- T. Takebe, T. Matsumoto, and A. Chaisawadai,
"Design of FIR partial response filters with equiripple stopband
attenuation (class II, V).",
*Electronics and Communications in Japan, Part 3 (Fundamental Electronic Science)*, Oct. 1989, vol.72, no.10, pp. 1-13.Abstract: Considers the design of transmitter and receiver FIR digital filters with partial response of class II and V for data transmission. The filters are required to band-limit the transmitting and receiving signal, while maintaining the overall impulse response with zero intersymbol interference (ISI). Two cases are considered: the case where the transmitter itself has the zero ISI impulse response; and the case where the transmitter and receiver filters are matched. In the former, the length of the filter is set to be equal to the number of samples between two zero-cross points, which are at a certain symmetrical distance from the center of the ideal impulse response. Then a linear-phase transfer function is derived with an equiripple approximation to the ideal amplitude frequency response. In the approximation, the weight in the stopband is set as less than 1, and ISI of less than 1 percent is obtained. In the design of the matched filter pair, the overall order is set in the same way as in the former. Applying the Herrman-Schuessler (1970) design method for the minimum phase-shift filter in the frequency domain, the transfer function is derived.

- I. H. Zabalawi,
"Delay equalization of recursive digital filters,"
in
*Linear Circuits, Systems and Signal Processing: Theory and Application*, eds. C. I. Byrnes, C. F. Martin, and R. E. Saeks, Amsterdam, Netherlands: North-Holland, pp. 225-30, 1988.Abstract: Presents a new algorithm for designing all-pass digital networks. The group delay response of the network is designed to equalize the delay of a selective minimum phase filter. The equalized delay approximates the desired flat delay in an equiripple manner over the nominal passband of the filter.

- Y.V.V.S. Murty and W. J. Smolinski,
"Digital filters for power system relaying,"
*International Journal of Energy Systems*, vol. 7, no. 3, pp. 125-9, 1987.Abstract: Describes the design of finite impulse response (FIR) digital filters which are used to remove the high frequency transients from transmission line voltage and current signals, as is required by certain digital distance relay algorithms. The design methods are based on optimal magnitude (Chebyshev) linear phase filter and optimal magnitude (Chebyshev) minimum phase filter. The digital simulation results of the distance relay algorithm with different types of filters are compared. The implementation of the digital filters along with the relay algorithm on Texas Instruments TMS320 digital signal processor is outlined. The results showed that the minimum phase filter gave the fastest relay operation time amongst the filters considered.

- F. Grenez,
"On the design of FIR digital filters with prescribed stopband or passband
deviation,"
*IEEE Transactions on Circuits and Systems*, vol. 33, no. 7, pp. 731-2, July 1986.Abstract: The utility of the constrained Chebyshev approximation for the design of FIR filters is discussed. It is argued that the constrained Chebyshev approximation can often replace an iterated execution of the classical Parks-McClellan (see IEEE Trans. Audio Electroacoust., vol.Au-21, p.506-26, 1973) program and has more flexibility for a number of applications. The author describes the use of the constrained approximation for the design of filters with arbitrary specifications for the suppression of parasitic ripples in multiband filters, and for the design of a linear-phase prototype with a nonnegative frequency response with the aim of deriving a minimum phase filter.

- K. Estola and T. Saramaki,
"A new method for designing equiripple error group delay filters,"
*Proc. Int. Sym. on Circuits and Systems*, pp. 271-4, Kyoto, Japan, Jun. 1985.Abstract: A method for designing digital all-pass filters with arbitrary group delay characteristics is presented. The method is based on the recursive relationship between the filter coefficients of a minimum-phase all-pole filter and the corresponding cepstral coefficients. It is shown that by splitting the actual group delay response into primary approximating function (a finite cosine series) and the truncation error function, the approximation problem can be solved using an iterative procedure. At each iteration, the truncation error of the previous iteration is included in the desired function and the primary approximating function is optimized using the Remez multiple exchange algorithm. This algorithm is continued until both the primary approximating function and the truncation error function remain the same. The method does not require any initial values and yields an equiripple error solution in most practical cases.

