Teager-Kaiser Operator Research Articles

A GPR 2D Teager-Kaiser energy operator based on the multivariate variational mode decomposition

ABSTRACT To delineate the anomalies related to subsurface target bodies and the geophysical events, a novel method based on the effective combination of the multivariate variational mode decomposition (MVMD) and 2D Teager-Kaiser operator (2D-TKEO) is proposed for ground-penetrating radar (GPR) data processing in this letter. The proposed method takes advantage of the multi-channel decomposition scheme of MVMD and the multi-directional localization of 2D-TKEO for tracking energy attributes. The time-frequency spectrum can be generated based on the IMF-slices decomposed by the MVMD, on which the 2D-TKEO is introduced to focus the spectrum energy, then the common frequency slices are extracted to reveal the energy components of different frequency ranges. The forward model and GPR field data are applied here to demonstrate that the time-frequency spectrum and the subsequent common-frequency slices based on the proposed MVMD-2DTKEO approach can depict the subsurface target bodies (e.g., voids and pipes) and subsurface layers with higher resolution and better stratigraphic continuity, compared with that of the S-transform and the VMD-1DTKEO.

Detection of hidden reservoirs under strong shielding based on bi‐dimensional empirical mode decomposition and the Teager–Kaiser operator

ABSTRACTIn this paper, we propose a method for revealing hidden reservoirs that are shielded by strong amplitudes. The bi‐dimensional empirical mode decomposition algorithm is used to decompose pre‐stack seismic data into several localized components, which generated from different discontinuities in the subsurface elastic properties. The two‐dimensional Teager–Kaiser energy operator process is applied to the first component, which includes a strong signal, to further locate the strong event. According to the located results, an energy weight matrix is established. By weighted summation of all the components, the strong event is suppressed, and the hidden reservoir becomes more prominent. Tests on a synthetic data and field data from Daniudi confirm that this method can separate strong signals from weaker responses and efficiently reveal shielded reservoirs.

Decimetre Level Range Resolution for Beidou B3I Signal-Based Passive SAR Imaging—Proof-of-Concept Experimental Demonstrations

The construction of the Beidou B3 satellite system, a new-generation global navigation satellite system, has been completed worldwide, however the respective implementation studies remain in the start-up stage. Accordingly, studies of passive Beidou B3I signal-based synthetic aperture radar (Beidou B3I-SAR) are very meaningful in terms of promoting the rapid development of the Beidou technique. This paper proposes methods for Beidou B3I SAR imaging of decimetre level range resolution. To separate aliased reflected B3I signals at range domain, we presented cascaded secondary order differentiation operator (Diff2) and cascaded Teager-Kaiser (TK) operator, applied them to the regions where exists range compressed pulses, respectively. Thereafter to eliminate the obvious side-lobes which brought by the proposed operators and with the values less than zero, zero thresholding scheme is employed. To obtain the final range compressed signals with decimetre range resolution, phase recovery component is performed to the respective zero thresholded pulses. To validate the proposed methods, both proof of concept simulation and the experiment with field Beidou B3I signal raw data are carried out for comparison. The results show that indeed main-lobe width of range compressed pulse can reach the level 0.4 m. This reveals that decimetre level range resolution can be achieved for Beidou B3I-SAR on the basis of proposed methods, in contrast to the current best result of meters level in passive GNSS-based SAR related studies. Meanwhile, in a comparison of the proposed methods on the basis of cascaded Diff2 operator and cascaded TK operator, the later is outer-performed, since the respective brought interference level in background region is less.

A new detection method for EMG activity monitoring.

