Differential Cepstrum Research Articles

Seismic fault detection with sliding windowed differential cepstrum–based coherence analysis

AbstractCepstral decomposition is beneficial for highlighting certain geological features within the particular quefrency bands which may be deeply buried within the wide quefrency range of the seismic data. Converting seismic traces into the corresponding cepstrum components can better analyse some characteristics of underground strata than the traditional spectral decomposition methods. We propose the sliding windowed differential cepstrum–based coherence analysis approach to delineate the fault features. First, the data are decomposed using a sliding windowed differential cepstrum, which results in multi‐cepstrum data of corresponding quefrency of certain bandwidth. These different multi‐cepstrum data may highlight the different stratigraphic features in a certain quefrency band. We select the first‐order common quefrency volume as the featured attribute. Then, eigenstructure‐based coherence is applied on the first‐order common quefrency data volume to statistically obtain the fault detection result with a finer and sharper image. Synthetic data and field data examples show that the proposed method has the ability to better visualize all the possible subtle and minor faults present in the data more accurately and discernibly than the traditional coherence method. Compared with the ant‐tracking method, the proposed method is more effective in revealing the major faults. It is hoped that this work will complement current fault detection methods with the addition of the cepstral‐based method.

A multi-level power grid enhanced identity authentication data management platform based on filtering algorithms

In response to the optimal extraction of DCT coefficients in facial images, the author proposes a DCT coefficient extraction method based on discriminant analysis. Based on the discriminant analysis of DCT coefficients, the DCT coefficients with high discriminant values are selected as features. Comparing the DPA based discrete cosine coefficient selection method proposed by the author with the traditional Zigzag discrete cosine coefficient selection method, experiments were conducted on the ORL face database and the Yale face database, respectively. The recognition performance on the ORL face database was higher than that on the Yale face database, as the facial image expression and lighting changes in the ORL database were relatively few, making it suitable for extracting key features. In response to the problem that the speech parameter MFCC is greatly affected by noise and can only reflect the static characteristics of speech, the author extracted gamma pass filtering cepstrum coefficients with human auditory characteristics and gamma pass sliding differential cepstrum coefficients that can reflect the dynamic characteristics of speech based on gamma tone filters and sliding differential cepstrum. In the NUST603 speech database, under pure background, the recognition rate based on GFSDCC features reached 89.88%, and the recognition effect based on GFCC features was 87.52%, which is 4.66% and 2.36% higher than that based on MFCC features. In noisy environments, the average recognition rates of speaker recognition systems based on GFCC and GFSDCC are 56.06% and 59.07%, while the average recognition rates of speaker recognition systems based on MFCC speech features are 53.89%, 2.17% and 5.18% higher, respectively. The gain in this recognition effect comes from the characteristics of the auditory model, as the Gammatone filter effectively reflects the noise resistance of the human auditory system.

Application of variational mode decomposition–based Hilbert marginal differential cepstrum for hydrocarbon detection

AbstractThe possibilities offered by the use of variational mode decomposition–based Hilbert marginal spectrum and the differential cepstrum for gas‐bearing detection are studied in this paper. We propose a novel variational mode decomposition–based Hilbert marginal differential cepstrum for hydrocarbon detection. Variational mode decomposition–based Hilbert marginal spectrum is first computed. Then discrete cosine transform is carried out to the differential logarithmic variational mode decomposition–based Hilbert marginal spectrum to obtain the variational mode decomposition–based Hilbert marginal differential cepstrum. For hydrocarbon detection, the seismic amplitude anomaly section is generated by extracting the first and second common quefrency sections. Compared with the traditional Fourier‐based cepstrum, the wavelet‐based cepstrum and the Berthil cepstrum, it has the ability to effectively reveal more detailed frequency‐dependent amplitude anomalies with high accuracy and resolution. Model tests and field data applications from a carbonate reservoir in China show that the variational mode decomposition‐based Hilbert marginal differential cepstrum can provide a better gas‐prone interpretation. The proposed method can be a complementary approach to current cepstrum‐based hydrocarbon detection methods and the spectrum decomposition methods.

