Nonlinear transient chirp signal modeling of the aortic and pulmonary components of the second heart sound

This paper describes a new approach based on the time-frequency representation of transient nonlinear chirp signals for modeling the aortic (A2) and the pulmonary (P2) components of the second heart sound (S2). It is demonstrated that each component is a narrow-band signal with decreasing instantaneous frequency defined by its instantaneous amplitude and its instantaneous phase. Each component is also a polynomial phase signal, the instantaneous phase of which can be accurately represented by a polynomial having an order of thirty. A dechirping approach is used to obtain the instantaneous amplitude of each component while reducing the effect of the background noise. The analysis-synthesis procedure is applied to 32 isolated A2 and 32 isolated P2 components recorded in four pigs with pulmonary hypertension. The mean +/- standard deviation of the normalized root-mean-squared error (NRMSE) and the correlation coefficient (rho) between the original and the synthesized signal components were: NRMSE = 2.1 +/- 0.3% and rho = 0.97 +/- 0.02 for A2 and NRMSE = 2.52 +/- 0.5% and rho = 0.96 +/- 0.02 for P2. These results confirm that each component can be modeled as mono-component nonlinear chirp signals of short duration with energy distributions concentrated along its decreasing instantaneous frequency.     

A linear model for TF distribution of signals

We describe a new linear time-frequency model in which the instantaneous value of each signal component is mapped to the curve functionally representing its instantaneous frequency. This transform is linear, uniquely defined by the signal decomposition, and satisfies linear marginal-like distribution properties. We further demonstrate the transform generated surface may be estimated from the short time Fourier transform by a concentration process based on the phase of the short-time Fourier transform (STFT), differentiated with respect to time. Interference may be identified on the concentrated STFT surface, and the signal with the interference removed may be estimated by applying the linear-time-marginal to the concentrated STFT surface from which the interference components have been removed.     

Bionic wavelet transform: a new time-frequency method based on an auditory model

In this paper, a new adaptive wavelet transform, named bionic wavelet transform (BWT), is developed based on a model of the active auditory system. The most distinguishing characteristic of BWT is that its resolution in the time-frequency domain can be adaptively adjusted not only by the signal frequency but also by the signal instantaneous amplitude and its first-order differential. The automatically adjusted resolution, even in a fixed frequency along the time-axis, is achieved by introducing the active control of the auditory system into the wavelet transform (WT). Other properties of BWT include that: 1) BWT is a nonlinear transform that has high sensitivity and frequency selectivity; 2) BWT represents the signal with a concentrated energy distribution; and 3) the inverse BWT can reconstruct the original signal from its time-frequency representation. In order to compare these three properties between BWT and WT, experiments were conducted on both constructed signals and real speech signals. The results show that BWT performs better than WT in these three aspects, and that BWT is appropriate for speech signal processing, especially for cochlear implants.     

Blind Source Separation of Instantaneous Mixture of Delayed Sources Using High‐Order Taylor Approximation

This paper deals with the problem of blind source separation (BSS), where observed signals are a mixture of delayed sources. In reference to a previous work, when the delay time is small such that the first‐order Taylor approximation holds, delayed observations are transformed into an instantaneous mixture of original sources and their derivatives, for which an extended second‐order blind identification (SOBI) approach is used to recover sources. Inspired by the results of this previous work, we propose to generalize its first‐order Taylor approximation to suit higher‐order approximations in the case of a large delay time based on a similar version of its extended SOBI. Compared to SOBI and its extended version for a first‐order Taylor approximation, our method is more efficient in terms of separation quality when the delay time is large. Simulation results verify the performance of our approach under different time delays and signal‐to‐noise ratio conditions, respectively.     

Instantaneous frequency and energy distribution of a signal

A theory is derived on a signal representation in an instantaneous frequency vs. time plane. It is observed that the usual frequency vs. time representation does not give a specific pattern for the signal. It is shown that by switching the frequency axis to an instantaneous frequency axis, and by distributing the energy of the signal on an instantaneous frequency vs. time plane it is possible to build up a coherent theory. As an example, patterns of speech signals (sustained vowels) are represented.     

