Refereed Publications

[1] Walden, A.T. and Prescott, P. (1980) The asymptotic distribution of the maximum of N wave crest heights for any value of the spectral width parameter. J. Geophys. Res., C85, 1905-1909.

[2] Walden, A.T. and Prescott, P. (1980) Approximate confidence intervals for port diagram curves. Proc. Instn. Civ. Engrs., Part 2, 69, 1015-1023.

[3] Prescott, P. and Walden, A.T. (1980) Maximum likelihood estimation of the parameters of the generalized extreme-value distribution. Biometrika, 67, 723-724.

[4] Walden. A.T., Prescott, P. and Webber, N.B. (1981) Some important considerations in the analysis of annual maximum sea levels. Coastal Eng., 4, 335-342.

[5] Walden. A.T., Prescott, P. and Webber, N.B. (1982) The examination of surge-tide interaction at two ports on the central south coast of England. Coastal Eng., 6, 59-70.

[6] Walden. A.T., Prescott, P. and Webber, N.B. (1982) An alternative approach to the joint probability method for extreme high sea level computations. Coastal Eng., 6, 71-82.

[7] Walden, A.T. and Prescott, P. (1983) Identification of trends in annual maximum sea levels using robust locally weighted regression. Estuarine Coastal and Shelf Science, 16, 17-26.

[8] Walden, A.T. and Prescott, P. (1983) Statistical distributions for tidal elevations. Geophys. J. R. Astr. Soc., 72, 223-236.

[9] Prescott, P. and Walden, A.T. (1983) Maximum likelihood estimation of the parameters of the three-parameter generalized extreme-value distribution from censored samples. J. Stat. Comp. Sim., 16, 241-250.

[10] Walden, A.T. and White, R.E. (1984) On errors of fit and accuracy in matching synthetic seismograms and seismic traces. Geophysical Prospecting, 32, 871-891.

[11] Walden, A.T. and Hosken, J.W.J. (1985) An investigation of the spectral properties of primary reflection coefficients. Geophysical Prospecting, 33, 400-435. (Winner of the Van Weelden award of the European Association of Exploration Geophysicists).

[12] Walden, A.T. (1985) NonGaussian reflectivity, entropy and deconvolution. Geophysics, 50, 2862-2888. (Paper selected for the Golden Anniversary Issue of Geophysics).

[13] Walden, A.T. and Hosken, J.W.J. (1986) The nature of the nonGaussianity of primary reflection coefficients and its significance for deconvolution. Geophysical Prospecting, 34, 1038-1066.

[14] Walden, A.T. (1986) Estimating confidence intervals for the gain and phase of frequency response functions. Geophysical J. R. Astr. Soc., 87, 519-537.

[15] Hosken, J.W.J., Longbottom, J.,Walden, A.T. and White, R.E. (1987) Maximum kurtosis phase and the phase of the seismic wavelet. Proc of 1986 Research Workshop on Deconvolution and Inversion, Rome, edited by Bernabini et al, 38-51. Basil Blackwell.

[16] Guttorp, P. and Walden, A.T. (1987) On the evaluation of geophysical models. Geophys. J. R. Astr. Soc., 91, 201-210.

[17] Longbottom, J., Walden, A.T. and White, R.E. (1988) Principles and application of maximum kurtosis phase estimation. Geophysical Prospecting, 36, 115-138.

[18] Walden, A.T. and Nunn, K.R. (1988) Correcting for coloured primary reflectivity in deconvolution. Geophysical Prospecting, 36, 282-297.

[19] Walden, A.T. (1988) Robust deconvolution by modified Wiener filtering. Geophysics, 53, 186-191.

[20] Walden, A.T. (1988) A comparison of stochastic gradient and MED-type deconvolution algorithms. Signal Processing, 15, 203-211.

[21] Walden, A.T. (1988) On phase-lag estimation from nonGaussian time series. Biometrika, 75, 785-787.

[22] Walden, A.T. and Hosken, J.W.J. (1988) Choosing the block averaging interval when calculating primary reflection coefficients from well logs. Geophysical Prospecting, 36, 799-824.

[23] Walden, A.T. (1989) Accurate approximation of a $0$-th order discrete prolate spheroidal sequence for filtering and data tapering. Signal Processing, 18, 341-348.