This paper introduces a new approach for electromyography (EMG) activity monitoring based on an improved version of the adaptive linear energy detector (ALED), a widely used technique in voice activity detection. More precisely, we propose a modified ALED technique (named M-ALED) to improve the method's robustness with respect to noise. To achieve this objective, M-ALED relies on the Teager-Kaiser operator for signal pre-conditioning to increase the SNR and uses the order statistics to gain robustness against the signal's impulsiveness. We propose again to exploit the order statistics for the initial signal baseline estimation to deal with the cases where such information is unavailable. Finally, since M-ALED detects the signal's activity at the frame level, we propose in a second stage to refine this detection (at the sample level) by using a constant false alarm rate (CFAR) approach leading to the fine M-ALED (FM-ALED) solution. The performance of FM-ALED is assessed via real and synthetic EMG signal recordings and the obtained results highlight its effectiveness as compared with the state-of-the-art methods (it reduces the mean error probability by a factor close to 2).

Comparison of recent S-wave indicating methods

Seismic event consists of surface waves and body waves. Due to the fact that the body waves are faster (P-waves) and more energetic (S-waves) in literature the problem of their analysis is taken more often. The most universal information that is received from the recorded wave is its moment of arrival. When this information is obtained from at least four seismometers in different locations, the epicentre of the particular event can be estimated [1]. Since the recorded body waves may overlap in signal, the problem of wave onset moment is considered more often for faster P-wave than S-wave. This however does not mean that the issue of S-wave arrival time is not taken at all. As the process of manual picking is time-consuming, methods of automatic detection are recommended (these however may be less accurate). In this paper four recently developed methods estimating S-wave arrival are compared: the method operating on empirical mode decomposition and Teager-Kaiser operator [2], the modification of STA/LTA algorithm [3], the method using a nearest neighbour-based approach [4] and the algorithm operating on characteristic of signals’ second moments. The methods will be also compared to wellknown algorithm based on the autoregressive model [5]. The algorithms will be tested in terms of their S-wave arrival identification accuracy on real data originating from International Research Institutions for Seismology (IRIS) database.

A Novel GPS Multipath Mitigation Method Based on the TKO and MPI Algorithm

Multipath is one of dominant error source in satellite positioning. Various multipath mitigation methods have been developed. This paper proposes a new efficient method. The motivation for this proposed method is to combine the Teager-Kaiser Operator (TKO) with the Multipath Indicator (MPI) algorithm to achieve a better mitigation performance by taking advantages of their merits. The method first applies the TKO on received signals’ Auto Correlation Function (ACF) to get an initiate estimation of GPS multipath, and at the same time limit the received signals within a certain range to meet the application condition of the MPI algorithm. Then we employ MPI module to make compensation for the code tracking error to have a more accurate estimation. Finally, by overcoming the respective shortcomings of the TKO and MPI algorithm, the simulation results show that compared to the traditional narrow Early-Minus-Late technique (nEML), the original TKO and the original MPI algorithm, the proposed method can get a smaller code tracking error and achieve the goal of the GPS multipath mitigation, especially in the low Signal-to-Noise Ratio (SNR) surroundings.

Assessing instantaneous energy in the EEG: a non-negative, frequency-weighted energy operator.

Signal processing measures of instantaneous energy typically include only amplitude information. But measures that include both amplitude and frequency do better at assessing the energy required by the system to generate the signal, making them more sensitive measures to include in electroencephalogram (EEG) analysis. The Teager-Kaiser operator is a frequency-weighted measure that is frequently used in EEG analysis, although the operator is poorly defined in terms of common signal processing concepts. We propose an alternative frequency-weighted energy measure that uses the envelope of the derivative of the signal. This simple envelope- derivative operator has the advantage of being nonnegative, which when applied to a detection application in newborn EEG improves performance over the Teager-Kaiser operator: without post-processing filters, area-under the receiver-operating characteristic curve (AUC) is 0.57 for the Teager-Kaiser operator and 0.80 for the envelope-derivative operator. The envelope-derivative operator also satisfies important properties, similar to the Teager-Kaiser operator, such as tracking instantaneous amplitude and frequency.

