Intrinsic Chirp Research Articles

Systematic analysis of an attosecond pulse generation by a subcycle laser field

We investigated the influence of subcycle driving fields on high-order harmonic generation (HHG), with a focus on driver's intrinsic chirp, carrier-envelope phase (CEP), and number of laser cycles. Our findings reveal that the center frequency of a laser pulse scales as τ−5/4 with pulse duration τ, and that attochirp exhibits a similar dependence on pulse duration. Additionally, we identified CEP-specific trends in harmonic yield: it increases as τ5/4 for ϕ0=0∘ and decreases as τ−4.1 for ϕ0=−90∘. Although subcycle pulses can generate intense isolated attosecond pulses (IAPs), they also tend to produce higher attochirp and reduced cutoff energies. However, effective compensation for attochirp can mitigate these drawbacks, thereby increasing the capability of subcycle pulses to generate short-duration, high-intensity IAPs. These results offer valuable insights into HHG using subcycle pulses and have important implications for the advancement of ultrafast light sources and the understanding of ultrafast phenomena at the attosecond timescale. Published by the American Physical Society 2025

Separation of overlapping non-stationary signals and compressive sensing-based reconstruction using instantaneous frequency estimation

Compressive sensing uses an incomplete sample set to consider signal reconstruction with sparse basis representations over a specific transform domain. This work examines the difficulties encountered in various signal processing applications, such as data overlap with the target signal in time and frequency domains. The conventional filtering and windowing processes fail to promote better results in recovering the desired signal. The non-stationary signal with time-frequency representations is highly significant for certain valuable applications. An efficient signal separation and reconstruction method based on instantaneous frequency estimate is proposed to improve the non-stationary signal outcome. The proposed research includes speech signal data acquisition, signal component decomposition, instantaneous frequency estimation, overlapped signal separation, and reconstruction. Two datasets, Dacon Overlapped Speech and LJ Speech Dataset, are utilized to generate a new overlapped signal dataset. Initially, the generated speech signals are collected and decomposed into several monocomponents using Synchrosqueezing Wavelet Transform (SynWav), Renyi's quadratic entropy (RQuad), Narrow bandpass filtering (NBand) and single frequency filtering (SFreq). The instantaneous frequencies are estimated using the Hilbert-Huang transform (HilHuT) to generate a time-frequency representation of multi-component signals. The overlapped signals are separated and reconstructed to a desired signal using a Compressive sensing-based Discrete Cosine transform with amended intrinsic chirp separation (CDcT_AIChirS). The proposed model is simulated using PYTHON to examine the performances. In comparison, the mean square error is calculated to be 2.71, the root mean square error is calculated to be 1.64, and the signal to noise ratio is calculated to be 32dB.

Interference-induced generation of a chirp-free short isolated attosecond pulse in the water window region with multicolor laser fields.

Compensating for the intrinsic attosecond chirp (atto-chirp) of wideband high-order harmonics in the water window region is a significant challenge, in order to obtain isolated attosecond pulses (IAPs) with a width of tens of attoseconds (as). Here, we propose to realize the generation of IAP with duration as short as 20 as, central energy of 365 eV, and bandwidth exceeding 150 eV from chirp-free high harmonics generated by a four-color driving laser, without the necessity for atto-chirp compensation with natural materials. Unlike any other gating methods that an IAP arises from only one electron ionization event, we take advantage of the interference between harmonic radiation produced by multiple ionizing events. We further demonstrate that such chirp-free short IAP survives after taking account of macroscopic propagation effects. Given that the synthesized multicolor laser field can also effectively increase the harmonic flux, this work provides a practical way for experiments to generate the broad bandwidth chirp-free IAPs in the water window region.

Varying Wave-Shape Component Decomposition: Algorithm and Applications

The decomposition problem for multiple sinusoidal component signals has been developed in the past decades. However, many complex time series are made up of wave-shape components, which invalidates signal decomposition methods based on sinusoidal components. Since wave-shape components are time-varying from one cycle to the other and often contaminated by strong noise, robustly decomposing a signal into wave-shape components is still a challenging task. In this paper, a varying wave-shape component decomposition (VWCD) method is proposed to extract time-varying and weak characteristics of wave-shape components from a multicomponent signal. Specifically, instantaneous frequencies (IFs) of varying wave-shape components are no longer inter multiples of a fundamental IF allowing the VWCD method more flexible in practical applications. We propose an instantaneous amplitudes and fundamental component phases estimation method based on an intrinsic chirp signal model and a regression coefficients initialization method by a fixed wave-shape signal model. The potential and effectiveness of the proposed VWCD method are verified by some simulated signals with different signal-to-noise ratios, a real-world electroencephalography seizure signal, and an experimental chest wall vibration signal from a microwave vital sign monitoring system.