[24] Walden, A.T. (1990) Improved low frequency decay estimation using the multitaper spectral analysis method. Geophysical Prospecting, 38, 61-86.

[25] Walden, A.T. (1990) Maximum likelihood estimation of magnitude-squared ordinary and multiple coherence. Signal Processing, 19, 75-82.

[26] Walden, A.T. (1990) Variance and degrees of freedom of a spectral estimator following data tapering and spectral smoothing. Signal Processing, 20, 67-75.

[27] Lendzionowski, V., Walden, A.T. and White, R.E. (1990) Seismic character mapping over reservoir intervals. Geophysical Prospecting, 38, 951-969.

[28] Walden, A.T. and White, R.E. (1990) Estimating the statistical bandwidth of a time series. Biometrika, 77, 699-707.

[29] Walden, A.T. (1991) Wavelet estimation using the multitaper method. Geophysical Prospecting, 39, 625-642.

[30] Walden, A.T. (1991) Making AVO sections more robust. Geophysical Prospecting, 39, 915-942.

[31] Walden, A.T. (1992) Clustering of attributes by projection pursuit for reservoir characterization. In Automated Pattern Analysis in Petroleum Exploration, eds. Palaz, I, and Sengupta, S.K., Springer-Verlag, 173-199.

[32] Walden, A.T. (1992) Deconvolution of non-Gaussian time series: the seismic experience. Paper presented at the ISI meeting on Statistics in the Earth and Space Sciences, Aug. 1989. In Statistics in the Environmental and Earth Sciences, eds A.T. Walden and P. Guttorp, Edward Arnold, 136-154. (Refereed).

[33] Walden, A.T. and White, R.E. (1992) Some fads and fallacies in seismic data analysis. Geophysical Prospecting, 40, 289-305.

[34] Walden, A.T.(1992) Asymptotic percentage points for Siegel's test statistic for compound periodicities. Biometrika, 79, 438-440.

[35] Hosken, J.W.J., Mayo, S.K. and Walden, A.T.(1992) The influence of reflection coefficient statistics on the seismic method: Scattering attenuation and transmission wavelets. Proc. R.Soc. Lond. A., 439, 1-23.

[36] Hosken, J.W.J., Mayo, S.K. and Walden, A.T.(1993) The influence of reflection coefficient statistics on the seismic method: Scattering and the minimum detectable reflection coefficient. Proc. R.Soc. Lond. A., 440, 221-240.

[37] Walden, A.T.(1993) Simulation of realistic synthetic reflection sequences. Geophysical Prospecting, 41, 313-321.

[38] Bell, B., Percival, D.B. and Walden, A.T.(1993) Calculating Thomson's spectral multitapers by inverse iteration. J. Comp. Graph. Stat., 2, 119-130.

[39] Walden, A.T. and Williams, M.L.(1993) Deconvolution, bandwidth and the trispectrum. J. Am. Stat. Assoc., 88, 1323-1329.

[40] Walden, A.T., McCoy, E. and Percival, D.B.(1994) The variance of multitaper spectrum estimates for real Gaussian processes. IEEE Trans. Sig. Proc., 42, 479-482.

[41] Walden, A.T.(1994) Interpretation of geophysical bore hole data via interpolation of fractionally differenced white noise. Applied Statistics, 43, 335-345.

[42] Walden, A.T.(1994) Spatial clustering: using simple summaries of seismic data to find the edge of an oil field. Applied Statistics, 43, 385-398.

[43] Walden, A.T.(1994) Some advances in nonparametric multiple time series and spectral analysis. Environmetrics, 5, 281-295.

[44] Walden, A.T.(1995) Multitaper estimation of the innovation variance of a stationary time series. IEEE Trans. Sig. Proc., 43, 181-187.

[45] Walden, A.T., McCoy, E.J. and Percival, D.B.(1995) The effective bandwidth of a multitaper spectral estimator. Biometrika, 82, 201-214.

[46] Grubb, H.J. and Walden, A.T. (1995) Smoothing of seismically derived velocities. Geophysical Prospecting, 43, 1061-1082.

[47] McCoy, E.J. and Walden, A.T. (1996) Wavelet analysis and synthesis of stationary long-memory processes. J. Comp. Graph. Stats., 5, 26-56.

[48] Grubb, H.J. and Walden, A.T. (1997) Characterising seismic time series using the discrete wavelet transform. Geophysical Prospecting, 45, 183-205.