On the Nonlinear Teager-Kaiser Operator for Energy Detection Based Impulse Radio UWB Receivers

In this paper, by modeling a narrowband interference (NBI) as a wide-sense stationary (WSS), zero-mean Gaussian bandpass random process, a systematic theoretical framework is developed for the first time to characterize the operation and performance improvement of energy detection (ED) based impulse radio ultra-wideband (IR-UWB) receivers that employ a nonlinear Teager-Kaiser operator (TKO) and a highpass filter. Furthermore, through both theoretical analysis and simulations, we have identified (1) that the TKO technique can effectively mitigate not only the performance degradation caused by an NBI but also that caused by additive white Gaussian noise and (2) that a larger bandwidth of the UWB signal leads to better mitigation. Therefore, the TKO technique is considered as a very promising technique to improve the overall performance of ED-based IR-UWB receivers no matter an NBI is present or not.

Howling Detection in Hearing Aids Based on Generalized Teager-Kaiser Operator

With the ongoing miniaturization in the hearing aid industry, acoustical coupling between the loudspeaker and the microphone(s) of the hearing aid causes a major problem to users. Howling is one of the most severe and annoying consequences of this acoustical coupling. This study presents a howling detection method using the Generalized Teager-Kaiser Operator (GTKO). Since the GTKO is both time and frequency sensitive, its resolution parameter must be assigned properly to ensure satisfactory performance of this operator in the frequency range of the input signal for the hearing aid. In order to cover the entire band of the input signal with appropriate resolution parameters, the input signal is decomposed into a filterbank (i.e., uniform and nonuniform filterbanks). GTKO is applied to the output of each band to detect the howling, and the resolution parameter of the GTKO block is selected depending on the central frequency of that particular band. Experimental results compare the performance of each proposed method with two known howling detection approaches, Peak-to-harmonic power ratio (PHPR) approach and a multiple-feature approach. The proposed method has high detection probability and short detection time. It is also shown that considering a hybrid algorithm which includes the PHPR approach with each of the proposed methods (i.e. combination of GTKO blocks with different types of filterbanks) results in lower false alarm probability.

A BOC Signal Synchronization Algorithm Based on TK Operator

The binary phase shift keying (BPSK) modulation method is generally utilized for the traditional navigation satellite systems; however, the new generation of GNSS, such as modernized GPS, European Galileo, Chinese Compass, etc., will apply binary offset carrier (BOC) modulation technique, which can efficiently split the spectrums of navigation signals using the same frequency so as to reduce the interferences among different systems. But the autocorrelation function of BOC modulated signals has the drawback of multimodality, so it’s very hard to synchronize to the right peak when acquiring and tracking signals, especially under low SNR circumstances, which can decrease the positioning accuracy and even lead to wrong positioning results. A BOC modulated signal synchronization algorithm based on TK (Teager-Kaiser) operator is proposed in this article, which could eliminate all the other peaks in autocorrelation function of BOC modulated signals, and create an ideal curve with only one right peak. As a result, this method could avoid the false lock of code phase and guarantee the high precision fix results.

A Multipath Cancellation Method Based on TK Operator for BOC Signals

The new generation of global navigation satellite systems will apply binary offset carrier (BOC) modulation technique, which can efficiently split the spectrums of navigation signals using the same frequency so as to reduce the interferences among different systems. But the autocorrelation function of BOC modulated signals has the drawback of multimodality, so it’s very hard to synchronize to the right peak when acquiring and tracking signals, especially under low SNR circumstances, which can decrease the positioning accuracy and even lead to wrong positioning results. Meanwhile, if there are multipath signals mixed in the receiving signal, the autocorrelation curve will be greatly distorted, and the number of side-peak will also increase exaggeratedly, which could deteriorate the situation mentioned above. A multipath cancellation method based on TK (Teager-Kaiser) operator is proposed in this article, which could not only detect the right peak in the autocorrelation curve, but also eliminate all the other multipath signals. As a result, this method could avoid the false lock of code phase and guarantee the high precision fix results.