采用局部特征尺度分解的跳频信号参数盲估计算法

针对现有跳频信号参数盲估计算法存在时间分辨率和频率分辨率矛盾这一问题,提出了一种基于局部特征尺度分解的跳频信号参数估计新算法。该算法将跳频信号迭代地分解成若干个内禀尺度分量并进行降噪处理,然后对其最大瞬时幅度进行小波变换和傅里叶变换即可估计出跳频信号的跳变时刻和跳频周期,最后根据得到的跳变时刻和跳频周期可以进一步估计出跳频频率集。该算法不受时频不确定性原理的影响,能够在未知先验知识的条件下估计出跳频信号的跳周期、跳变时刻和跳频频率集。最后通过仿真验证了算法的有效性。      

Polarization Ellipse Analysis of Nonstationary Random Signals

We present a novel way of extending rotary-component and polarization analysis to nonstationary random signals. If a complex signal is resolved into counterclockwise and clockwise rotating phasors at one particular frequency only, it traces out an ellipse in the complex plane. Rotary-component analysis characterizes this ellipse in terms of its shape and orientation. Polarization analysis looks at the coherence between counterclockwise and clockwise rotating phasors and whether there is a preferred rotation direction of the ellipse (counterclockwise or clockwise). In the nonstationary case, we replace this ellipse with a time-dependent local ellipse that, at a given time instant, gives the best local approximation of the signal from a given frequency component. This local ellipse is then analyzed in terms of its shape, orientation, and degree of polarization. A time-frequency coherence measures how well the local ellipse approximates the signal. The ellipse parameters and the time-frequency coherence can be expressed in terms of the Rihaczek time-frequency distribution. Under coordinate rotation, the ellipse shape, the degree of polarization, and the time-frequency coherence are invariant, and the ellipse orientation is covariant. The methods presented in this paper provide an alternative to ellipse decompositions based on wavelet ridge analysis.      

Signal energy distribution in time and frequency

The Fourier representation of signals and its relation to the signal structure in time and frequency, and more generally the inherent properties of phase-modulated signals, have received considerable attention in the past. These topics have led to such seemingly unrelated studies as the representation of a signal in a combined time-frequency plane, "instantaneous power spectra," and the ambiguity function and its transform relations. It is shown in this paper that the studies can be unified by the introduction of the concept of the complex energy density function of a signal. The function is an extension and combination of the one-dimensional energy density functions in time and frequency, the energy density spectrum|Psi(f)|^{2}, and energy density waveform|psi (t)|^{2}. On the basis of the complex energy density function, the significance of complicated-appearing transform relations is readily understood. The new concept also conveys a good insight into the internal structure of phase-modulated signals.     

Modified Cohen-Lee time-frequency distributions and instantaneousbandwidth of multicomponent signals

Cohen (1989, 1995) has introduced and extensively studied and developed the concept of the instantaneous bandwidth of a signal. Specifically, instantaneous bandwidth is interpreted as the spread in frequency about the instantaneous frequency, which is itself interpreted as the average frequency at each time. This view stems from a joint time-frequency distribution (TFD) analysis of the signal, where instantaneous frequency and instantaneous bandwidth are taken to be the first two conditional spectral moments, respectively, of the distribution. However, the traditional definition of instantaneous frequency, namely, as the derivative of the phase of the signal, is not consistent with this interpretation, and new definitions have therefore been proposed previously. We show that similar problems arise with the Cohen-Lee (1988, 1989) instantaneous bandwidth of a signal and propose a new formulation for the instantaneous bandwidth that is consistent with its interpretation as the conditional standard deviation in frequency of a TFD. We give the kernel constraints for a distribution to yield this new result, which is a modification of the kernel proposed by Cohen and Lee. These new kernel constraints yield a modified Cohen-Lee TFD whose first two conditional moments are interpretable as the average frequency and bandwidth at each time, respectively     