Detection and time–frequency analysis of multiple plant-wide oscillations using adaptive multivariate intrinsic chirp component decomposition

Analyzing plant-wide oscillations is a challenging task owing to the presence of noise, nonstationarity, and multiple modes in a process control system. Multivariate intrinsic chirp component decomposition (MICCD) is a novel powerful tool for multivariate signal processing. Nevertheless, MICCD requires users to provide component number in advance, which restricts its adaptability. This study proposes an adaptive MICCD (AMICCD) that can adaptively determine the component number by utilizing the permutation entropy of instantaneous frequency. An AMICCD-based time–frequency analysis framework is presented to detect and characterize the multiple plant-wide oscillations. Compared to the latest methods, such as multivariate empirical mode decomposition and multivariate intrinsic time-scale decomposition, the proposed method can process not only single/multiple plant-wide oscillations, but also time-invariant/time-varying plant-wide oscillations. In particular, the proposed method can directly provide the time–frequency curves of multiple plant-wide oscillations, which have not been achieved by the state-of-the-art techniques. Finally, the effectiveness and advantages of the proposed approach are demonstrated on a wide variety of simulations and industrial cases.

Generation of quasi-chirp-free isolated attosecond pulses from atoms under the action of orthogonal two-color combined pulse of fundamental frequency and higher intensity second harmonic fields

The intrinsic chirp of high-order harmonic generation is an important factor limiting the production of ultrashort attosecond pulses. Based on numerically solving the time-dependent Schrödinger equation, the generation process of high-order harmonic from the He atom under the action of orthogonal two-color combined pulse of fundamental frequency and higher intensity second harmonic fields is studied. In this paper, we propose to achieve quasi-chirp-free isolated attosecond pulses by superimposing a higher second-harmonic field on the orthogonal direction of the fundamental frequency field. It is found that the high-energy part of its harmonic emission exhibits small chirp characteristics, which can be used to synthesize isolated attosecond pulses. Through the analysis of the wave packets evolution and the classical motion trajectories of the electron, it is demonstrated that the quasi-chirp-free harmonic can be attributed to the simultaneous return of electrons ionized at different times to the parent particle. The influence of the relative phase of the two pulses on the harmonics is further analyzed, and it is observed that this phenomenon is sensitive to the relative phase, but it can still generate isolated attosecond pulses within a certain phase.

Identification of forced time-varying systems via intrinsic chirp component decomposition

Modal parameter identification is significant in the field of vibration and control for tracking structural vibrations and evaluating structural performances. A novel parameter identification method based on the intrinsic chirp component decomposition (ICCD) and the Hilbert transform is proposed for forced time-varying systems. The developed ICCD decomposes the measured response signal into a limited number of intrinsic chirp components, and instantaneous modal parameters of the system are identified by the Hilbert transform of each intrinsic chirp component. The effectiveness and the accuracy of the proposed approach are investigated in two case studies, that is, a discrete mass-spring-damper oscillator and a cantilever beam. Smooth and periodical parameter variations are discussed in each case. Comparison with the empirical mode decomposition based method validates that the proposed method has better identification ability on estimating the instantaneous natural frequency of the system with the presence of noise. Results demonstrate that the ICCD-based approach could be a reasonable alternative for identification of forced time-varying systems in a noise environment.

A tacholess order tracking method based on extended intrinsic chirp component decomposition for gears under large speed variation conditions

Abstract Order tracking has been considered as the most effective non-stationary signal analysis technique for condition monitoring and fault diagnosis. Conventional order tracking is performed with a reference signal measured by the auxiliary device, which is expensive and inconvenient to install. In order to to break the constraint of the traditional order tracking technique, some tacholess order tracking methods have been developed in the past few years. However, current tacholess order tracking approaches are only applicable to slightly varying speed applications. To overcome the shortcoming above, a novel tacholess order tracking method is proposed in this paper. In the proposed method, each mode of the vibration signal is reconstructed by a method called extended intrinsic chirp component decomposition, and the Hilbert transform is used to estimate the instantaneous phase of reference shaft. Then the vibration signal is resampled to the angle domain, and the fault characteristic orders can be identified in the order spectrum accurately. The effectiveness of the proposed method has been validated by a simulated meshing gear vibration signal. The result illustrates that the proposed method can realize gears fault diagnosis under large speed variation conditions.

