Use of the kepstrum in signal analysis

2006 IEEE International Symposium on Signal Processing and Information Technology

Jeong

2006

A technique is shown for the direct identification of non-minimum phase terms with application to system identification. No polynomial root finding is necessary with this approach. The method uses a combination of kepstrum analysis to first estimate a minimum phase term and the residual all-pass transfer functions which have the non-minimum phase information are then estimated with a cascaded recursive-least squares (RLS) algorithm.

Section: Kepstrum Identification: For Reflected and Minimum Phasementioning

confidence: 99%

Section: Ux Ikomentioning

confidence: 99%

Section: Kepstrum Identification: For Reflected and Minimum Phasementioning

confidence: 99%

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Identification of Non-Minimum Phase Transfer Function Components

2006 IEEE International Symposium on Signal Processing and Information Technology

Jeong

2006

“…, k N −1 are the estimated kepstrum coefficients for the noise-only case. The transfer functions for the individual spectral factors can be found by the recursion method of Silvia & Robinson (1978). For the two series, we find the recursions as follows.…”

Section: (B) Spectral Factor Determination From Estimated Kepstrum Comentioning

confidence: 99%

“…A distinction is made here between 'kepstrum' (Silvia & Robinson 1978) and 'complex cepstrum' (Oppenheim et al . 1968;Oppenheim & Schafer 1975), in that the kepstrum coefficients, as given by the Kolmogorov power series, are theoretical values, while the complex cepstra using the fast Fourier transform (FFT) are estimates of these.…”

Section: Introductionmentioning

confidence: 99%

A kepstrum approach to filtering, smoothing and prediction with application to speech enhancement

Barrett²

2003

Proc. R. Soc. Lond. A

A kepstrum (or complex-cepstrum) approach to minimum-phase Wiener filtering of stationary scalar processes is proposed and solved for the case of signal plus coloured noise, where the noise possibly includes a white-noise component. A general solution is found in an innovations form. The spectral factorization of the noise model and of the signal-plus-noise model required for the solution are determined from data using the kepstrum technique with the fast Fourier transform. This approach avoids dependence on any form of multidimensional state-space or polynomial-based model and so avoids use of recursive parameter estimation or of Diophantine equations.

Spectral factorization using FFTs for large‐scale problems

Adaptive Control & Signal

2014

A method is provided for scalar systems, which uses FFTs and provides spectral factorization directly from the periodogram. The method is block recursive, providing better estimates as time progresses with more data available. Although spectral factorization is a mature technique, the current methods available are generally too slow to cope with acoustic problems of the scale discussed here. SPECTRAL FACTORIZATION USING FFTs 955 problem, some simpler than others. For example, the earliest discrete-time attempt was due to Kolmogorov [3] and later a computational method by Wilson [4]. Since then, there has been a good number of approaches mostly summarized here [5]. The particular approach that concerns this paper is the feedback method proposed by Moir [6] and used for system identification [7]. In fact, the spectral factorization problem appears in all classes of frequency-domain problems where a quadratic cost function is involved. So besides the optimal filtering problem [2], it also has application in optimal control [8-10]. There is another method available for spectral factorization using FFTs, however. For example the cepstrum or kepstrum approach [11][12][13] can be used, but these approaches, when used on real data, need a great deal of smoothing to achieve accurate results. Although such a method could in principle be used for our application, the two methods are totally unrelated. We also note here that the estimation of the polynomial a.´ 1 / is not unique for the more general case when the spectrum has non-minimum-phase zeros. For second-order statistics, it is well established that it is only possible to estimate the minimum-phase equivalent (i.e. the zeros are reflected back within the unit circle of the´-plane). Although this can be a disadvantage, we can also use this as an advantage to obtain stable polynomials as shown in a later section applied to acoustics. Whilst it is possible to apply a similar approach to higher-order statistics, it is known that such an approach can lead to an error surface that is not convex and has local minima.rf .v 0 ; v 1 ; : : :be zero. 956 T. J. MOIR Now, as " k D L V k , we find by differentiating again P j D0w i w i Cj ; i D 0; 1 : : : n. Note that this operation is equivalent in the´-domain to the operation a.´ 1 /a.´/ D ja.´/j 2 . What we are effectively doing is re-forming the Laurent series based on the estimated spectral factor and creating SPECTRAL FACTORIZATION USING FFTs 959 frequency-domain method, which requires a primary and reference input [14]. Although other blind methods exist, for example, [15][16][17][18][19][20], these methods require special input signals associated with communication systems, for example, code division multiple access, or alternatively require signals that have higher-order statistics [21]. The possible exception to this is the Kepstrum method [11,12,22], which has found application in adaptive filtering [23]. It should be made clear however that no method that has Gaussian noise as the driving signal can reconstruct accurate...