Regularized Spectral Matching for Blind Source Separation. Application to fMRI Imaging

The main contribution of this paper is to present a Bayesian approach for solving the noisy instantaneous blind source separation problem based on second-order statistics of the time-varying spectrum. The success of the blind estimation relies on the nonstationarity of the second-order statistics and their intersource diversity. Choosing the time-frequency domain as the signal representation space and transforming the data by a short-time Fourier transform (STFT), our method presents a simple EM algorithm that can efficiently deal with the time-varying spectrum diversity of the sources. The estimation variance of the STFT is reduced by averaging across time-frequency subdomains. The algorithm is demonstrated on a standard functional resonance imaging (fMRI) experiment involving visual stimuli in a block design. Explicitly taking into account the noise in the model, the proposed algorithm has the advantage of extracting only relevant task-related components and considers the remaining components (artifacts) to be noise.     

Time-Frequency Coherent Modulation Filtering of Nonstationary Signals

Modulation filtering is a class of techniques for filtering slowly-varying modulation envelopes of frequency subbands of a signal, ideally without affecting the subband signal's temporal fine-structure. Coherent modulation filtering is a potentially more effective type of such techniques where, via an explicit product model, subband envelopes are determined from demodulation of the subband signal with a coherently detected subband carrier. In this paper we propose a coherent modulation filtering technique based on detecting the instantaneous frequency of a subband from its time-frequency representation. We devise theory to show that coherent modulation filtering imposes a new bandlimiting constraint on the product of the modulator and carrier as well as the ability to recover arbitrarily chosen envelopes and carriers from their modulation product. We then formally show that a carrier estimate based on the time-varying spectral center-of-gravity satisfies the bandlimiting condition. This bandwidth constraint leads to effective and artifact-free modulation filters, offering new approaches for potential signal modification. However, the spectral center-of-gravity does not, in general, satisfy the condition of arbitrary carrier recovery. Finally, the results from modulation-filtering a speech signal are then used to validate the theory.     

Compensating for window effects in the calculation of spectrographic instantaneous bandwidth

Exact results derived by Cohen and Lee are used to study the distortion induced by the window in the computation of instantaneous bandwidth via the spectrogram. These concepts have been recently used in an interesting study regarding lesion-induced blood flow disturbances, where an approximation was made to compensate for the window effects. We show that this compensation is accurate for stationary signals, but becomes increasingly poorer as the signal becomes less stationary (e.g., large frequency modulations). We propose an alternative technique to reduce the window distortions, and point out the use of other time-frequency distributions that do not suffer such distortions.     

Generalized instantaneous parameters and window matching in thetime-frequency plane

The concept of instantaneous parameters, which has previously been associated exclusively with 1-D measures like the instantaneous frequency and the group delay, are extended to the 2-D time-frequency plane. Such generalized instantaneous parameters are associated with the short-time Fourier transform. They may also be interpreted as local moments of certain time-frequency distributions. It is shown that these measures enable local signal behavior to be characterized in the time-frequency plane for nonstationary deterministic signals. The usefulness of the generalized instantaneous parameters is demonstrated in their application to optimal selection of windows for spectrograms. This is achieved through window matching in the time-frequency plane. An algorithm is provided that illustrates the performance of this window matching. Results based on simulated and real data are presented     

Theory and applications of adaptive constant-Q distributions

A new class of signal adaptive time-frequency representations called the adaptive constant-Q distribution (AQD) is introduced. The AQD exploits a priori knowledge about a signal's instantaneous frequency and bandwidth to perform signal-dependent smoothing of the Wigner distribution. The objective is to achieve a good tradeoff between reducing the variance and preserving the resolution by means of time-frequency dependent smoothing (specifically for use in medical Doppler ultrasound). A numerical, alias-free implementation of the AQD is presented. Deterministic, multicomponent signals as well as synthetic Doppler ultrasound signals were analyzed with the AQD. The performance of the AQD was compared with the power spectrogram, the exponential distribution, and the adaptive optimum kernel representation as well as with theory. The error was consistently lowest for the AQD. In conclusion, a new signal adaptive class of time-frequency distributions has been developed, and its potential in nonstationary signal analysis has been demonstrated     