- J. L. Rasmussen and D. M. Etter,
"A comparison of methods for adaptively designing minimum phase
FIR models,"
*Proc. Asilomar Conference on Signals, Systems and Computers*, vol. 2, pp. 1220-4, Pacific Grove, CA, Nov. 1993.Abstract: Given a set of filters with the same magnitude response, the minimum phase filter is the one with the minimum phase lag. This filter will also have the minimum group delay and the minimum energy delay. Obtaining the minimum phase FIR estimate of an unknown system is a constrained optimization problem because the zeros of the model must be constrained to be within the unit circle. The authors compare several structures for adaptively obtaining the optimum FIR minimum phase filter model for an unknown FIR system.

- C.-Y. Chi and W.-T. Chen,
"Maximum-likelihood blind deconvolution: non-white Bernoulli-Gaussian
case,"
*IEEE Transactions on Geoscience and Remote Sensing*, vol. 29, no. 5, pp. 790-5, Sep. 1991.Abstract: The authors present a maximum-likelihood deconvolution (MLD) algorithm for estimating nonwhite Bernoulli-Gaussian signals mu (k), which were distorted by a linear time-invariant system upsilon (k) taking into account the measured spectrum of mu (k) such as that obtained from sonic logs. The proposed MLD algorithm can recover both the phase of a minimum-phase coloring filter upsilon /sub 1/(k) and that of upsilon (k) as long as the spectrum of mu (k) is known in advance. The authors also present some simulation results which support the proposed MLD algorithm.

- T. Takebe and T. Yoshida,
"A method for designing parallel-type pseudo-minimum-phase FIR
QMF banks,"
*Electronics and Communications in Japan, Part 3 (Fundamental Electronic Science)*, vol. 74, no. 7, pp. 34-44, July 1991.Abstract: Presents a design method for the equal-bandwidth parallel-type quadrature mirror filter (QMF) bank (used in subband coding of speech) with smaller delay by allowing some delay distortion. The amplitude and phase constraints on each channel filter are shown so that the transmitted signal can be reconstructed approximately at the receiver. A design example is presented for the 4-band filter bank, where the amplitude constraint is satisfied by a minimum-phase filter and the phase constraint is satisfied by an all-pass circuit cascaded to the filter. The designed low-pass filter is of 50 percent roll-off, and the bandpass filter is a 100 percent roll-off. The attenuation is 43 dB. The delay is almost flat in characteristic and the amount is reduced to approximately one-half that of the linear-phase filter bank.

- J. Foldvari-Orosz, T. Henk, and E. Simonyi,
"Simultaneous amplitude and phase approximation for lumped and sampled
filters,"
*Int. Journal of Circuit Theory and Applications*, vol. 19, no. 1, pp. 77-100, Jan.-Feb. 1991.Abstract: A simultaneous amplitude and phase approximation method is presented for reciprocal and non-reciprocal lumped or sampled filters realized by LC, CCD, active RC, cascaded SC, digital or wave digital IIR filters. The approximation is based on the fictive decomposition of a non-minimum phase filter into a minimum phase and an allpass network in such a way that some poles and zeros should coincide with each other and so the filter order should decrease. In this way the amplitude and phase approximations can be carried out alternately, though the minimum phase and the allpass networks do not occur in the resulting filter. Both approximations are based on linear interpolation of specified functions with a possible application of the Remez algorithm. The interpolation algorithms can be used in other arbitrary approximation problems as well. Illustrative examples are given for some lowpass and bandpass filters.

- J. L. Rasmussen and D. M. Etter,
"An adaptive technique for designing minimum phase models,"
*Proc. IEEE Asilomar Conference on Signals, Systems and Computers*, vol. 2, pp. 654-8, Pacific Grove, CA, Nov. 1991.Abstract: The authors have developed a novel filter structure, called a stochastic filter, that consists of a bank of fixed filters with a set of corresponding probabilities. The fixed filters can be viewed as the basis set of filters for the stochastic filter, with the probabilities determining the specific realization represented by the stochastic filter. If the probabilities are allowed to vary with time, the stochastic filter is an implementation of an adaptive filter. The authors present a configuration, using FIR (finite impulse response) fixed filters in the stochastic filter, that can be used to adaptively model unknown systems. It is shown theoretically that this form of adaptive stochastic filter converges to a minimum phase FIR filter model.

