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Time-Frequency and Time-Scale Analysis, 1994., Proceedings of the IEEE-SP International Symposium on

Date 25-28 Oct. 1994

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  • Proceedings of IEEE-SP International Symposium on Time- Frequency and Time-Scale Analysis

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    Freely Available from IEEE
  • Application of the discrete wavelet transform to identification of questioned documents

    Page(s): 318 - 321
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    Identification of questioned documents (QDs) is the process of associating documents produced by an unknown writer with labeled archival samples. Here we use the discrete wavelet transform (DWT) to extract characteristics of letters and words of archival database samples, and questioned documents that need to be identified. Using standard clustering techniques, database document characteristics are categorized into distinct classes. These classes are labeled by the names of the known database writers. Identification of QDs is then made on the basis of the distance between QD characteristics and the database classes. We provide preliminary examples on a database of documents that was generated by nine writers. Seven different DWTs (and a voting scheme) were employed to make decisions about the QD's associations. The high success rate in identification of these samples indicates the potential that DWT-based method have in QD identification View full abstract»

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  • Wavelets and scaling functions as envelope waveforms for modulation

    Page(s): 504 - 507
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    We demonstrate that the use of scaling functions and wavelets as envelope waveforms for modulation is natural in light of the first Nyquist criterion for intersymbol interference (ISI) removal. The discrete orthonormal sequences generated using the filter bank theory can be used as practical means of generating such envelope functions. These waveforms can be used to modulate different information on adjacent channels that overlap in frequency. Using wavelet packets, we increase the number of dimensions available to the modulator per unit time, approaching the limit set by the dimensionality theorem View full abstract»

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  • Wigner distribution and continuous wavelet transforms for image analysis: relationships and interpretation

    Page(s): 314 - 317
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    In this paper we discuss the relationships between space-scale, and space-frequency representations for 2D images. We compare the interpretation of the two representations and show that the affine smoothed Wigner distribution class may also be advantageously used in image processing View full abstract»

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  • Time-frequency analysis using the residual interference signal canceller filter bank

    Page(s): 500 - 503
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    We describe a procedure for tracking the nonstationary components present in a real-valued signal. Each component is assumed to be a generalized sinusoid whose envelope and frequency vary slowly with time. This method is an extension of our previously proposed algorithm for tracking complex-valued components. When applied to voiced-speech signals, we demonstrate that if the number of trackers and their bandwidths are appropriately chosen, either the formants or the harmonics can be tracked View full abstract»

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  • Adaptive RID kernels which minimize time-frequency uncertainty

    Page(s): 96 - 99
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    The reduced interference distribution (RID) satisfies many of the desirable properties of time-frequency distributions (TFDs), including reduced interference. Using simple rules, it is possible to define kernels which guarantee the RID properties. A primitive h(t) is the starting point for kernel design. Starting with this primitive h(t), one may evolve a RID which enjoys all of the desirable properties. In addition, RIDs designed by this means also exhibit scale invariance in addition to the time-shift invariance and frequency-shift invariance exhibited by members of Cohen's class relevant to these properties. Such RIDs also exhibit a property which we call information invariance. Information invariance is defined under Renyi's generalized information. Renyi information has been found to be a useful quantifier of resolution in TFDs wherein minimum values of Renyi information are related to maximum resolution of the signal components. In this paper, we show that h(t) may be adapted to minimize Renyi information and thus achieve very good time-frequency resolution View full abstract»

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  • A simple model for fractional non-Gaussian processes

    Page(s): 444 - 447
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    Fractionally differenced Gaussian noise processes have been found to be useful for modeling the long-term dependencies exhibited by many real processes. Non-Gaussian processes have also been observed which exhibit long-term dependencies, but simple models have been lacking. A simple model which is a generalization of the fractionally differenced Gaussian noise process is proposed. The model should be useful for generating the random vectors needed for simulating systems which produce some result based on a finite length block of observations View full abstract»

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  • Wavelet transform analysis of the arterial pressure waveform

    Page(s): 568 - 571
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    The objective of this research was to devise a method of accurately and consistently locating both the dicrotic notch and the systolic peak from the arterial blood pressure signal for a range of heart rates, arrhythmias and irregular pressure waveforms. The pressure signal has been analyzed by applying the dyadic wavelet transform at several scales to the derivative of the waveform. Simultaneous occurrences of peaks in the magnitudes of the dyadic wavelet transform across several consecutive dyadic scales indicates a transient in the pressure waveform, from which the corresponding temporal location of the dicrotic notch is determined. A final algorithm analyzes the transform results and labels the locations of the dicrotic notch points as well as the systolic peaks View full abstract»

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  • Time-frequency kernel design by the two-dimensional frequency transformation method

    Page(s): 92 - 95
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    A subclass of Cohen's class of time-frequency (t-f) distributions is introduced in which t-f distribution kernels are characterized by finite extent in time and frequency and thereby referred to as finite time-frequency (FTF) kernels. FTF kernels are provided via the frequency transformation method (FTM), used in two-dimensional (2-D) filter design View full abstract»