Nonlinear Blind Narrowband Interference Mitigation for Energy Detection Based UWB Receivers

In this paper, a blind narrowband interference (NBI) mitigation technique using the combination of a square law (SL) device and a band pass filter (BPF) is proposed for energy detection (ED) based ultra-wideband (UWB) receivers. Both theoretical analysis and computer simulations show that without requiring any prior knowledge about the NBI, the SL technique can considerably improve signal-to-interference ratio of the received UWB pulses and hence allows ED-based UWB receivers achieve much better bit error rate. Furthermore, the proposed SL technique has the same NBI mitigation performance as the Teager-Kaiser operator (TKO) technique. Unlike TKO, there are many commercial off-the-shelf SL devices are available for IR-UWB applications. Thus, the proposed SL technique is a simple, implementable, and highly effective blind NBI mitigation technique for ED-based IR-UWB receivers.

On the Effects of Filterbank Design and Energy Computation on Robust Speech Recognition

In this paper, we examine how energy computation and filterbank design contribute to the overall front-end robustness, especially when the investigated features are applied to noisy speech signals, in mismatched training-testing conditions. In prior work (“Auditory Teager energy cepstrum coefficients for robust speech recognition,” D. Dimitriadis, P. Maragos, and A. Potamianos, in Proc. Eurospeech'05, Sep. 2005), a novel feature set called “Teager energy cepstrum coefficients” (TECCs) has been proposed, employing a dense, smooth filterbank and alternative energy computation schemes. TECCs were shown to be more robust to noise and exhibit improved performance compared to the widely used Mel frequency cepstral coefficients (MFCCs). In this paper, we attempt to interpret these results using a combined theoretical and experimental analysis framework. Specifically, we investigate in detail the connection between the filterbank design, i.e., the filter shape and bandwidth, the energy estimation scheme and the automatic speech recognition (ASR) performance under a variety of additive and/or convolutional noise conditions. For this purpose: 1) the performance of filterbanks using triangular, Gabor, and Gammatone filters with various bandwidths and filter positions are examined under different noisy speech recognition tasks, and 2) the squared amplitude and Teager-Kaiser energy operators are compared as two alternative approaches of computing the signal energy. Our end-goal is to understand how to select the most efficient filterbank and energy computation scheme that are maximally robust under both clean and noisy recording conditions. Theoretical and experimental results show that: 1) the filter bandwidth is one of the most important factors affecting speech recognition performance in noise, while the shape of the filter is of secondary importance, and 2) the Teager-Kaiser operator outperforms (on the average and for most noise types) the squared amplitude energy computation scheme for speech recognition in noisy conditions, especially, for large filter bandwidths. Experimental results show that selecting the appropriate filterbank and energy computation scheme can lead to significant error rate reduction over both MFCC and perceptual linear predicion (PLP) features for a variety of speech recognition tasks. A relative error rate reduction of up to ~ 30% for MFCCs and ~ 39% for PLPs is shown for the Aurora-3 Spanish Task.

The Teager-Kaiser Energy Operator in Presence of Multiple Narrowband Interference

As the analog front-end of an energy detector is highly susceptible to narrowband interference a modified energy detection scheme based on the Teager-Kaiser operator and high-pass filtering is considered. This letter analyzes the Teager-Kaiser operator output for an arbitrary number of narrowband band-pass signals having different amplitudes, center frequencies and bandwidths. The analysis reveals that additional cross components occur at the operator's output in case of multiple narrowband interference. Hence, a simple narrowband interference suppression with Teager-Kaiser operator and high-pass filtering can be insufficient.

Root and pre-constant signals of the 1D Teager-Kaiser operator

We give an input/output characterization of the Teager-Kaiser operator, then we classify the root signals (those that remain invariant) and the pre-constant signals (those that produce a constant output) of the operator. With the gained knowledge, a simple detector of sinusoidal signals and of their corresponding frequencies is designed. The methods used allow for a certain amount of generalization providing a paradigm of sorts for the design of quadratic and other polynomial filters.