- Bessios, A.G.; Nikias, C.L.
A new blind equalization algorithm using higher order statistics in a
decision feedback structure.
IN: Conference Record of the Twenty-Fifth Asilomar Conference on Signals,
Systems and Computers (Cat. No.91CH3112-0). (Conference Record of the
Twenty-Fifth Asilomar Conference on Signals, Systems and Computers (Cat.
No.91CH3112-0), Pacific Grove, CA, USA, 4-6 Nov. 1991). Los Alamitos, CA,
USA: IEEE Comput. Soc. Press, 1991. p. 721-5 vol.2.
Abstract: The authors present a novel adaptive blind equalization algorithm named POTEA (power cepstrum and tricoherence equalization algorithm) using a nonlinear structure. It is based on the combined use of second- and fourth-order statistics of the received sequence. A nonlinear decision-feedback equalization (DFE) structure is proposed for equalizing nonminimum-phase channels with severe distortion, since a linear equalizer does not perform well in cases of channels with deep spectral nulls in their amplitude characteristics. The direct-form structure of the DFE consists of a feedforward T-spaced filter with an all-pass mixed phase transfer function, and a feedbackward T-spaced filter with a minimum phase one. The performance of POTEA for linear and decision-feedback equalizers is tested for the cases of 16-QAM (quadrature amplitude modulation) and 64-QAM.

- Pei, S.-C.; Jaw, S.-B.
Improved design of minimum-phase FIR digital filters by cepstrum and fast
Hartley transform.
Electronics Letters, 5 July 1990, vol.26, (no.14):1063-4.
Abstract: An equiripple minimum-phase FIR filter is designed using the cepstrum and the fast Hartley transform (FHT). This fast procedure is performed entirely in the real domain and requires only two short-length FHT computations. This method avoids complicated phase wrapping and greatly reduces the aliasing error.

- Alhakim, S.S.; Abdullah, S.N.
Flexible pseudobinary and pseudoquaternary detectors for 9600 bit/s modem.
IEE Proceedings I (Communications, Speech and Vision), April 1990, vol.137,
(no.2):97-102.
Abstract: The authors describe two new detection processes for a modem that has been designed for operation at 9600 bit/s over the public switched telephone network. The modem is a synchronous serial system, using a 16-point QAM signal, with near-maximum-likelihood detection at the receiver. The detector is preceded by an adaptive filter that is adjusted to make the sampled impulse response of the channel and filter minimum phase. Results of computer simulation tests are presented, comparing the tolerance to additive white Gaussian noise of the new detectors with the most recent near-maximum-likelihood detector, when operating over models of two different telephone circuits. An estimate of the relative complexities of the different near-maximum-likelihood detectors suggests that the developed detection process achieves a much better compromise between performance and complexity than the others.

- A. T. Walden,
"Wavelet estimation using the multitaper method,"
*Geophysical Prospecting*, vol. 39, no. 5, pp. 625-42, July 1991.Abstract: An accurate estimate of the seismic wavelet on a seismic section is extremely important for interpretation of fine details on the section and for estimation of acoustic impedance. Thomson's (1982) multitaper method of cross-spectral estimation, which suffers little from side-lobe leakage, is applied and is compared with the result of using frequency smoothing with the Papoulis (1973) window. The multitaper method seems much less prone to estimating spuriously high coherences at very low frequencies. The wavelet estimated by the multitaper approach from the data used here is equivalent to imposing a low-frequency roll-off of some 48 dB/oct (below 3.91 Hz) on the amplitude spectrum. Using Papoulis smoothing the equivalent roll-off is only about 36 dB/oct. Thus the multitaper method gives a low-frequency decay rate of the amplitude spectrum which is some four times greater than for Papoulis smoothing. It also gives more consistent results across the section.