A history of cepstrum analysis and its application to mechanical problems

It is not widely realised that the first paper on cepstrum analysis was published two years before the FFT algorithm, despite having Tukey as a common author, and its definition was such that it was not reversible even to the log spectrum. After publication of the FFT in 1965, the cepstrum was redefined so as to be reversible to the log spectrum, and shortly afterwards Oppenheim and Schafer defined the “complex cepstrum”, which was reversible to the time domain. They also derived the analytical form of the complex cepstrum of a transfer function in terms of its poles and zeros. The cepstrum had been used in speech analysis for determining voice pitch (by accurately measuring the harmonic spacing), but also for separating the formants (transfer function of the vocal tract) from voiced and unvoiced sources, and this led quite early to similar applications in mechanics. The first was to gear diagnostics (Randall), where the cepstrum greatly simplified the interpretation of the sideband families associated with local faults in gears, and the second was to extraction of diesel engine cylinder pressure signals from acoustic response measurements (Lyon and Ordubadi). Later Polydoros defined the differential cepstrum, which had an analytical form similar to the impulse response function, and Gao and Randall used this and the complex cepstrum in the application of cepstrum analysis to modal analysis of mechanical structures. Antoni proposed the mean differential cepstrum, which gave a smoothed result. The cepstrum can be applied to MIMO systems if at least one SIMO response can be separated, and a number of blind source separation techniques have been proposed for this. Most recently it has been shown that even though it is not possible to apply the complex cepstrum to stationary signals, it is possible to use the real cepstrum to edit their (log) amplitude spectrum, and combine this with the original phase to obtain edited time signals. This has already been used for a wide range of mechanical applications. A very powerful processing tool is an exponential “lifter” (window) applied to the cepstrum, which is shown to extract the modal part of the response (with a small extra damping of each mode corresponding to the window). This can then be used to repress or enhance the modal information in the response according to the application.

Study on Characteristic Parameters of Speech Anti-Deliberate Imitation System

Deliberate imitation which is the reproduction of another speakers voice and speech behavior can pose a threat to the security of the voice authentication system. Therefore effective characteristic parameters are the key to the anti-deliberate imitation. The study chose speech database of anti-deliberate imitation and investigated some common feature parameters separating capacity and descriptive power against voice deliberate imitation. The study compared the ranking of subjective evaluation and feature parameters Euclidean distance of imitators. The comparison results indicate that Mel frequency cepstrum coefficient (MFCC) combined with its differential cepstrum parameters (WMFCC) have the best performance for anti-deliberate imitation. And the results were validated by the experiment based on VQ speaker verification system.

Two-Dimensional Partially Differential Cepstrum and Its Applications on Filter Stabilization and Phase Unwrapping

A new type of differential cepstrum (DC) named as partially DC (PDC) is introduced. While compared with the previously defined DC, the PDC saves half the computational complexity since only one dimension of the partial derivative is considered. Nevertheless, for the calculation of the complex cepstrum (CC), using the PDC avoids the phase-unwrapping routine as well. One application is to construct the minimum-phase sequence from a mixed-phase one through a windowing technique, which can be further applied to filter stabilization. Another application is performing phase unwrapping on 2-D phase data to which we propose a much simpler technique using the PDC. These applications can be implemented in a more efficient and convenient way with the PDC than with the traditional DC.

Vector quantization based on the dynamic threshold of speaker recognition

Code splitting threshold is one of the important factors to initialize codebook in Speaker Recognition based on the Vector Quantitation (VQ), but traditional threshold is not easy to determine and needs a large number of experiments to determine the value. This paper used dynamic and random method to select the threshold in a certain range, and combined with differential cepstrum thresholds to establish speaker recognition model. The results show that given the method improves the recognition rate, the training time and the recognition time have improved significantly.

