Showing papers on "Cepstrum published in 1977"

The cepstrum: A guide to processing

Abstract: This paper is a pragmatic tutorial review of the cepstrum literature focusing on data processing. The power, complex, and phase cepstra are shown to be easily related to one another. Problems associated with phase unwrapping, linear phase components, spectrum notching, aliasing, oversampling, and extending the data sequence with zeros are discussed. The advantages and disadvantages of windowing the sampled data sequence, the log spectrum, and the complex cepstrum are presented. The influence of noise upon the data processing procedures is discussed throughout the paper, but is not thoroughly analyzed. The effects of various forms of liftering the cepstrum are described. The results obtained by applying whitening and trend removal techniques to the spectrum prior to the calculation of the cepstrum are discussed. We have attempted to synthesize the results, procedures, and information peculiar to the many fields that are finding cepstrum analysis useful. In particular we discuss the interpretation and processing of data in such areas as speech, seismology, and hydroacoustics. But we must caution the reader that the paper is heavily influenced by our own experiences; specific procedures that have been found useful in one field should not be considered as totally general to other fields. It is hoped that this review will be of value to those familiar with the field and reduce the time required for those wishing to become so.

Some Geophysical Applications of Autoregressive Spectral Estimates

Abstract: This paper discusses the practical application of autoregressive spectral analysis to three different geophysical data sets. In all cases the amount of available data was limited so that autoregressive methods might give more detailed spectra than those obtainable by the classical windowed spectral estimate methods. For each series, the Burg technique, which guarantees positive-definite autocorrelation functions, is used to determine the prediction error coefficients. The degree of spectral instability known to result from the use of Burg's algorithm is not crucial to our results. Algorithms due to Akaike and Parzen are applied to the time series to aid in order-number determination. For the first example, autoregressive spectral analysis of a complex time series is applied to the log spectrum of short-period seismograms. The resultant spectrum, the so-called complex cepstrum, allows one to determine the depth below the earth's surface at which the seismic event originated. The other examples concern the analysis of real time series due to two somewhat unusual data sets. One of these is the analysis of the time rate at which earthquakes occur. The purpose is to determine if periodicities exist that correspond to known astronomical and terrestrial rotational periods. The other is a study of biological and chemical parameters measured in core samples of oceanbottom sediments where displacement down the core is calibrated in geological time. The measurements directly infer the amount of ice on the earth's surface.

The Old and the New in Seismic Deconvolution and Wavelet ESTIMATION

Abstract: Various seismic deconvolution operators can be determined by estimating a seismic wavelet and subsequently designing an appropriate inverse filter which converts the wavelet to a spike. Seismic wavelets and deconvolution operators must be estimated in a time adaptive sense due to the nonstationarity of the seismic trace. The wavelet estimation methods considered either use the assumption of a minimum phase wavelet and a random impulse response, or the assumption that the wavelet cepstrum is readily separable from the cepstrum of the seismic trace. The former assumption is required in using the Hilbert transform and Wiener-Levinson wavelet estimations, while the latter assumption is used in homomorphic deconvolution. These wavelet estimates can be used in the design of multichannel Wiener and Kalman deconvolution operators. Multichannel usage of homomorphic deconvolution can also be implemented through various types of cepstral stacking. The discussion of deconvolution filter design focuses on the problems of filter length degree of prewhitening and nonstationarity. In designing time adaptive deconvolution filters, the autocorrelation function can be used to monitor the nonstationarity of the seismic trace. The autocorrelation function, which is used in the computation of least squares inverse filters, can be estimated in an optimum fashion by using the maximummore » entropy method. Differences between minimum phase Wiener deconvolution and maximum entropy deconvolution become more pronounced for shorter data gates. As a result the maximum entropy approach is preferred for time adaptive deconvolution. The performance of various wavelet estimators and inverse filters is discussed using real and synthetic seismic data. Discussions of homomorphic deconvolution and maximum entropy prediction error filtering are merged with descriptions of conventional approaches to deconvolution.« less

The computation of two-dimensional cepstra

Abstract: In this paper we shall explore two methods of computing the complex cepstrum of a two-dimensional (2-D) signal. The two principal methods for computing 1-D cepstra, using discrete Fourier transforms (DFT's) and the complex logarithm function or using a recursion relation for minimum-phase signals, may be extended to two dimensions. These two algorithms are developed and simple examples of their use are given. As a matter of course, we shall also be drawn into considering the definitions of 2-D causality and 2-D minimum-phase signals. In addition, we shall explore the relationship among the nonzero regions of a signal, its inverse, and its cepstrum.