- N. S. Neidell,
"Could the processed seismic wavelet be simpler than we think?"
*Geophysics*, vol. 56, no. 5, pp. 681-90, May 1991.Abstract: J.P. Lindsey (1988) concludes that most of the roots of a seismic wavelet as expressed by its z-transform representation lie on or are very near the unit circle. The author seeks to characterize the form of those seismic wavelets, that have been processed with deconvolutions or 'inversion' type operators to have reduced length, broadened bandwidth, and some desirable phase property. For such wavelets, remarkably simple operations having very few parameters can be extremely effective. Processed seismic wavelets tend to be of 40-100 ms duration with a smooth and unimodal amplitude spectrum of 'peak' or 'central' frequency between 15 and 30 Hz. A z-transform root structure having essentially all of its roots only on the unit circle and on the real axis seems able to

- C. H. Mehta, B. S. Goel, D. D. Bhatta, and S. Radhakrishnan,
"Minimum phase wavelet by ARMA factorization,"
*IEEE Transactions on Signal Processing*, vol. 39, no. 2, pp. 512-15, Feb. 1991.Abstract: An algorithm is presented for computing a minimum phase wavelet, given only the causal part of its autocorrelation function r/sup +/ (k),k > or = 0. The algorithm falls in the category of spectral factorization techniques, with the difference that instead of factoring the symmetric autocorrelation, its ARMA model is factored, and the ARMA model for symmetric autocorrelation is obtained directly from that of r/sup +/ (k) via a simple identity. It is found that, at least in seismic context, this procedure works better than the conventional spectral factorization as it involves ARMA polynomials which are of much lower order than MA polynomials. The algorithm is supported by two theorems and a detailed numerical example. The treatment is essentially deterministic.

- T. H. Wilson,
"Model studies of shallow common-offset seismic data,"
*Geophysics*, vol. 55, no. 4, pp. 394-401, April 1990,Abstract: For simplicity, optimum-window common-offset data-acquisition procedures are frequently employed to collect near-surface, high-resolution, seismic reflection data. However, because of large incidence angles, interpretations of the data often cannot be evaluated accurately using zero-offset simulations alone. Common-offset hammer seismic data collected in the central Appalachian plateau province of West Virginia are examined. Synthetic shot records using a minimum-phase wavelet estimated from the data and subsurface acoustic properties derived from full-waveform and other geophysical logs are used to simulate the offset seismic response of near-surface, coal-bearing Pennsylvanian aged rocks. Zoeppritz equations are used to model amplitudes.

- A. T. Walden,
"Improved low-frequency decay estimation using the multitaper spectral
analysis method,"
*Geophysical Prospecting*, vol. 38, no. 1, pp. 61-86, Jan. 1990.Abstract: Seismic spectra exhibit very large dynamic ranges particularly at low frequencies. Estimation of low-frequency decay is very important for accurate modelling. However, when using traditional spectral estimates incorporating smoothing windows, too much sidelobe energy leaks from high power into low power areas. The multitaper method of spectral analysis, which uses a set of orthogonal data tapers, yields much less sidelobe contamination, while maintaining a stable estimate. The trace is tapered by each of a subset of the orthogonal tapers, and a raw spectral estimate produced in each case. These are combined to produce a final spectral estimate. The technique can be made adaptive by applying different weights to the different raw spectra at different frequencies. A comparison of seismic spectral estimation using this multitaper technique with a traditional approach having the same analysis bandwidth and stability demonstrates the very different estimates of spectral decay in the areas of high dynamic range.

- T. Stathaki, A. Constantinides, and G. Stathakis,
"Minimum phase FIR filter design from linear phase systems using root
moments,"
*Proc. IEEE Int. Conf. on Acoustics, Speech and Signal Processing*, vol. 3, pp. 1317-20, Seattle, WA, May 1998.Abstract: In this contribution we propose a method for a minimum phase finite impulse response (FIR) filter design from a given linear phase FIR function with the same amplitude response. We concentrate on very high degree polynomials for which factorisation procedures for root extraction are unreliable. The approach taken involves using the Cauchy residue theorem applied to the logarithmic derivative of the transfer function. This leads to a set of parameters derivable directly from the polynomial coefficients which facilitate the factorisation problem. The concept is developed in a way that leads naturally to the celebrated Newton identities. In addition to solving the above problem, the results of the proposed design scheme are very encouraging as far as robustness and computational complexity are concerned.