BLIND SYSTEM IDENTIFICATION USING MATRIX MEAN DIFFERENTIAL CEPSTRUM WITH QR-CHOLESKY DECOMPOSITION

A further development of the matrix mean differential cepstrum technique for blind identification of convolved mixtures in multiple-input-multiple-output mechanical systems is presented. The stability of the technique for application on the whitened response measurements can be improved with the use of the QR-Cholesky decomposition instead of the SVD-EVD set. Two simulated two-input two-output, two degree of freedom systems of differing damping coefficients are tested. The improved results with smoother frequency response functions of the system are presented and compared to prior results.

Investigations of independence of distortion scales in objective evaluation of synthesized speech quality

Using factor analysis, we have investigated the independence of five distortion scales, namely, differential spectrum distortion, phase distortion, waveform distortion, cepstrum distance, and amplitude distortion, that are widely used in the objective evaluation of synthesized speech quality. We have found that the above distortion scales can be constructed from two factors. The first factor is constructed from cepstrum distance, amplitude distortion, and waveform distortion, and the second factor is constructed from phase distortion and differential spectrum distortion. When a multiple linear regression model is used as a prediction model of MOS, the prediction accuracy is the highest when the cepstrum distance is used as the distortion scale for the first factor and the differential spectrum distortion for the second factor. Investigating the correspondence of psychological quality factors with the physical distortion factors, it was found that the first physical factor is related to “clarity” and second factor is related to “sensation.” Moreover, the importance of differential spectrum distortion in the future quality prediction of low-bit-rate synthesized speech is demonstrated. © 2000 Scripta Technica, Electron Comm Jpn Pt 3, 83(5): 14–22, 2000

Asymptotically exact computation of differentialcepstrum using FFT approach

A new concept of the differential cepstrum calculation is presented which uses the FFT with interpolation in the frequency domain. The algorithm assures asymptotically exact values, without cepstral aliasing. It completely separates the causal and the anticausal part of the cepstrum and it does not suffer from signal singularities, i.e. zeros on the unit circle in the z-plane. The algorithm's computational complexity is at least four times lower than for any other cepstral aliasing reduction method, while no extended memory signal buffer is required.

Root moments: a digital signal-processing perspective

The use of cepstral parameters is gaining importance in many areas. However, their introduction is usually through an approach which often mars their simplicity and beauty. The differential cepstrum is an important variant of this class of signal transformations. It has been defined in terms of the logarithmic derivative of the z transform of a given signal. However, a more useful approach is through the Cauchy residue theorem, which yields additional insight and properties. The entire concept and additional properties may be developed in a way that leads naturally to the celebrated Newton identities. These identities are developed and elaborated in the paper. Furthermore, they are employed innovatively in signal-processing problems, including the determination of the minimum phase component of a signal, a stability test for linear systems and the detection of abrupt changes in a signal.

Formulas for computation of 2-D logarithmic and 2-D differential cepstrum

Exact analytical formulas for the 2-D logarithmic cepstrum and the 2-D differential cepstrum of a class of 2-D signals are derived. They permit an easy evaluation consisting in a finite number of arithmetic operations on a finite domain of the cepstral plane. The results are demonstrated by examples with explicit expressions.

The complex cepstrum of higher order cumulants and nonminimum phase system identification

A computationally efficient identification procedure is proposed for a nonGaussian white-noise-driven linear, time-invariant, nonminimum phase system. The method is based on the idea of computing the complex cepstrum of higher order cumulants of the system output. In particular, the differential cepstrum parameters of the nonminimum phase impulse response are estimated directly from higher-order cumulants by least-squares solution or two-dimensional FFT operations. The method reconstructs the minimum-phase and maximum-phase impulse response components separately. It is flexible enough to be applied on autoregressive (AR), moving average (MA), or ARMA system without a priori knowledge of the type of the system. Benchmark simulation examples demonstrate the effectiveness of the method even with short length data records.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Signal delay and waveform estimation through differential cepstrum averaging

The differential cepstrum (DC) was introduced as a new tool for homomorphic deconvolution, a method which possesses the shift invariant property. The delay in the time samples will effect only the second sample of the DC. This property of the DC is used for estimating the signal delay and the waveform, in the presence of signal jitter and noise. Simulation results are presented to demonstrate the applicability of this technique for processing the signals embedded in white Gaussian noise. Better noise suppression has been observed through DC averaging as compared to group delay averaging or unwrapped phase averaging methods.