A joint 2D AM–FM estimation based on higher order Teager–Kaiser energy operators

In this work, an image demodulation algorithm based on two-dimensional higher order Teager–Kaiser (TK) operators is presented. We show quantitatively and qualitatively that the introduction of higher orders in TK operator improves amplitude modulation (AM) and frequency modulation (FM) estimation results, compared to classical approaches such as the Discrete Energy Separation Algorithm (DESA) or the Analytic Signal (AS) method. Indeed, for a wide class of images, obtained demodulation errors for both the amplitude and frequency are numerically lower than the obtained ones with the DESA and AS method. The proposed method is illustrated on both synthetic and real images. Moreover, it turns out for some real images that the algorithm is very efficient in the sense that it tracks the most significant part in images and segments regions of interests, particularly, the AM counterpart. Finally, an application of our approach to the segmentation of mines’ shadows in Sonar images is presented. This is very important for both civil and military applications.

A Comparison of the Squared Energy and Teager-Kaiser Operators for Short-Term Energy Estimation in Additive Noise

Time-frequency distributions that evaluate the signal's energy content both in the time and frequency domains are indispensable signal processing tools, especially, for nonstationary signals. Various short-time energy computation schemes are used in practice, including the mean squared amplitude and Teager-Kaiser energy approaches. Herein, we focus primarily on the short- and medium-term properties of these two energy estimation schemes, as well as, on their performance in the presence of additive noise. To facilitate this analysis and generalize the approach, we use a harmonic noise model to approximate the noise component. The error analysis is conducted both in the continuous- and discrete-time domains, deriving similar conclusions. The estimation errors are measured in terms of normalized deviations from the expected signal energy and are shown to greatly depend on both the signals' spectral content and the analysis window length. When medium- and long-term analysis windows are employed, the Teager-Kaiser energy operator is proven superior to the common squared energy operator, provided that the spectral content of the noise is more lowpass than the corresponding signal content, and vice versa. However, for shorter window lengths, the Teager-Kaiser operator always outperforms the squared energy operator. The theoretical results are experimentally verified for synthetic signals. Finally, the performance of the proposed energy operators is evaluated for short-term analysis of noisy speech signals and the implications for speech processing applications are outlined.

Two-dimensional continuous higher-order energy operators

An extension of the 2-D discrete Teager-Kaiser energy operator and the 1-D higher-order energy operators to the 2-D continuous case is proposed. These 2-D continuous operators are flexible enough to apply a large class of image gradient filters, and consequently different discrete energy operators are derived. Particularly, the proposed model takes into account the diagonal directions, through the partial derivatives. The obtained operators are computationally very simple, like the classical 2D Teager-Kaiser operator, and are well suited for image-processing applications such as image demodulation or image contrast enhancement. Results of demodulation of synthetic and real images, to estimate envelope information, are presented to show the feasibility of the proposed operators.

A Highly Efficient Generalized Teager-Kaiser-Based Technique for LOS Estimation in WCDMA Mobile Positioning

Line-of-sight signal delay estimation is a crucial element for any mobile positioning system. Estimating correctly the delay of the first arriving path is a challenging topic in severe propagation environments, such as closely spaced multipaths in multiuser scenario. Previous studies showed that there are many linear and nonlinear techniques able to solve closely spaced multipaths when the system is not bandlimited. However, using root raised cosine (RRC) pulse shaping introduces additional errors in the delay estimation process compared to the case with rectangular pulse shaping due to the inherent bandwidth limitation. In this paper, we introduce a novel technique for asynchronous WCDMA multipath delay estimation based on deconvolution with a suitable pulse shape, followed by Teager-Kaiser operator. The deconvolution stage is employed to reduce the effect of the bandlimiting pulse shape.

Subchip multipath delay estimation for downlink WCDMA system based on Teager-Kaiser operator

Accurate detection and estimation of overlapping fading multipath components is vital for many communication systems, particularly for positioning technologies. Traditional approaches used for channel estimation generally fail in estimating closely-spaced multipath components in code-division multiple access (CDMA) systems. Here, we present a highly efficient technique for asynchronous downlink WCDMA multipath delay estimation with subchip resolution capability based on nonlinear Teager-Kaiser operator concept. The behavior of this technique is influenced considerably by the pulse shape waveform. Both rectangular and root raised cosine pulse shaping filters are considered.