Decomposition for Multi-Component Micro-Doppler Signal With Incomplete Data

When echoes of micromotion targets are overlapping in the time-frequency (TF) domain and sampling data are missing, the decomposition of the multicomponent micro-Doppler (m-D) signals is challenging. To address this issue, this letter proposes a method for multicomponent m-D signal decomposition by iterations of the instantaneous frequencies (IFs), individual components, and complex envelopes. To initialize the IFs, the well-focused time-frequency representation (TFR) is obtained by sparse reconstruction of the incomplete data, and then the IFs of the TFR can be estimated by the short-time variational mode decomposition (STVMD) algorithm. After initialization, the IFs, individual components, and complex envelopes are updated by the intrinsic chirp component decomposition (ICCD), alternating direction method (ADMM) of multipliers, and least-square-error criterion (LSEC), respectively. Finally, the proposed method is verified by simulation and application to real data.

Time-Frequency Bandpass Filter with Nonstationary Signal Decomposition Application

In various applications such as speech processing, underwater sound, radar application and mechanical fault diagnosis, there are large number of nonstationary signals. In order to achieve nonstationary signal decomposition, the instantaneous frequency ridge is extracted through interactive mode, and a time-frequency bandpass filter (TFBPF) method is proposed. This method is the modified version of Intrinsic Chirp Component Decomposition (ICCD) and has the physical essence of time-frequency domain bandpass filter. The superiority and application potential of TFBPF in complex engineering signal decomposition are demonstrated through two numerical examples. In the first one, we prove that TFBPF can decompose the weak signal component directly through analyzing the vibration signal of hydraulic turbine; While in the second one, we prove that TFBPF can effectively overcome the drawbacks of ICCD through analyzing the vibration signal during the speed-up process of a complex equipment. TFBPF is still very effective even for complex signal decomposition in a strong noise environment.

Multivariate intrinsic chirp mode decomposition

A multivariate intrinsic chirp mode decomposition (MICMD) algorithm is proposed to process multivariate/multichannel signals. In contrast to most existing multivariate time-frequency decomposition techniques, the proposed MICMD can efficiently extract time-varying signals by solving a multivariate linear system. In this paper, we first define a multivariate intrinsic chirp mode (MICM) by assuming the presence of a joint or common instantaneous frequency (IF) among all channels. Then the IFs and instantaneous amplitudes (IAs) are modeled as Fourier series. IFs can be estimated using the framework of the general parameterized time-frequency transform and then the corresponding MICMs are reconstructed by solving multivariate linear equations through an extended least square method. MICMD can characterize a set of multivariate modes without requiring more user-defined parameters than the original ICMD. Its properties and advantages, including mode-alignment, computational complexity, filter bank structure, quasi-orthogonality, channel number and noise robustness, are investigated successively. MICMD outperforms both multivariate empirical mode decomposition (MEMD) and multivariate variational mode decomposition (MVMD) in extracting time-varying components. The computational complexity of the proposed MICMD is proven to be O(N), thus much faster than MNCMD, which is of O(N3) complexity. In the end, we highlight the utility and superiority of MICMD in three real-world cases, including the periodicity analysis in meteorology (three-channel), the α-rhythm separation in electroencephalogram (EEG) (four-channel), and the plant-wide oscillation detection in industrial control system (eleven-channel).

Three-dimensional micromotion trajectory reconstruction of rotating targets by interferometric radar

Imaging, feature extraction, and recognition of targets with micromotion by retrieving their three-dimensional micromotion trajectories (3-D MMTs) have attracted a lot of interest in recent years. We propose a method for retrieving the 3-D MMT of a rotating target based on the interferometric phases obtained using a wideband interferometric radar system with three antennas positioned in L-shape. First, the micro-Doppler effect of rotating target is theoretically analyzed with formulas derived. Then, the instantaneous frequencies are extracted via the short-time Fourier transform and the Viterbi algorithm. The echo signals received by these three antennas are decomposed by the intrinsic chirp component decomposition method, and the interferometric phases of different scatterers are respectively obtained. Finally, the 3-D MMTs of rotating target are reconstructed by exploring the interferometric phases and the range-slow-time data. The effectiveness of the proposed method is validated by both simulations and practical experiment using a Ka-band interferometric radar.

