Time/Frequency and Time/Scale Analysis

Adaptive Window in the PWVD for the IF Estimation of FM Signals in Additive Gaussian Noise

Authors:

Braham Barkat,
Boualem Boashash,
Ljubisa J. Stanković,

Page (NA) Paper number 1068

Abstract:

The peak of the polynomial Wigner-Ville distribution is known to be a consistent estimator of the instantaneous frequency for polynomial FM signals. In this paper, we present an algorithm for the design of an optimal time- varying window length for this estimator when noisy non-linear, not necessarily polynomial, FM signals are considered. The results obtained show that the estimator is accurate and outperforms any fixed window time- frequency distribution based estimator.

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Filter Design for CWT Computation Using the Shensa Algorithm

Authors:

Y T Chan, Royal Military College of Canada (Canada)
K C Ho,

Page (NA) Paper number 1271

Abstract:

Direct computation of CWT using FFT requires O(N log_2 N) operations per scale, where N is the data length. The Shensa algorithm is a fast algorithm to compute CWT that uses only O(N) operations per scale. The application of the algorithm requires the design of a bandpass and a lowpass filter for a given mother wavelet function. Previous design method involves multi-dimensional numerical search and is computationally intensive. This paper proposes an iterative method to design the optimum filters. It computes in each iteration least-squares solutions only and does not need numerical search. The proposed filter design method is corroborated by simulations.

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Gabor's Signal Expansion On A Quincunx Lattice And The Modified Zak Transform

Authors:

Arno J van Leest, Technische Universiteit Eindhoven, Faculteit Elektrotechniek, EH 5.29,P.O. Box 513, 5600 MB Eindhoven, Netherlands (The Netherlands)
Martin J Bastiaans, Technische Universiteit Eindhoven, Faculteit Elektrotechniek, EH 5.34,P.O. Box 513, 5600 MB Eindhoven, Netherlands (The Netherlands)

Page (NA) Paper number 1372

Abstract:

Gabor's expansion of a signal on a quincunx lattice with oversampling by a rational factor is presented for continuous-time signals. It is shown how a modified Zak transform instead of the ordinary Zak transform can be helpful in determining Gabor's signal expansion coefficients and how it can be used in finding the dual window. Furthermore, some examples of dual windows for the quincunx case are given and compared with dual windows for the rectangular case.

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On Analytic Signals with Nonnegative Instantaneous Frequencies

Authors:

Xiang-Gen Xia,
Leon Cohen,

Page (NA) Paper number 1483

Abstract:

In this paper, we characterize all analytic signals with band-limited amplitudes and polynomial phases. We show that a signal with band-limited amplitude and polynomial phase is analytic if and only if it has nonnegative constant instantaneous frequency, i.e., the derivative of the phase is a nonnegative constant, and the constant is greater than or equal to the minimum bandwidth of the amplitude.

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Minimax Robust Time-Frequency Filters for Nonstationary Signal Estimation

Authors:

Gerald Matz,
Franz Hlawatsch,

Page (NA) Paper number 1558

Abstract:

We introduce minimax robust time-varying Wiener filters and show a result that facilitates their calculation. Reformulation in the time-frequency domain yields simple closed-form expressions of minimax robust time-frequency Wiener filters based on three different uncertainty models. For one of these filters, an efficient implementation using the multi-window Gabor transform is proposed.

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Spatial Averaging Of Time-Frequency Distributions

Authors:

Yimin Zhang, DEPT. of ELECTRICAL AND COMPUTER ENGINEERING, VILLANOVA UNIV., USA (USA)
Moeness G. Amin, DEPT. of ELECTRICAL AND COMPUTER ENGINEERING, VILLANOVA UNIV., USA (USA)

Page (NA) Paper number 1696

Abstract:

This paper presents a novel approach based on time-frequency distributions (TFDs) for separating signals received by a multiple antenna array. This approach provides a significant improvement in performance over the recently introduced spatial time-frequency distributions, specifically for signals with close time-frequency signatures. In this approach, spatial averaging of the time-frequency distributions of the sensor data is performed to eliminate the interactions of the sources signals in the time-frequency domain, and as such restore the realness property and the diagonal structure of the source TFDs, which are necessary for source separation. It is shown that the proposed approach yields improved performance over both cases of no spatial averaging and averaging using time-frequency smoothing kernels.

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Optimization of Time and Frequency Resolution for Radar Transmitter Identification

Authors:

Bradford W Gillespie,
Les E Atlas,

Page (NA) Paper number 2127

Abstract:

An entirely new set of criteria for the design of kernels for time-frequency representations (TFRs) has been recently proposed. The goal of these criteria is to produce kernels (and thus, TFRs) which will enable accurate classification without explicitly defining, a priori, the underlying structure that differentiates individual classes. These kernels, which are optimized to discriminate among multiple classes of signals, are referred to as signal class-dependent kernels, or simply class-dependent kernels. Until now, our technique has utilized the Rihaczek TFR as the base representation, deriving the optimal smoothing in time and frequency from this representation. Here the performance of the class-dependent approach is investigated in relation to the choice of the base representation. Classifier performance using several base TFRs is analyzed within the context of radar transmitter identification. It is shown that both the Rihaczek and the Wigner-Ville distributions yield equivalent results, far superior to the short-time Fourier transform. In addition, a correlation reduction step is presented here. This improves performance and extensibility of the class-dependent approach.

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New Time-Frequency Symbol Classification

Authors:

Byeong-Gwan Iem,
Antonia Papandreou-Suppappola,
G. Faye Boudreaux-Bartels,

Page (NA) Paper number 2146

Abstract:

We propose new time-frequency (TF) symbols as the narrowband Weyl symbol (WS) smoothed by an appropriate kernel. These new symbols preserve time and frequency shifts on a random process. Choosing specific smoothing kernels, we can obtain various new symbols (e.g. Levin symbol and Page symbol). We link a quadratic form of the signal to the new symbols and Cohen's class of quadratic time-frequency representations, and we derive a simple kernel constraint for unitary symbols. We also propose an affine class of symbols in terms of the wideband Weyl symbol (PoWS). These symbols preserve scale changes and time shifts. Furthermore, we generalize the smoothed versions of the WS and PoWS to analyze random processes undergoing generalized frequency shifts or generalized time shifts.

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An Inverse Signal Approach to Computing the Envelope of a Real Valued Signal

Authors:

Ramdas Kumaresan,

Page (NA) Paper number 2187

Abstract:

We address the problem of estimating the envelope of a real-valued signal, s(t), that is observed for a duration of T seconds. We model s(t) using a Fourier series, by considering periodic extensions of the signal. By using an analog of the autocorrelation method of linear prediction on the Fourier coefficients of s(t), the envelope of the signal is estimated without explicitly computing the analytic signal through Hilbert transformation. Using this method the envelope of a non-stationary signal can be computed by processing the signal through a sliding T-second window.

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Frames in Rotated Time-Frequency Planes

Authors:

Aykut Bultan,
Ali N Akansu,

Page (NA) Paper number 2418

Abstract:

Weyl-Heisenberg frames are complete signal representations corresponding to rectangular tiling of the time-frequency plane. Extensions of these frames are obtained in the rotated time-frequency planes by using the fractional Fourier transformation. It is shown that, rotation does not affect the frame bounds. For some specific angles, lattices in rotated coordinates will map to the lattices in the Cartesian coordinates. The rotated Weyl-Heisenberg frames obtained are more suitable for chirp-like signal analysis and synthesis.

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