Abstract:
Multi-components sinusoidal engineering signals who are non-stationary signals were considered in this study since their separation and segmentations are of great interests in many engineering fields. In most cases, the segmentation of non-stationary or multi-component signals is conducted in time domain. In this paper, we explore the advantages of applying joint time-frequency (TF) distribution of the multi-component signals to identify their segments. The Spectrogram that is known as Short-Time Fourier Transform (STFT) will be used for obtaining the time-frequency kernel. Time marginal of the computed kernel is optimally used for the signal segmentation. In order to obtain the desirable segmentation, it requires first to improve time marginal of the kernel by using two-dimensional Wiener mask filter applied to the TF kernel to mitigate and suppress non-stationary noise or interference. Additionally, a proper choice of the sliding window and its overlaying has enhanced our scheme to capture the discontinuities corresponding to the boundaries of the candidate segments.

Abstract:
This paper presents a new method for detecting EEG spikes using the time-frequency distribution of the signal. As spikes are short-time broadband events, their energy patterns are represented as ridges in the time-frequency domain. In this domain, the high instantaneous energy of the spikes makes them more distinguishable from the background. To detect spikes, the time-frequency distribution of the signal of interestis first enhanced to attenuate the noise. Two frequency slices of the enhanced time-frequency distribution arethen extracted and subjected to the smoothed nonlinear energy operator (SNEO). Finally, the output of the SNEO is thresholded to localise the position of the spikes in the signal. The SNEO is employed to accentuate the spike signature in the extracted frequency slices. A spike is considered to exist in the time domain signalif the spike signature is detected at the same position in both frequency slices. The performance of the proposed method is evaluated and compared with an existing spike detection method using both synthetic and newborn EEG signals.

In this
paper, a new signal separation method mainly for AM-FM components blended in
noises is revisited based on the new derived time-varying bandpass filter
(TVBF), which can separate the AM-FM components whose frequencies have
overlapped regions in Fourier transform
domain and even have crossed points in time-frequency distribution (TFD)
so that the proposed TVBF seems like a “soft-cutter” that cuts the frequency
domain to snaky slices with rational physical sense. First, the Hilbert
transform based decomposition is analyzed for the analysis of nonstationary
signals. Based on the above analysis, a hypothesis under a certain condition
that AM-FM components can be separated successfully based on Hilbert transform
and the assisted signal is developed, which is supported by representative
experiments and theoretical performance analyses on a error bound that is shown
to be proportional to the product of frequency width and noise variance. The
assisted signals are derived from the refined time-frequency distributions via
image fusion and least squares optimization. Experiments on man-made and
real-life data verify the efficiency of the proposed method and demonstrate the
advantages over the other main methods.

With the new system radar put into practical use, the characteristics of complex radar signals are changing and developing. The traditional analysis method of one-dimensional transformation domain is no longer applicable to the modern radar signal processing, and it is necessary to seek new methods in the two-dimensional transformation domain. The time-frequency analysis method is the most widely used method in the two-dimensional transformation domain. In this paper, two typical time-frequency analysis methods of short-time Fourier transform and Wigner-Ville distribution are studied by analyzing the time-frequency transform of typical radar reconnaissance linear frequency modulation signal, aiming at the problem of low accuracy and sen-sitivity to the signal noise of common methods, the improved wavelet transform algorithm was proposed.

Abstract:
Due to the poor
understanding of the small-scale processes at the air-water interface, some lab
experiments are done in a water tank by infrared techniques. With the help of
ESMD method, the stochastic temperature sequences extracted from the infrared
photographs are decomposed into several empirical modes of general periodic
forms. The corresponding analyses on the modes reveal that, within certain
limits, both spatial and temporal frequencies increase along the wind speed. As
for the amplitudes, the existence of wind may result in fold increasing of
their values. In addition, when the wind speed is added from 4 m/s to 5 m/s,
both frequency and amplitude of the surface temperature decrease and it implies
an enhanced mixing and a weakened temperature gradient under the force of wind
blowing.

Abstract:
we consider in this paper wigner type representations wigt depending on a parameter t ∈ [0,1] as defined in [2]. we prove that the cohen class can be characterized in terms of the convolution of such wigt with a tempered distribution. we introduce furthermore a class of ？quadratic representations？ spt based on the t-wigner, as an extension of the two window spectrogram (see [2]). we give basic properties of spt as subclasses of the general cohen class.

Abstract:
The characterization of non-stationary signal requires joint time and frequency information. However, time and frequency are a pair of non-commuting variables that cannot constitute a joint probability density in the time-frequency plane. The time-frequency distributions have difficult interpretation problems arising from negative and complex values or spurious components. In this paper, we get time-frequency information from the marginal distributions in rotated directions in the time-frequency plane. The rigorous probability interpretation of the marginal distributions is without any ambiguities. This time-frequency transformation is similar to the computerized axial tomography (CT or CAT) and is applied to signal analysis and signal detection and reveals a lot of advantages especially in the signal detection of the low signal/noise (S/N).

Abstract:
We consider in this paper Wigner type representations Wig t depending on a parameter t ∈ [0,1] as defined in [2]. We prove that the Cohen class can be characterized in terms of the convolution of such Wig t with a tempered distribution. We introduce furthermore a class of “quadratic representations” Sp t based on the t-Wigner, as an extension of the two window Spectrogram (see [2]). We give basic properties of Sp t as subclasses of the general Cohen class. Nosotros consideramos en este artículo representaciones de tipoWigner Wig t dependiendo de um parámetro t ∈ [0,1] como definido en [2]. Probamos que la clase Cohen puede ser caracterizada en terminos de la convolución de tales Wig t con una distribución temperada. Introducimos también la clase de “representaciones cuadraticas” Sp t basado en el t-Wigner, como una extensión de dos ventanas espectrograma (ver [2]). Nosotros damos propiedades básicas de Sp t como subclases de la clase Cohen.

Abstract:
A conceptually new approximation method to study the time-frequency properties of dynamical systems characterized by linear ordinary differential equations is presented. We bypass solving the differential equation governing the motion by writing the exact Wigner distribution corresponding to the solution of the differential equation. The resulting equation is a partial differential equation in time and frequency. We then show how it lends itself to effective approximation methods because in the time frequency plane there is a high degree of localization of the signal. Numerical examples are given and compared to exact solutions.

Abstract:
We examine the problem of blind separation of nonstationary sources in the underdetermined case, where there are more sources than sensors. Since time-frequency (TF) signal processing provides effective tools for dealing with nonstationary signals, we propose a new separation method that is based on time-frequency distributions (TFDs). The underlying assumption is that the original sources are disjoint in the time-frequency (TF) domain. The successful method recovers the sources by performing the following four main procedures. First, the spatial time-frequency distribution (STFD) matrices are computed from the observed mixtures. Next, the auto-source TF points are separated from cross-source TF points thanks to the special structure of these mixture STFD matrices. Then, the vectors that correspond to the selected auto-source points are clustered into different classes according to the spatial directions which differ among different sources; each class, now containing the auto-source points of only one source, gives an estimation of the TFD of this source. Finally, the source waveforms are recovered from their TFD estimates using TF synthesis. Simulated experiments indicate the success of the proposed algorithm in different scenarios. We also contribute with two other modified versions of the algorithm to better deal with auto-source point selection.