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  • A fast wavelet algorithm on the interval

    Page(s): 287 - 289
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    The Franklin system is an orthonormal basis of L2[0,1]. The authors give a multiresolution analysis of L2[0,1] using the Faber-Schauder system. Exact reconstruction is now allowed; the authors perform a comparison with the Stromberg system (on [0,1]) where an edge error appears when the reconstruction is made. They derive a fast algorithm which enables one to analyze and synthesize a given signal on an interval. When using the Franklin system, it appears that special considerations are held near the edges where the extension of the signal over the edges is no longer needed (zero-padding method...etc.). Numerical simulations are provided to emphasize the performances of the results View full abstract»

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  • New abrupt change detector using Walsh functions

    Page(s): 213 - 216
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    This paper deals with parametric model abrupt change detection. Within this field, a time varying autoregressive (TAR) modeling is presented, using Walsh functions as basis functions. Then, a new abrupt change detector based on this modeling is derived. An associated deflation algorithm leads to a complete detection tool with a maximum error of about 2 or 4 points around the estimated value View full abstract»

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  • Feature-based epileptic seizure detection and prediction from ECoG recordings

    Page(s): 564 - 567
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    This paper discusses the observation and interpretation of chirp-like striation patterns in processed spectrograms of single channel electrocorticograms associated with epileptic patients. A pulse amplitude modulation model is presented as a possible mechanism for the appearance of the chirp-like patterns View full abstract»

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  • Quadratically and linearly constrained statistically dependent time-frequency kernel design

    Page(s): 88 - 91
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    Time-frequency kernel design is formulated as a minimum variance constrained minimization problem. The minimized cost function is quadratic and depends on the second order statistics of the underlying process. In addition to the original constraints leading to the marginal and the support properties, quadratic constraints are employed to add flexibility in kernel design and to allow the user to compromise between the kernel statistical performance under two or more processes. Computer simulations are presented which illustrate statistical performance of the t-f kernel under the original and the additional linear and quadratic t-f constraints View full abstract»

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  • An optimal frequential based splitting approach in signal restoration: the mixed-filter-bank, realisation and validation

    Page(s): 140 - 143
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    In the area of music signal restoration, methods based on the short-time-Fourier-transform (STFT) are usually used. They yield good results when the local signal to noise ratios (SNR) are higher than 10 dB on the whole band. Most of time, this condition is not respected and a poor detection of musical components is engendered. In the paper, a mixed filter bank approach is proposed The signal is first split in a Δf/f filter bank by means of a wavelet transform and then a noise reduction method based on STFT is used with different window lengths in each subband The choice of parameters in these subbands is connected to the local SNR. Listening tests have shown a real audible improvement of this method applied to an old musical recording View full abstract»

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  • Diminishing the asymmetry of Daubechies' wavelets

    Page(s): 5 - 8
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    The author shows that the asymmetry of Daubechies' scaling functions and wavelets can be diminished using, as a measure of asymmetry for the wavelet generating discrete-time filter, a special second moment of energy distribution in time. The moment is involved in the uncertainty relation for discrete-time signals. The generating filter is chosen such that the moment is minimized. Some other measures of asymmetry are addressed too View full abstract»

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  • Signal component separation using the wavelet transform

    Page(s): 560 - 563
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    Many contributions to the wavelet theory by mathematicians have initiated a flurry of activity in using the wavelet transforms for practical applications. To solve a particular problem, one is confronted with the choice of the mother wavelet and the wavelet grid that should be used in the transform. Given some a priori information about the signals, the authors have attempted to design the mother wavelet and the associated grid for signal classification or separation applications. Analysis of ECG signals for the presence of late potentials is explored View full abstract»

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  • Time-limited signals and Gabor expansion

    Page(s): 268 - 271
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    Gabor (1946) expansion suffers from the consequences of the zero theorem which states that all continuous functions have a zero on the unit square in the Zak space. In particular the Gaussian function routinely selected for a window in the Gaborian analysis has a zero at (1/2,1/2). As a result a zero-matching scheme between the signal and the window must be employed, which limits the class of signals that can be analyzed. We demonstrate that for a broad class of signals existence of zero of the window does not affect stability of the Gabor expansion and the zero-matching procedure can be avoided. It is shown that signal time-limited to the (-1/2,1/2) interval must have a zero at (1/2,1/2) in the Zak space, thus allowing a legal Gabor expansion based on a Gaussian window View full abstract»

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  • Adaptive hot clutter mitigation using subbanding

    Page(s): 476 - 479
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    Hot clutter mitigation using an adaptive array is the focus of the paper. A model that includes all relevant hot clutter parameters such as spatial delay, Doppler, and carrier phase angle is developed. Subbanding using DFT or the wavelet transform is implemented prior to adaptive processing and tap delay filtering. A comparison between the two subbanding techniques using the cancellation ratio as a performance measure is presented. The effects of the number of tap delays, jamming angle of arrival, Doppler spread, and jammer relative bandwidth on the performance of an adaptive array are examined View full abstract»