On the computation of complex cepstrum through differential cepstrum

A relation between complex cepstrum and differential cepstrum is derived. The problem of aliasing associated with the computation of complex cepstrum through differential cepstrum is demonstrated with an example.

Design of minimum-phase FIR digital filters by differential cepstrum

The differential cepstrum is introduced to design equiripple minimum phase FIR filters by using cepstral deconvolution; this fast procedure only takes three FFT computation and avoids the complicated phase wrapping and polynomial root-finding algorithms.

Design of minimum-phase FIR digital filter through cepstrum

A method to design an equiripple minimum-phase FIR filter using the cepstrum is described. This method avoids the complicated polynomial root-finding algorithm of Herrman and Schuessler (1970), or the phase-unwrapping algorithm associated with the complex cepstrum of Mian and Nainar (1982). The differential cepstrum method proposed by Pei and Lu (1986) has aliasing problems and requires the computation of three FFTs. The proposed method requires only two FFT computations and avoids the processing of phase.

The two-dimensional differential cepstrum

The two-dimensional (2-D) differential cepstrum, which has no ambiguity in its phase relationship, is introduced as a new basis for homomorphic deconvolution. Its properties and implications are discussed.

A low bit rate vocoder based on an improved cepstral method

By using a log spectrum approximation filter modeling a true log spectral envelope, a low bit rate and high‐quality vocoder was realized. The true log spectral envelope is represented by the low‐quefrency portion of the cepstrum modified by the low‐quefrency components involved in the rectified fine structure of the log spectrum. It can be obtained through an iteration of DFT‐rectifying‐IDFT for the higher quefrency portion of the speech cepstrum. In this vocoder, the speech synthesis is not based on the homomorphic method. The synthesis filter can be obtained without transforming the cepstrum to an impulse response, and the computation for the filter coefficients is very simple. The spectral envelope information is transmitted in the form of a differential cepstrum corresponding to the difference of two adjacent log spectral envelopes, and the data rate is very low.

Newer concepts of the pitch, the loudness and the timbre of musical tones

It is not widely realised that the first paper on cepstrum analysis was published two years before the FFT algorithm, despite having Tukey as a common author, and its definition was such that it was not reversible even to the log spectrum. After publication of the FFT in 1965, the cepstrum was redefined so as to be reversible to the log spectrum, and shortly afterwards Oppenheim and Schafer defined the “complex cepstrum”, which was reversible to the time domain. They also derived the analytical form of the complex cepstrum of a transfer function in terms of its poles and zeros. The cepstrum had been used in speech analysis for determining voice pitch (by accurately measuring the harmonic spacing), but also for separating the formants (transfer function of the vocal tract) from voiced and unvoiced sources, and this led quite early to similar applications in mechanics. The first was to gear diagnostics (Randall), where the cepstrum greatly simplified the interpretation of the sideband families associated with local faults in gears, and the second was to extraction of diesel engine cylinder pressure signals from acoustic response measurements (Lyon and Ordubadi). Later Polydoros defined the differential cepstrum, which had an analytical form similar to the impulse response function, and Gao and Randall used this and the complex cepstrum in the application of cepstrum analysis to modal analysis of mechanical structures. Antoni proposed the mean differential cepstrum, which gave a smoothed result. The cepstrum can be applied to MIMO systems if at least one SIMO response can be separated, and a number of blind source separation techniques have been proposed for this. Most recently it has been shown that even though it is not possible to apply the complex cepstrum to stationary signals, it is possible to use the real cepstrum to edit their (log) amplitude spectrum, and combine this with the original phase to obtain edited time signals. This has already been used for a wide range of mechanical applications. A very powerful processing tool is an exponential “lifter” (window) applied to the cepstrum, which is shown to extract the modal part of the response (with a small extra damping of each mode corresponding to the window). This can then be used to repress or enhance the modal information in the response according to the application.