines, lossless and cut-off. In order to analyze these lines, we discuss signal flow graphs of steady state voltage and current. The reflection factors we obtain here are the same as that for an active power or a diagonal element of a scattering matrix, which is zero in conjugate matching. By using this reflection factor, we obtain band-pass filters synthesized with the cut-off lines. We also describe an analysis method for nonuniform line related to Riccati differential equation.

In this paper, an ARMA order selection method is proposed with a fuzzy reasoning method. In order to identify the reference model with the ARMA model, we need to determine its ARMA order. A less or more ARMA order, other than a suitable order causes problems such as; lack of spectral information, increasing calculation cost, etc. Therefore, ARMA order selection is significant for a high accurate ARMA model identification. The proposed method attempts to select an ARMA order of a time-varying model with the following procedures: (1) Suppose the parameters of the reference model change slowly, by introducing recursive fuzzy reasoning method, the estimated order is selected. (2) By introducing a fuzzy c-mean clustering methed, the period of the time during which the reference model is changing is detected and the forgetting factor of the recursive fuzzy reasoning method is set. Further, membership functions used in our algorithm are original, which are realized by experiments. In this paper, experiments are documented in order to validate the performance of the proposed method.