Time‐based multi‐component irregular FM micro‐Doppler signals decomposition via STVMD

The decomposition of multi-component micro-Doppler signals overlapping in the time-frequency (T-F) domain is critical and challenging, especially in the case of irregular instantaneous Doppler frequency. The authors propose a novel time-based decomposition method called the short-time variational mode decomposition (STVMD) to analyse the irregular (FM) micro-Doppler signals, and present an optimal model combined with T-F transformation. Then, considering the STVMD may fail to extract the instantaneous frequency (IF) of overlapped components, an improved STVMD algorithm is put forward. Since the dependence of the STVMD algorithm on the initial value, they adopt the Kalman filtering to implement IF tracking and regrouping under the global constraint, further accelerating the convergence of the algorithm. Furthermore, due to the mode aliasing at the intersection point, they adopt a degenerate STVMD model to decompose the signals with known centre frequencies, which can be viewed as a Wiener filter. With the two steps, the improved STVMD algorithm can effectively solve the decomposition of T-F overlapping irregular FM micro-Doppler signals. Compared with the peak ridge technique and the ridge path regrouping and intrinsic chirp component decomposition (RPRG + ICCD), the proposed method shows the effectiveness and adaptability even for irregular FM signals with large T-F spectrum amplitude fluctuation in the low signal-to-noise ratio environment.

Chirp-dispersion management inducing regeneration of truncated Airy pulses in fiber optics links

In this paper, we introduce another technique of Airy pulse regeneration in fiber links using the interaction between group velocity dispersion (GVD) and the initial value of frequency chirp. This technique of regeneration consists of managing the product of G V D × c h i r p over each piece f i = 1 … N of fiber line having N pieces in the case of zero-third-order dispersion (TOD) systems. This work follows [Phys. Rev. A 89, 043817 (2014)PLRAAN1050-294710.1103/PhysRevA.89.043817], which studied the nonzero-TOD system. Three models are considered: the first consists of alternation of the GVD with the chirp being constant, the second consists of alternation of the chirp with a constant GVD, and the third consists of the alternation of both parameters. Through the numerical results obtained in the linear optical system, we show that the first model with an initial condition corresponding to the asymmetric inversion (A.I.) mechanism, G V D × c h i r p < 0 , is the best at yielding interesting regeneration for both a single finite energy Airy pulse (FEAP) and for the symmetric FEAPs previously defined in [Opt. Commun. 399, 16 (2017)OPCOB80030-401810.1016/j.optcom.2017.04.064]. There is a need to achieve the A.I. mechanism on each piece of fiber through the condition s × C ′ < 0 , where the GVD sign s alternates and C ′ is the intrinsic chirp developed by the pulse itself within the current piece f i before its injection into the next piece f i + 1 . The main parameter that is beneficial for this kind of chirp-dispersion management (CDM) regeneration of FEAPs in fiber links is found to be the initial chirp whose dimensionless optimal absolute value is | C | ∈ [ 1 ; 3 ] in order to combine the quality and good intensity. In contrast, the temporal gap τ B and nonlinearity have a deleterious impact on regeneration. Moreover, the noise in the regeneration originates from the alternation of the chirp, the simultaneous alternation of both the GVD and the chirp, the drastic increase in chirp, and nonlinearity.

Modal identification of multi-degree-of-freedom structures based on intrinsic chirp component decomposition method

Modal parameter identification is a mature technology. However, there are some challenges in its practical applications such as the identification of vibration systems involving closely spaced modes and intensive noise contamination. This paper proposes a new time-frequency method based on intrinsic chirp component decomposition (ICCD) to address these issues. In this method, a redundant Fourier model is used to ameliorate border distortions and improve the accuracy of signal reconstruction. The effectiveness and accuracy of the proposed method are illustrated using three examples: a cantilever beam structure with intensive noise contamination or environmental interference, a four-degree-of-freedom structure with two closely spaced modes, and an impact test on a cantilever rectangular plate. By comparison with the identification method based on the empirical wavelet transform (EWT), it is shown that the presented method is effective, even in a high-noise environment, and the dynamic characteristics of closely spaced modes are accurately determined.