[49] Walden, A.T. and White, R.E. (1998) Seismic wavelet estimation: A frequency domain solution to a geophysical noisy input-output problem. IEEE Trans. Geoscience and Remote Sensing, 36, 287-297.

[50] McCoy, E.J., Walden, A.T. and Percival, D.B. (1998) Multitaper spectral estimation of power law processes. IEEE Trans. Signal Processing, 46, 655-668.

[51] Walden, A.T. and Contreras Cristan, A. (1998) Matching pursuit by undecimated discrete wavelet transform for non-stationary time series of arbitrary length. Statistics and Computing, 8, 205-219.

[52] Walden, A.T. and Contreras Cristan, A. (1998) The phase-corrected undecimated discrete wavelet packet transform and its application to interpreting the timing of events. Proc. Roy. Soc. Lond. Ser.~A., 454, 2243-2266.

[53] Walden, A.T., Percival, D.B. and McCoy, E.J. (1998) Spectrum estimation by wavelet thresholding of multitaper estimators. IEEE Trans. Signal Processing, 46, 3153-3165.

[54] Denison, D.~G.T. and Walden, A.T. (1999) The search for solar gravity-mode oscillations: an analysis using Ulysses magnetic field data. The Astrophysical Journal, 514, 972-978.

[55] Denison, D., Walden, A.T., Balogh, A. and Forsyth, R.J. (1999) Multitaper testing of spectral lines and the detection of the solar rotation frequency and its harmonics. Applied Statistics, 48, 427-439.

[56] Serroukh, A., Walden, A.T. and Percival, D.B. (2000) Statistical properties and uses of the wavelet variance estimator for the scale analysis of time series. J. American Stat. Assoc., 95, 184-196.

[57] Serroukh, A. and Walden, A.T. (2000) Wavelet scale analysis of bivariate time series I: motivation and estimation. J. Nonparametric Statistics, 13, 1-36.

[58] Serroukh, A. and Walden, A.T. (2000) Wavelet scale analysis of bivariate time series II: statistical properties for linear processes. J. Nonparametric Statistics, 13, 37-56.

[59] Walden, A.T. (2000) A unified view of multitaper multivariate spectral estimation. Biometrika, 87, 767-787.

[60] Strela, V. and Walden, A.T. (2001) Signal and image denoising via wavelet thresholding: orthogonal, biorthogonal, scalar and multiple wavelet transforms. Presented on 7th December 1998 at the Data Analysis Workshop, part of the programme on Nonlinear and Nonstationary Signal Processing at the Isaac Newton Institute for Mathematical Sciences, Cambridge, U.K. In Nonlinear and Nonstationary Signal Processing, eds. W.F. Fitzgerald, R.L. Smith, A.T. Walden and P.C. Young, Cambridge University Press, 395-441. (Refereed).

[61] Walden, A.T. (2001) Wavelet analysis of discrete time series. In Proceedings of the European Congress of Mathematics, Barcelona, 2000, Birkhauser, 000-000.

[62] Walden, A.T. and Serroukh, A. (2002) Wavelet analysis of matrix-valued time series. Proc. R. Soc. Lond. A., 458, 157-179.

[63] Tsakiroglou, E. and Walden, A.T. (2002) From Blackman-Tukey pilot estimators to wavelet packet estimators --- a modern perspective on an old spectrum estimation idea. Signal Processing, 82, 1425-1441.

[64] Olhede, S.C. and Walden, A.T. (2002) Generalized Morse wavelets. IEEE Trans. Signal Processing, 50, 2661-2670.

[65] Contreras Cristan, A. and Walden, A.T. (2002) Multitaper power spectrum estimation and thresholding: wavelet packets versus wavelets. IEEE Trans. Signal Processing, 50, 2976-2986. ( Supplemental proof.)

[66] Olhede, S.C. and Walden, A.T. (2003) Polarization phase relationships via multiple Morse wavelets --- Part I: Fundamentals. Proc. R. Soc. Lond. A. 459, 413-444.

[67] Olhede, S.C. and Walden, A.T. (2003) Polarization phase relationships via multiple Morse wavelets --- Part II: Data analysis. Proc. R. Soc. Lond. A. 459, 641-657.

[68] Olhede, S.C. and Walden, A.T. (2003) Noise reduction in directional signals illustrated on quadrature Doppler ultrasound. IEEE Trans. on Biomedical Engineering 50, 51-57.