Computation of the complex cepstrum by factorization of the z-transform

Abstract: We compute the complex cepstrum of a finite duration slgnal by completely factoring its z-transform and summing the easily obtained complex cepstra of the factors. The method requires no phase unwrapping and introduces no aliasing. The only approximation is the unavoidable finite time window. Thus the factorization method provides a means for evaluating other methods for computing the complex cepstrum.

A stability test for 2-D recursive digital filters using the complex cepstrum

Abstract: A procedure is presented for testing the stability of 2-D recursive filters. This test is based on the mapping properties of the complex cepstrum. A numerical algorithm for computing the 2-D cepstrum is described, and subsequently used in calculating numerical examples of the stability test.

Short-time homomorphic analysis

Abstract: Homomorphic deconvolution has been successfully applied in a variety of areas. In many cases of interest, including speech and seismic processing, the signals to be analyzed are non-stationary and approximately follow a convolutional model only on a short-time basis. Thus, a window is applied to the data. In this paper a first attempt is made to understand the interaction between short-time windowing and homomorphic deconvolution. A model for short-time homomorphic analysis is proposed, which provides a framework for the interpretation of window effects encountered in speech and seismic data processing.

Waveform Detection and Classification with SAW Cepstrum Analysis

Abstract: A prototype real time cepstrum analyzer incorporating surface acoustic wave (SAW), Fourier transform processors is reported. This system offers sophisticated wideband signal processing for radar, sonar, and communications applications. Practical results demonstrate its capabilities when analyzing bandwidths in excess of 10 MHz in a few microseconds with simulated pulsed RF waveforms in the presence of multipath echoes. Pulse duration, repetition interval, and binary code length are resolved and the potential to characterize unknown chirp waveforms is briefly reported.

A stability criterion for N-dimensional zero-phase recursive digital filters

Abstract: This paper presents an extension of the work of Pistor to N dimensions. The stability of an N-dimensional recursive digital filter is shown to be related to the properties of its cepstrum. A procedure is also given for the decomposition of unstable recursive digital filters having a nonzero nonimaginary frequency response into a set of stable single-quadrant recursive filters.

Automatic speaker recognition for use over communication channels

Abstract: A system is described for the automatic comparison of speakers given short samples of their speech. The method does not depend on knowing what is being said, and is to a large extent independent of the degradations likely to be suffered by the speech during transmission. A small computer has been used to generate statistics on fundamental frequency and spectral shape information produced by a real-time cepstrum processor. Fundamental frequency is intrinsically resistant to most transmission degradations, and the spectral statistics taken are independent of linear spectral shaping. A useful level of recognition performance has been obtained using a total of 154 20s samples of read speech from thirteen typical speakers of British English.

Real Time Wideband Cepstrum Analysis Based on SAW Devices

Abstract: Cepstrum analysis usinq Surface Acoustic Wave Fourier (Chirp) Transform processors has application in waveform detection and classification. Analyser capabilities are demonstrated theoretically and practically measuring the pulse width, duration, period and frequency of unknown input waveforms.

Comparison of seismic features extracted by digital signal processing techniques

Abstract: During the past four years extensive effort has been made by this research group to digitally enhance the seismic data and to seek for the best mathematical features to discriminate between the natural earthquake and the nuclear explosion events. In this paper the recognition results based on different sets of seimic data base are reported. In particular, a critical comparison is made with the most recent seismic data base on the feature sets: autocovariance, power cepstrum, Alpha minus C energy estimate and entropy. The four feature sets are all effective but the autocovariance features provide the best performance with 89.32% correct recognition based on 16 features, 7 best learning samples from each class and the nearest neighbor classification rule. Although the theoretical comparison is not possible, computer results presented are reliable because of the reasonably large sample size used.