Parametric identification of time-varying systems from free vibration using intrinsic chirp component decomposition

Time-varying systems are applied extensively in practical applications, and their related parameter identification techniques are of great significance for structural health monitoring of time-varying systems. To improve the identification accuracy for time-varying systems, this study puts forward a novel parameter identification approach in the time–frequency domain using intrinsic chirp component decomposition (ICCD). ICCD is a powerful tool for signal decomposition and parameter extraction, with good signal reconstruction capability in a high-noise environment. To maintain good identification effects for the time-varying system in a noisy environment, the proposed method introduces a redundant Fourier model for the non-stationary signal, including instantaneous frequency (IF) and instantaneous amplitude (IA). The accuracy and effectiveness of the proposed approach are demonstrated by a single-degree-of-freedom system with three types of time-varying parameters, as well as an example of a multi-degree-of-freedom system. The effects of different levels of measured noise on the identified results are also discussed in detail. Numerical results show that the proposed method is very effective in tracking the smooth, periodical, and non-smooth variations of time-varying systems over the entire identification time period even when the response signal is contaminated by intense noise.

Micro‐Doppler feature extraction method for vibration targets based on the segmental intrinsic chirp component decomposition

Based on the three-antenna interferometric radar system, a novel micro-Doppler feature extraction method for vibration targets is proposed in this study. First, the theory of interferometric processing of echo signal for vibration targets is introduced and explained. Second, short-time Fourier transform is conducted with the time–frequency diagram of echo signal obtained. Then, the signals received by three-antenna model are decomposed based on the segmental intrinsic chirp component decomposition. Finally, the 2D trajectory of vibration target is reconstructed and its micro-Doppler features are effectively extracted via the interferometric phase. Besides, the micro-Doppler parameters can also be estimated with the method. Two simulation experiments are conducted to validate the proposed method.

Intrinsic chirp analysis of a single dual-drive silicon PAM-4 optical modulator.

We propose an analytical model to investigate the intrinsic frequency chirp with the method of 4-level pulse-amplitude-modulation (PAM-4) optical modulation by driving a single dual-drive silicon optical modulator. With the analytical model, we calculate the chirp parameters of this PAM-4 generation numerically. The intensity and phase of output signal changes with the PAM levels' switching, which results in the frequency chirp. We find that the modulator operating at different quadrature points (Q- and Q+) will have different frequency chirp behavior. The Q- modulator has mainly negative chirp parameters while Q+ modulator has mainly positive chirp parameters. We characterize the eye diagrams and BER of the optical PAM-4 signals generated by the Q- and Q+ modulator at the modulation rates of 25 Gbaud and 32 Gbaud, respectively, for both back-to-back and 2 km transmission in single mode fiber. The BER results show the Q- modulator has a small power penalty attribute to the positive fiber dispersion, which is suited for the short-distance transmission in data center application.

Parameterized model based blind intrinsic chirp source separation

The blind source separation (BSS) concerns recovering sources from their mixtures. Specifically, the sources in this paper, named intrinsic chirp sources (ICSs), are modeled as the linear combination of non-linear chirp components (NCCs). A novel method is developed here to address the blind separation issue of them. Firstly, all the mixtures at each channel are decomposed into a series of NCCs by a parameterized decomposition approach. It can adapt to NCCs with time-frequency (T-F) distribution suffering from bad T-F concentration and non-disjoint T-F overlapping. Next, the reconstructed NCCs can be clustered into corresponding ICS according to the fact that the NCCs belonging to the identical ICS share the same column in mixing matrix. The source recovery and mixing matrix estimation are finally accomplished based on the clustering consequence. Three simulations demonstrate the capability of our method in dealing with challenging under-determined BSS cases and its potential in practical applications.

High-precision frequency estimation for FMCW radar applications based on parameterized de-alternating and modified ICCD

In this paper, aiming to achieve high-resolution frequency estimation for frequency-modulated continuous wave (FMCW) radar applications, a novel frequency estimation algorithm based on parameterized de-alternating (PDA) is proposed. According to the beat signal model, the proposed PDA method is performed with a matched kernel function to achieve the best de-alternating performance (i.e. the maximum conversion from an oscillating signal to a constant signal). The kernel parameter is estimated by solving an optimization problem which is simple and computationally efficient. Moreover, for a multiple target scenario, the intrinsic chirp component decomposition (ICCD) method is employed to isolate different components of the beat signal, which can eliminate the mutual interference between adjacent components when performing the PDA method. Compared with the commonly used FFT technique, our method can greatly improve the frequency estimation resolution and achieve superior ranging performance with a limited bandwidth. Both simulated and experimental validations are provided to show the effectiveness of the proposed methods.