- Shen, J.; Strang, G.
"Asymptotics of Daubechies filters, scaling functions, and wavelets,"
*Applied and Computational Harmonic Analysis*, vol. 5, no. 3, pp. 312-31, Jul. 1998.Abstract: We study the asymptotic form as p to infinity of the Daubechies orthogonal minimum phase filter h/sub p/[n], scaling function phi /sub p/(t), and wavelet w/sub p/(t). Kateb and Lemarie (1995) calculated the leading term in the phase of the frequency response H/sub p/( omega ). The infinite product phi /sub p/( omega )= Pi H/sub p/( omega /2/sup k/) leads us to a problem in stationary phase, for an oscillatory integral with parameter t. The leading terms change form with tau =t/p and we find three regions for phi /sub p/( tau ): (1) an Airy function up to near tau /sub 0/: /sup 3/ square root (42 pi /p) Ai(-/sup 3/ square root (42 pi p/sup 2/)( tau - tau /sub 0/))+o(p/sup -1/3/); (2) an oscillating region square root (2/ pi pG'( omega /sub tau /))cos[p(G/sup (-1)/( omega /sub tau /)- G( omega /sub tau /) omega /sub tau /)+ pi /4]+o(p/sup -1/2/); (3) a rapid decay after tau /sub 1/: (1/p pi )(1/( tau - tau /sub 1/))sin[p(G/sup (-1)/( pi )- tau pi )]+o(p/sup -1/). The numbers tau /sub 0/ approximately=0.1817 and tau /sub 1/ approximately=0.3515 are known constants. The function G and its integral G/sup -1/ are independent of p. Regions 1 and 2 are matched over the interval p/sup -2/3/(( tau - tau /sub 0/))1. The wavelets have a simpler asymptotic expression because the Airy wavefront is removed by the high-pass filter. We also find the asymptotics of the impulse response h/sub p/[n], a different function g( omega ) controls the three regions. The difficulty throughout is to estimate the phase.

- S. Hirobayashi, T. Kosaka, H. Kimura, and T. Oyabu,
"Approximate linear scheme for analysing gas sensor responses of flow
fields,"
*IEEE Transactions of Japan, Part E*, vol. 118-E, no. 2, pp. 106-12, Feb. 1998.Abstract: Identification of the primary factors responsible for indoor environment gas sensor responses is difficult due to the residual components in the room. By removing these components from the observed sensor signal, we analysed the linear components of the gas transfer route. Gas transfer routes, generally expressed by the Navier Stokes equation, are nonlinear fields. However, gas transfer routes can be approximated to a linear field by reducing flow velocity. We report here a model of indoor flow field generated using a linear system, and applied this model to experimental results. The results of this study indicated that over 90% of residual components of the gas sensor response were linear. Thus, the identification can be improved by reducing residual components from the sensor response using the minimum phase inverse filter.

- G. Jovanovic-Dolecek and J. Javier Diaz Carmona,
"Lowpass minimum phase filter design using IFIR filters,"
*Electronics Letters*, vol. 33, no. 23, pp. 1933-5, Nov. 6, 1997.Abstract: A design procedure for minimum-phase FIR filters using an interpolated FIR (IFIR) filter is proposed. The IFIR technique allows two linear-phase filters of much lower order to be designed thereby making it easier to apply mipizing than is possible in high order FIR prototype filters. In this way, the problem of finding the roots of high order polynomials is overcome.

- C.-Y. Chi,
"Fourier series based nonminimum phase model for second- and
higher-order statistical signal processing,"
*Proc. IEEE Signal Processing Workshop on Higher-Order Statistics*, pp. 395-9, Banff, Alta., Canada, Jul. 1997.Abstract: In the paper, a parametric Fourier series based model (FSBM) for or as an approximation to an arbitrary nonminimum-phase linear time-invariant (LTI) system is proposed for statistical signal processing applications where a model for LTI systems is needed. Based on the FSBM, a (minimum-phase) linear prediction error (LPE) filter for amplitude estimation of the unknown LTI system together with the Cramer Rao (CR) bounds is presented. Then an iterative algorithm for obtaining the optimum mean-square LPE filter with finite data is presented which is also an approximate maximum likelihood algorithm when the data are Gaussian. Then three iterative algorithms using higher-order statistics with finite non-Gaussian data are presented for estimating parameters of the FSBM followed by some simulation results to support the efficacy of the proposed algorithms. Finally, we draw some conclusions.

