All-zero Model Research Articles

Application of Speech Signals to Deterministic Signal Modeling Techniques

Signal modeling is concerned with the representation of signals. The modeled signal consists of parameters, using which the original signal can be reconstructed or recovered. When once it is possible to accurately model a signal, then it becomes possible to perform important signal processing tasks such as signal compression, interpolation, prediction. The models used are AR (Auto Regressive) or All-Pole model, MA (Moving Average) or All-Zero model, ARMA (Auto Regressive Moving Average) or Pole-Zero model. Various methods have been suggested for the coefficients determination among which are Prony, Pade, Shank, Autocorrelation, Covariance techniques. In this paper, these techniques are applied for speech signals and comparisons are carried out. The comparisons are entirely based on the value of the coefficients obtained.

An indirect interpolation method for Head-Related Transfer Function pole-zero models

School of Electronic and Information Engineering, Dalian University of Technology, 116023 P.R. China(Received 22 February 2008, Accepted for publication 1 April 2008)Keywords: HRTF, Interpolation, Pole-zero model, All-zero modelPACS number: 43.60.Gk, 43.66.Qp [doi:10.1250/ast.29.329]1. IntroductionHead-related transfer function (HRTF), which describesthe path between the sound source and the ear, plays animportant role in 3D sound system [1]. The spatial perceptionusing headphone can be controlled by binaural synthesisthrough HRTF. However, the system has to store the HRTFsof all directions to realize natural spatial perception, since theHRTF varies as a function of the sound direction. In fact, it isimpossible to obtain the HRTFs of all directions throughmeasurements because of the enormous amounts of time andphysical loads of the listener. One solution to this problem isto obtain the HRTFs in arbitrary directions from a limitednumber of measured HRTFs.Some interpolation methods have been developed whichmainly focused on HRTF all-zero models, such as the linearinterpolation method [2], the inter-positional transfer function(IPTF) method [3], etc. But pole-zero model is more preferredin binaural synthesis because of its low computation andmemory cost. In [4], balanced model truncation method isemployed to reduce the order of HRTFs. In [5], the IIR filterof HRTF is designed taking the log-magnitude errors intoaccount. And in [6], the IIR filter is designed in warpedfrequency domain. Although pole-zero modeling of HRTF hasobtained great progress, interpolation methods that are bothautomatic and effective for pole-zero models have not beendeveloped so far. Generally, interpolation of pole-zero modelsmay be realized by convex combinations of pole (zero) valuesfrom the neighboring HRTF models [7]. As an improvementof the convex combination method [7], records the pole (zero)tracks during the iterated approximation, and incorporatesthem to increase the interpolation accuracy. But the improvedmethod in [7] is not applicable since extra information of thepole (zero) tracks has to be stored.In this paper, an indirect interpolation method for HRTFpole-zero models is developed based on the all-zero interpo-lation methods. First, the method transforms the pole-zeromodels to all-zero models. Then, the target HRTF is interpo-lated from the reference all-zero models using the linearinterpolation method. Last, the interpolated all-zero model istransformedbacktothepole-zeromodel.Theproposedmethodhas better interpolation accuracy than conventional methods,and does not need calculating the pole (zero) positions.2. The indirect interpolation methodSuppose two reference pole-zero models B

Common acoustical pole and zero modeling of room transfer functions

A new model for a room transfer function (RTF) by using common acoustical poles that correspond to resonance properties of a room is proposed. These poles are estimated as the common values of many RTF's corresponding to different source and receiver positions. Since there is one-to-one correspondence between poles and AR coefficients, these poles are calculated as common AR coefficients by two methods: (i) using the least squares method, assuming all the given multiple RTF's have the same AR coefficients and (ii) averaging each set of AR coefficients estimated from each RTF. The estimated poles agree well with the theoretical poles when estimated with the same order as the theoretical pole order. When estimated with a lower order than the theoretical pole order, the estimated poles correspond to the major resonance frequencies, which have high Q factors. Using the estimated common AR coefficients, the proposed method models the RTF's with different MA coefficients. This model is called the common-acoustical-pole and zero (CAPZ) model, and it requires far fewer variable parameters to represent RTF's than the conventional all-zero or pole/zero model. This model was used for an acoustic echo canceller at low frequencies, as one example. The acoustic echo canceller based on the proposed model requires half the variable parameters and converges 1.5 times faster than one based on the all-zero model, confirming the efficiency of the proposed model. >

Pole and zero modeling of room transfer functions

The feasibility of using all-pole and all-zero model approximations of room transfer functions was examined especially in respect to the degree that such approximations are suitable for removing room reverberation from signals. Two aspects of the above models were assessed: their success in reducing room transfer function order and their insensitivity to measurements taken for different source and receiver positions inside a room. Both these aspects are crucial to the success of practical dereverberation methods. The tests were carried out on simulated and measured data and it was found that all-pole models are most suitable than all-zero models when both of the above two aspects must be satisfied by the approximation model. It was also shown that, for a given room, an optimum all-pole model order exists which approximates the room transfer function.

Adaptive control of plants using all-zero model for dead-time identification

In the design of identification algorithms, the dead-time is usually modelled by some form of a polynomial function that adequately approximates the dead-time behaviour over relevant frequency bands.The application of all-zero models for approximation of plant dead-times is discussed. Gain-error criterion is established for a general model, whereas phase-error criterion is presented for first-order approximations. It is shown that if a plant transfer function has lowpass features, it is possible to determine a satisfactory all-zero model for the delay.The modelling technique is applied in a recursive least-squares based identification algorithm. This is used to obtain a delay-model predictor. Adaptive controllers, of the k-incremental predictive type, are set up using the identification results.

Accurate autoregressive spectrum estimation at low signal-to-noise ratio using a phase matching technique

This paper describes a new method of accurately estimating the parameters of an autoregressive (AR) process contaminated by high-level white noise. Based on the phase matching technique, it minimizes the difference between the phase of the all-zero model and the phase of the maximum phase signal reconstructed from the power spectrum of the observed signal. The parameters of the AR model are obtained from the finite length sequence of the estimated all-zero model. The proposed method works only when the order of the AR model is known a priori at present. However, since the phase matching technique satisfies the conditions needed to apply the least mean-square method, the AR parameters are estimated accurately even at a low signal-to-noise ratio. With the iterative or noniterative methods as discussed in the recent literature, it is not possible to reconstruct the all-zero model from the power spectrum when there are dips and peaks having no correlation with the poles of original AR signal in the power spectrum. The method proposed in this paper allows one to accurately reconstruct the phase from the power spectrum in such cases. Finally, it is confirmed with computer simulations and experiments that the proposed method is useful for accurate estimation of the AR parameters.