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  • Space-scale-frequency representation and fixed chosen noise restoration (image)

    Page(s): 302 - 305
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    We propose an image restoration with fixed chosen noise. We tune the threshold of wavelet packets coefficients in homogeneous areas by taking into account the noise signal dependance and the modulation transfer function of the optic instrument View full abstract»

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  • ARMA processes in multirate filter banks with applications to radar signal classification

    Page(s): 136 - 139
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    Considers stochastic modeling in a scale space defined by multirate filter banks using autoregressive moving average (ARMA) models. The authors show that signals at coarser scales in analysis filter banks follow ARMA models if the signal at a finer scale is an ARMA process. The model for a coarser scale signals can be identified from the model of a finer scale signal. Reconstruction of a finer scale signal from a partial set of decomposed signals at a coarser scale is considered as an optimal estimation problem. The authors developed a recursive minimum mean square error (MMSE) estimation algorithm for reconstruction of a finer scale signal. The stochastic modeling approach in scale space is applied to classification of radar signals View full abstract»

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  • Multi-component power and frequency estimation for a discrete TFD

    Page(s): 620 - 623
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    In a previous article of Pielemeier and Wakefield (see Proc. of IEEE Symposium on Time-Frequency and Time-Scale Analysis, Oct. 4-6, p.421-424, 1992) a discrete time-frequency distribution (TFD) in Cohen's class was developed for multicomponent musical signals. This TFD's separable kernel employs low pass filtering in time to achieve limited superposition between components, and either constant-bandwidth or constant-Q smoothing in frequency. We develop instantaneous power and frequency estimators for the components analyzed by this TFD. In the literature, frequency estimators for discrete distributions often compute frequency based on discrete finite phase differences using periodic statistics. We instead start with the underlying continuous analog signal, and using linear statistics, show that estimates from the discrete distribution can be made arbitrarily accurate for the single component cast, while for the multicomponent case, the estimates are minimally biased by time smoothing. Results are demonstrated showing much less bias than common spectrogram estimators. Multicomponent examples include signals which are inharmonic and contain widely varying levels, and AM and FM signals View full abstract»

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  • Robust multiscale representation of processes and optimal signal reconstruction

    Page(s): 1 - 4
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    We propose a statistical approach to obtain a “best basis” representation of an observed random process. We derive statistical properties of a criterion first proposed to determine the best wavelet packet basis, and, proceed to use it in constructing a statistically sound algorithm. For signal enhancement, this best basis algorithm is followed by a nonlinear filter based on the minimum description length (MDL) criterion. We show that it is equivalent to a min-max based algorithm proposed by Donoho and Johnstone (1992) View full abstract»

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  • Parameter estimation of FM signals using cyclic statistics

    Page(s): 248 - 251
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    Estimating the modulation index of an FM signal in stationary additive noise is encountered in many applications. The authors propose a simple scheme which relies on the cyclostationarity of the FM process, and employs relevant cyclic statistics. The large sample variance expression of the modulation index estimator is also derived. Numerical examples corroborate the theoretical results View full abstract»

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  • System identification and modeling of non-stationary signals using the Wold-Cramer representation

    Page(s): 421 - 424
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    In this paper we present an application of the Wold-Cramer representation of non-stationary signals to system identification and modeling. According to the Wold-Cramer representation, a non-stationary signal can be expressed as an infinite sum of sinusoids with time-varying random magnitudes and phases. For the identification of linear time-invariant (LTI) systems, we relate the Wold-Cramer representations of the system's input and output to obtain estimates of the magnitude and phase frequency responses of the system. Our procedure permits the identification of non-minimum phase systems. Furthermore, we show that when the system output is noisy, and the noise is stationary it is possible to avoid the effects of the noise in the identification. If the noise is non-stationary and Gaussian, one needs to consider the evolutionary bispectrum, recently introduced by Priestley, to get rid of the noise. The analysis also provides a model for a non-stationary signal, as the output of a cascade of a linear time-varying and a linear time-invariant systems with stationary white noise as input. To illustrate our procedure, we present a simulation of the identification of a non-minimum phase system View full abstract»

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  • A time-varying kernel for ultrasound Doppler spectra

    Page(s): 556 - 559
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    A new time-varying kernel has been formulated and tested for the bilinear time-frequency representation (BTFR) of signals. This kernel reshapes itself to track the instantaneous frequency of the signal, so that kernel smoothing does not necessarily yield poor resolution. Performance analyses were based upon mono-component FM (deterministic) and ultrasound Doppler (non-deterministic) signals. The results show that the new kernel improves the compromise between cross-terms (or variance) reduction and time-frequency resolution View full abstract»

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