- N. Aikawa, H. Isomura, and T. Ishikawa,
"Design of finite impulse response transmitter and receiver filters for
data communication system,"
*Electronics and Communications in Japan, Part 3 (Fundamental Electronic Science)*, vol. 79, no. 11, pp. 25-34, Nov. 1996.Abstract: Finite impulse response (FIR) transmitter and receiver filters for data transmission require simultaneous frequency domain and time domain approximation. Previously, linear programming techniques have been used to design such filters; however, those techniques require many calculations and lengthy computation time. This paper proposes a design method of FIR transmitter and receiver filters for data transmission that uses the successive projections method. The design method of a matched filter pair is first described. It can have maximum signal-to-noise ratio (SNR) when Gaussian noise exists on the transmission line and where both the transmitter and receiver filters have the same amplitude response. Since the matched filter has double zeros in the stopband, it can also be used to derive the transfer function of a bandpass minimum phase filter. Then, the value of zero in the sampling interval is chosen such that the total impulse response of the matched filter pair has zero intersymbol interference. A design method with a constraint in the time domain is thus described.

- N. Aikawa, H. Isomura, and I. Ishikawa,
"Design of FIR transmitter and receiver filters for data communication
system,"
*IEEE Transactions of the Institute of Electronics, Information and Communication Engineers A*, vol. 79-A, no. 3, pp. 608-15, Mar. 1996. (in Japanese)Abstract: A method of designing FIR transmitter and receiver filter pairs for data communication systems is presented. They have the property that their cascade is equivalent to a Nyquist filter and thereby satisfies the zero intersymbol interference constraint. In addition both filters have the same amplitude response in the frequency domain. Therefore the characteristic of cascaded filter has double-zeros in the stopband, As the proposed technique is a direct approximation method of such filter, the bandpass minimum phase FIR filter, with the different attenuation in each stopband, can be also derived. This technique is an iterative approximation and it is simple.

- M. Boumahdi,
"Blind identification using the kurtosis with applications to field data,"
*Signal Processing*, vol. 48, no. 3, pp. 205-1, Feb. 1996.Abstract: In this paper we present an estimation method for a non-minimum phase MA, AR or ARMA models. This method is based on the maximum kurtosis property. Firstly the spectrally equivalent minimum-phase (SEMP) filter is estimated from the output statistics, then the kurtosis allows us to localise the zeros of the true transfer function from the zeros of its SEMP filter. For the ARMA process we adopt two ways of identification, the first uses a residual times series approach (RTS) and the second uses a minimum-phase-allpass decomposition. On field seismic data, we compare the deconvolution results using the proposed methods and the minimum-phase approach. Using data from field underwater explosions we show the interest of modelling the secondary waves of the gas bubble, using a non-causal AR filter.

- S. S. Rao and A. Ramasubrahmanyan,
"Evolving IIR approximants for FIR digital filters,"
*Proc. IEEE Asilomar Conference on Signals, Systems and Computers*, vol. 2, pp. 976-9, Nov. 1995.Abstract: This paper describes a new technique for approximating an FIR digital filter by a reduced order IIR filter. The technique yields the globally optimal IIR filter, in the sense of minimizing the output error between the given FIR filter and the IIR approximant to a random white noise input. The model order of the IIR filter can either be specified or it is taken as the one that minimizes the Akaike information criterion. Simulated evolutionary optimization, a multi-agent stochastic search technique is used to optimize the coefficients. The technique permits stipulation of additional constraints on the filter to make it stable, minimum-phase and any other designer specifications. Also being inherently parallel, the technique requires significantly less computation time, compared to algorithms that optimize coefficients serially. Simulation results indicate that the proposed method performs better than classical LMS and system identification based methods like the Stieglitz-McBride method.

- I. Kale, G. D. Cain, and R. C. S. Morling,
"Minimum-phase filter design from linear-phase startpoint via balanced
model truncation,"
*Electronics Letters*, vol. 31, no. 20, pp. 1728-9, Sep. 28, 1995,Abstract: A new practical design approach for minimum-phase FIR or IIR filters, setting out from a high dimensionality FIR linear-phase prototype is described. The novelty of this technique lies in overcoming the inherent problem of finding the roots of a high order polynomial with repeated and/or very closely clustered roots.