[69] Olhede, S.C. and Walden, A.T. (2004) The Hilbert spectrum via wavelet projections. Proc. R. Soc. Lond. A. 460, 955-975.

[70] Olhede, S.C. and Walden, A.T. (2004) `Analytic' wavelet thresholding. Biometrika 91, 955-973.

[71] Olhede, S.C. and Walden, A.T. (2005) A generalized demodulation approach to time-frequency projections for multicomponent signals. Proc. R. Soc. Lond. A. 461, 2159-2179.

[72] Olhede, S.C. and Walden, A.T. (2005) Wavelet denoising for signals in quadrature. Integrated Computer-Aided Engineering 12, 109-117. Invited paper for Special Issue on Digital Wavelets, dedicated to Prof. Enders Robinson.

[73] Olhede, S.C. and Walden, A.T. (2005) Local directional denoising. IEEE Trans. Signal Processing 53, 4725-4730.

[74] Medkour, T. and Walden, A.T. (2007) Attenuation estimation from correlated sequences. IEEE Trans. Signal Processing 55, 378-383.

[75] Medkour, T. and Walden, A.T. (2007) A variance equality test for two correlated complex Gaussian variables with application to spectral power comparison. IEEE Trans. Signal Processing 55, 881-888.

[76] Rubin-Delanchy, P. and Walden, A.T. (2007) Simulation of improper complex-valued sequences. IEEE Trans. Signal Processing (to appear).

[77] Medkour, T. and Walden, A.T. (2008) Statistical properties of the estimated degree of polarization. IEEE Trans. Signal Processing (to appear).

[78] Walden, A.T. and Medkour, T. (2008) Ensemble estimation of polarization ellipse parameters. Proc. R. Soc. Lond. A. (to appear).

Books

Percival, D.B. and Walden, A.T. (1993) Spectral Analysis for Physical Applications.. Cambridge University Press, 583pp.

Percival, D.B. and Walden, A.T. (2000) Wavelet Methods for Time Series Analysis,. Cambridge University Press, 600pp.

Walden, A.T. and Guttorp, P. (eds.) (1992) Statistics in the Environmental and Earth Sciences. Hodder Headline.

Fitzgerald, W.F., Smith, R.L., Walden, A.T. and Young, P.C. (eds.) (2001) Nonlinear and Nonstationary Signal Processing. Cambridge University Press.

Some Recent Conference Papers

Walden, A.T. and Contreras Cristan, A. (1997) The phase-corrected undecimatedwavelet packet transform and the recurrence of high latitude interplanetary shock waves. Proc. IEEE UK Symposium on Applications of Time-Frequency and Time-Scale Methods, University of Warwick, 27-29th August, 1997, pp. 9-12.

Serroukh, A., Walden, A.T. and Percival, D.B. (1998) Statistical properties of the wavelet variance estimator for non-Gaussian/non-linear time series. International Wavelet Conference, Tanger, Morocco, April 13-17, 1998.

Strela, V. and Walden, A.T. (1998) Orthogonal and biorthogonal multiwavelets for signal denoising and image compression. SPIE's 12th Annual International Symposium on Aerospace/Defense Sensing, Simulation, and Controls. Orlando, Fl, April 13-17, 1998. Proc. SPIE, Vol. 3391.

Contreras Cristan, A. and Walden, A.T. (2001) Wavelet packet thresholding and spectrum estimation. Joint Statistical Meetings. Atlanta, GA, August 8, 2001. ( Supplemental proof.)

Olhede, S. and Walden, A.T. (2002) Noise reduction in Doppler ultrasound using multiple wavelets. The 2002 International Conference of the Royal Statistical Society . Plymouth, 3--6 September.

Olhede, S. and Walden, A.T. (2003) The Hilbert spectrum and wavelet projections. 2003 SIAM Annual Meeting. June 16--20, Montreal, Canada.

Olhede,~S. and Walden, A.T. (2003) Multiple Morse wavelets and their uses. Wavelets and Statistics. Grenoble, France, 4-7 September.

Walden,~A.T. and Olhede,~S.C. (2005) The `analytic' vector in stochastic time-frequency analysis. Wavelet and Time-Frequency Analysis for Earth Sciences, European Geosciences Union. Vienna.