Experiments with echo detection in the presence of noise using the power cepstrum and a modification

Abstract: The power cepstrum of a function is found by computing the power spectrum of the logarithm of the power spectrum of that function. In addition, some applications of the cepstrum employ a smoothing (windowing) function immediately before or after the logarithm operation. This paper describes some experiments in echo-time detection and quefrency-band power measurements performed on ultrasound waveforms, both by the standard cepstral method and by the deletion of either or both of the window and the logarithm from that method. It is shown that echo-time detection in the presence of noise is achieved more reliably without the logarithm step for the waveforms of interest. Our experimental findings compare favorably with theoretical results reported recently by Hassab and Boucher [2].

Digital analysis of loudspeaker performance

Abstract: There is growing awareness of the usefulness of digital signal processing in audio. One area of application is the use of digital techniques in loudspeaker performance analysis. This paper describes an interactive computer system for loudspeaker measurement. In particular, the use of the cepstrum is discussed for the characterization of loudspeaker and room responses and for the determination of group delay and minimum-phase group delay curves for loudspeakers.

Complex cepstrum processing of digitized transient calibration data for removal of echoes

Abstract: : The complex cepstrum technique was investigated for possible use in removing echoes casued by early reflections when low-frequency, peaked-response transducers are calibrated with transient signals. The calibration environment permits a high signal-to-noise ratio and a free choice of input waveforms, both of which are advantages in complex cepstrum processing. The proper method of computation with this technique is discussed in detail. Cepstrum filtering methods are discussed. Synthetic measurement data produced by a J9 projector driven with a damped sinusoidal pulse and a pressure-release reflection are shown, and real measurement data from a low-frequency line array driven by a single-cycle sinusoid with complex surface and bottom reflections are also shown. In both the synthetic and the real data, the echoes were successfully removed using the complex cepstrum technique. Data were digitized directly and stored on digital magnetic tape. Oversampling was reduced by sifting to achieve the correct sampling rate required by the complex cepstrum method. The results indicate that echo removal performed by complex cepstrum processing can be accurate enough to have potential usefulness in calibration procedures. (Author)

The Computation of Two-Dimensional Cepstra

Abstract: In this paper we shall explore two methods of computing the complex cepstrum of a two-dimensional (2-D) signal. The two principal methods for computing 1-D cepstra, using discrete Fourier transforms (DFT's) and the complex logarithm function or using a recursion relation for minimum-phase signals, may be extended to two dimensions. These two algorithms are developed and simple examples of their use are given. As a matter of course, we shall also be drawn into considering the definitions of 2-D causality and 2-D minimum- phase signals. In addition, we shall explore the relationship among the nonzero regions of a signal, its inverse, and its cepstrum.

Signal Processing and Pattern Recognition of Ultrasonic Waveforms for the Nondestructive Evaluation of Materials.

Abstract: : The overall goal of this project has been to further investigate signal processing and pattern recognition techniques as to how they apply in the nondestructive evaluation of materials for classifying ultrasonic pulse echo waveforms. Computer programs were developed to implement algorithms to generate power spectrum, cepstrum, and auto-correlation waveforms from the ultrasonic pulse echo waveforms. These algorithms have a firm statistical foundation and also have properties associated with them that allow the Fast Fourier Transform to be utilized in an efficient manner. Also, statistical features were extracted from the waveforms. The features were then input to pattern recognition techniques in order to classify the data into appropriate material defects. The procedure outlined above was implemented with 49 ultrasonic pulse echo waveforms obtained from flat-bottom holes of eight different diameters. A recognition accuracy of 98% has been attained when the flat-bottom holes are classified into two categories using only one feature from the original ultrasonic pulse echo waveforms reflected from the flat-bottom holes. The same results are achieved when the one feature is either the maximum amplitude, the root-mean-square value, or the variance of the waveform. An unexpected result was also observed when a time series method was applied to the portions of the ultrasonic pulse echo waveforms that were reflected from the backwalls instead of the flat-bottom holes.