- C.-Y. Chi and J.-Y. Kung,
"A new identification algorithm for allpass systems by higher-order
statistics,"
*Signal Processing*, vol. 41, no. 2, pp. 239-56, Jan. 1995.Abstract: Based on a single cumulant of any order M >= 3, a new allpass system identification algorithm with only non-Gaussian output measurements is proposed in this paper. The proposed algorithm, which includes both parameter estimation and order determination of linear time-invariant (LTI) allpass systems, outperforms other cumulant based methods such as least-squares estimators simply due to the more accurate model (allpass model) used by the former. It is applicable in channel equalization for the case of a phase distorted channel. Moreover, the well-known (minimum-phase) prediction error filter has been popularly used to deconvolve seismic signals where the source wavelet can be nonminimum phase and speech signals where the vocal-tract filter can be nonminimum phase. Therefore, the proposed algorithm can be used to remove the remaining phase distortion of the nonminimum-phase source wavelet and nonminimum-phase vocal-tract filter in predictive deconvolved seismic signals and speech signals, respectively. It is also applicable in the minimum-phase-allpass decomposition based ARMA system identification method. Some simulation results and experimental results with real speech data are provided to support the claim that the proposed algorithm works well.

- F. Perez and C. Mosquera,
"Algebraic LTI filter synthesis for simultaneously making a convex
combination of discrete-time plants SPR,"
*IEEE Conference on Decision and Control*, vol. 1, pp. 780-1, New Orleans, LA, USA, Dec. 1995.Abstract: Given a segment of discrete-time plants that are not strictly positive real (SPR), we give a synthesis procedure that obtains a rational, causal and minimum-phase filter that makes the family SPR. Connections between the existence of this filter and a parity interlacing property are unveiled. The degree of the solution can be a priori bounded and depends on the number of crossings of the unwrapped phases of the two extremal plants. The synthesis procedure is an adaptation of the Youla-Saito algorithm (1967).

- M. Boumahdi and J.-L. Lacoume,
"Blind identification using the kurtosis: results of field data
processing,"
*Proc. Int. Conf. on Acoustics, Speech, and Signal Processing*, vol. 3, pp. 1980-3, Detroit, MI, USA, 9-12 May 1995,Abstract: Presents a method to estimate non-minimum phase AR or ARMA systems based on maximum kurtosis properties. First the spectrally equivalent minimum phase (SEMP) filter is estimated from output statistics, then the kurtosis allows to localise the zeros of the associated transfer function from the zeros of its SEMP filter. Combining kurtosis properties and singular value decomposition (SVD) properties the authors propose a new ARMA orders determination method. On field seismic data they compare the proposed method to Giannakis-Mendel's (1989) algorithm and Tugnait's (1991) algorithms. On field underwater explosions data they present a new results showing the interest of estimating a non-causal AR filter to model the secondary waves. The results obtained on a short length of data (128 samples) confirm the robustness of the proposed method.

- A. F. Linville,
"Single-channel digital filter design for seismic applications,"
*Geophysics*, Oct. 1994, vol. 59, no. 10, pp. 1584-92.Abstract: A general least-squares, time-domain filter design methodology has been developed that is easy to use for a variety of seismic filtering applications. The 1D finite-impulse response frequency filter can efficiently provide the noise attenuation and selectivity needed in modern data processing. Flexibility of design allows a choice of all basic types of single-channel filters commonly used in processing. These include low-pass, high-pass, bandpass, band-reject, and notch filters. In addition, multiple bands may be passed or rejected using a single operator design without increasing the length of the filter. The ability to reject multiple noise bands with one filter is convenient and also reduces data processing costs. The filter can be viewed as a minimum-phase Wiener-Levinson predictive deconvolution filter designed to reject specified frequency bands. The filter is designed from an exact mathematical description of the specified stop bands that provide an explicit expression for the required autocorrelation lags in the normal equations. The filter's desired frequency response (transition zone width and rejection level) is simply related to two input parameters-operator length and white noise level.