Hybrid linear/quadratic time-frequency attributes

We present an efficient method for robustly calculating time-frequency attributes of a signal, including instantaneous mean frequency, bandwidth, kurtosis, and other moments. Most current attribute estimation techniques involve a costly intermediate step of computing a (highly oversampled) two-dimensonal (2-D) quadratic time-frequency representation (TFR), which is then collapsed to the one-dimensonal (1-D) attribute. Using the principles of hybrid linear/quadratic time-frequency analysis (time-frequency distribution series), we propose computing attributes as nonlinear combinations of the (slightly oversampled) linear Gabor coefficients of the signal. The method is both computationally efficient and accurate; it performs as well as the best techniques based on adaptive TFRs. To illustrate, we calculate an attribute of a seismic cross section     

Investigation of short-term changes in visual evoked potentials with windowed adaptive chirplet transform

We propose a new application of the adaptive chirplet transform that involves partitioning signals into non-overlapping sequential segments. From these segments, the local time-frequency structures of the signal are estimated by using a four-parameter chirplet decomposition. Entitled the windowed adaptive chirplet transform (windowed ACT), this approach is applied to the analysis of visual evoked potentials (VEPs). It can provide a unified and compact representation of VEPs from the transient buildup to the steady-state portion with less computational cost than its non-windowed counterpart. This paper also details a method to select the optimal window length for signal segmentation. This approach will be useful for long-term signal monitoring as well as for signal feature extraction and data compression.     

具有迭代结构的时频分布计算方法

本文讨论了时频分布中的迭代算法的问题.通过选择特殊的计算窗口,时频分布的迭代运算形式能够有效地利用前面数据段的分析结果,从而避免了重复性的运算,使得计算效率得到提高.本文对原有的利用单边窗口的时频分布迭代算法的性能进行了分析,提出了采用对称型窗口的迭代计算形式.与单边窗口相比,双边形式的计算窗口不但可以有效地提高时频表示精度,同时还能够更为准确的表示信号的瞬时频率.文章对各项理论分析结果提供了相应的仿真实验结果.     

Analysis and filtering using the optimally smoothed Wignerdistribution

The authors consider the analysis and filtering of a deterministic signal with slowly time-varying spectra using the optimally smoothed Wigner distribution (OSWD). They compare this mixed time-frequency representation (MTFR) to other MTFRs such as the spectrogram, the short-time Fourier transform (STFT), and the Wigner and pseudo-Wigner distributions. The authors propose an approach to designing linear time-varying filters for slowly time-varying signals which is based on the concept of local nonstationarity cancellation and show that it is equivalent to masking the optimal STFT. The performance of the filter in suppressing white noise and in decomposing a slowly time-varying signal into its components is studied and compared to the performance of the techniques based on the STFT     

Time-frequency analysis of transients

A new representation of electromagnetic transients associated with perfectly-conducting finite-size objects is proposed. Our proposal is motivated by the fact that both time representation and frequency representation of suchlike transients are not fully satisfactory. We examine a tool for imaging transients in the time-frequency domain, namely the Page instantaneous spectrum. This is illustrated in a number of examples with pulse excited dipoles that the Page spectrum leads to readable picture of time-frequency evolution of the transient process.     

基于子带分解WVD的雷达信号时频分析方法

研究利用谐波小波子带分解消除 Wigner-Ville 分布交叉项的雷达信号时频联合分析方法。通过对多分量信号进行子带分解预处理来消除信号之间以及信号与噪声之间的相互影响， 并求取个独立分量的 WVD，最后进行线性求和获得原始信号时频分布。仿真分析结果表明，对于在频域无交叉点的多分量信号，该方法能够有效抑制交叉项和噪声的干扰，提高了时频分辨效果并能准确提取出目标的特征信息，检测效果优于传统 WVD 分析方法，将有助于提高雷达信号检测、特征提取的能力。