- M. J. Hinich and W. E. Weber,
"Estimating linear filters with errors in variables using the Hilbert
transform,"
*Signal Processing*, vol. 37, no. 2, pp. 215-28, May 1994.Abstract: Presents a consistent estimator for a linear filter (distributed lag) when the independent variable is subject to observational error. Unlike the standard errors-in-variables estimator which uses instrumental variables, the present estimator works directly with observed data. It is based on the Hilbert transform relationship between the phase and the log gain of a minimum phase-lag linear filter. The results of using the method to estimate a known filter and to estimate the relationship between consumption and income demonstrate that the method performs quite well even when the noise-to-signal ratio for the observed independent variable is large. The authors also develop a criterion for determining whether an estimated phase function is minimum phase-lag.

- R. C. S. Morling, I. Kale, C. W. Tsang, S. J. Morris, and others,
"The design of a sigma-delta codec for mobile telephone applications,"
*Proc. Int. Conf. on Advanced A-D and D-A Conversion Techniques and Their Applications*, pp. 11-17, Jul. 1994.Abstract: The algorithmic, structural, and architectural design of a 13-bit linear sigma-delta ADC and DAC for use with digital mobile telephone systems is described. Analog and digital third-order single-loop modulators running at 512 kHz (64X oversampled) are used to keep the power dissipation low. The ADC uses a two-stage decimation process. The first stage uses a fourth-order "slink" filter to reduce the sample rate to 16 kHz. This is implemented very efficiently using a "running sum" decimator. The second stage is implemented using an IIR minimum-phase lowpass filter which also compensates for the frequency gain distortion of the first stage. The interpolation function of the DAC is realised using a minimum-phase IIR lowpass filter operating at 32 kHz which also compensates for the passband distortion of the zero-order-hold rate converters preceding and following the filter. The digital signal processing of the codec is implemented using two processors. One realises the digital modulator and the high data rate part of the slink decimator while the other, a two-instruction RISC processor, handles the remaining operations. The codec has to operate with three different master clock frequencies, 12.8, 13 and 19.44 MHz. A third processor synthesises the 512 kHz convertor clock. The circuit has been fabricated in a nominal 1.2 mu m double-metal double-poly CMOS process. The conformance of the design to the specification was obtained through the use of bit-true functional simulation which acted as bridge between the algorithmic simulation and the logic level simulation.

- S. Cherif, Ch. Vignat, M. Jaidane, and S. Marcos,
"Nonlinearity on the control error for recursive adaptive filters,"
*Proc. EUSIPCO Signal Processing, Theories and Applications*, vol. 2, pp. 1165-8, Sep. 1994.Abstract: This paper proves that the introduction of a nonlinearity into the structure of a recursive filter has stabilizing and convergence properties compared to the linear case. The effect of this nonlinearity on the performance of fixed and adaptive recursive filters is presented. The stability domain is shown to expand, for a stochastic input, as a function of a so-called saturation degree of the nonlinearity. The modification of the error surface as a function of the nonlinearity is also investigated. It thus appears that the inversion of a non-minimum phase filter is made possible by the introduction of a nonlinearity. The nonlinearity also modifies the gradient-based optimization methods like the LMS and FMRLMS algorithms. Simulation results are given to show a better convergence compared to the linear structure case.

- M. Boujida and J.-M. Boucher,
"Higher order statistics applied to wavelet identification of marine
seismic signals,"
*Proc. EUSIPCO Signal Processing, Theories and Applications*, vol. 1, pp. 93-6, Trieste, Italy, Sep. 1996.Abstract: The purpose of this paper is to present the use of higher order statistics to solve the blind identification problem of reflection seismic data. We develop and compare some nonparametric and parametric methods based on higher order statistics. To compare these methods, the non-minimum phase wavelet and the non-Gaussian reflectivity function are simulated. They are then applied to real data of high resolution marine seismic reflection.

- R. Saatcilar and N. Canitez,
"The lattice filter in ground-roll suppression,"
*Geophysics*, vol. 59, no. 4, pp. 623-31, April 1994.Abstract: Seismic reflections are sometimes masked by Rayleigh-type surface waves that are termed ground roll in seismic literature. An adaptive lattice filter is used to recover reflected signals contaminated by ground roll. Experiments on synthetic and field data showed that the adaptive lattice filter technique is very effective in ground-roll elimination. In addition, the filter works as a whitening operator, compresses the signal, and increases the signal-to-noise ratio.

Last Updated 10/17/98.