Instantaneous Frequency Rate Research Articles

Multiple synchro-tuning chirplet transform

Time-frequency analysis (TFA) is an effective tool for characterizing non-stationary signals. Due to the limited time-frequency resolution capability, traditional TFA methods cannot achieve the optimal time-frequency representation (TFR). Based on the post-processing technique, a novel TFA method named multiple synchro-tuning chirplet transform (MSTCT) is proposed to obtain high-resolution and robust TFR for non-stationary signals. The MSTCT first estimates the spectral energy, instantaneous frequency (IF), and chirp rate (CR) of non-stationary signals with high time-frequency resolution, enabling precise energy localization on the time-frequency plane. Then, a multiple reassignment procedure is proposed to concentrate the blurry time-frequency energy and yield a better TFR. Moreover, benefiting from the multiple squeezing mechanism in the frequency axis, the MSTCT holds the potential to reconstruct the signal with high accuracy. Both the simulation results and the real-world experiment using the bat echolocation data demonstrate that the proposed MSTCT algorithm achieves superior performance in the time-frequency resolution, noise immunity, and reconstruction capability compared to the state-of-art linear TFA methods.

Instantaneous Frequency and Chirp Rate Estimation for Noisy Quadratic FM Signals by CNN

Deep learning and machine learning are widely employed in various domains. In this paper, Artificial Neural Network (ANN) and Convolution Neural Network (CNN) are used to estimate the Instantons Frequency (IF), Linear Chirp Rate (LCR), and Quadratic Chirp Rate (QCR) for Quadratic Frequency Modulated (QFM) signals under Additive White Gaussian (AWG) noise and Additive Symmetric alpha Stable (ASαS) noise. SαS distributions are impulsive noise disturbances except for a few circumstances, lack a closed-form Probability Density Function (PDF), and an infinite second-order statistic. Geometric SNR (GSNR) is used to determine the impulsiveness of mixture noise for Gaussian and SαS noise. ANN is a machine learning classifier with few layers that reduce FE, LCRE, and QCRE complexity and achieve high accuracy. CNN is a deep learning classifier that is built with multiple layers of FE, LCRE, and QCRE. CNN is more accurate than ANN when dealing with large amounts of data and determining optimal features. The results reveal that SαS noise is substantially more damaging to FE, LCRE, and QCRE than Gaussian noise, even when the magnitude is modest, and it is less damaging when alpha is greater than one. After training DCNN for FE, LCRE, and QCRE estimation of QFM signals. The 2D-CNN model accuracy achieved 98.7603 and 1D-CNN is 75.8678 for ten epochs. ANN model accuracy achieved 37.5 for 1000 epochs. The accuracy of TFD (spectrogram & pspectrum) for frequency estimation of QFM signals was 38.4254 by spectrogram and 38.6746 by pspectrum.

The second-order local polynomial Fourier transform as instantaneous frequency and chirp rate estimator

Statistical properties, bias and variance, of the second-order local polynomial Fourier transform (LPFT) in the instantaneous frequency (IF) and chirp rate (CR) estimation are considered. We have derived expressions based on the error linearization around the exact value of signal parameters as it is commonly done in this field. However, we have also demonstrated the limits of this methodology. Two particularly important frequency modulated (FM) signals are considered as test cases: quadratic and cubic phase signals. Approximative expression for the bias and variance in the latter case are also derived. It is demonstrated that the optimal design parameter of the LPFT, i.e., window width, must be optimized independently for the IF and CR estimation to produce the minimum mean squared error (MSE). The derived expressions are checked by simulations.

Frequency dynamics of power systems with temporally distributed disturbances

The frequency dynamics and stability of power systems is essentially affected by nature and characteristics of the disturbances occurring in the system. Conventionally, frequency transients are examined assuming a single disturbance applied at a given time. However, actual incidents in the power systems can be generally composed of a temporal sequence of events, and thus characterized by multiple power imbalances of different magnitudes and time offsets. The consideration of the effects of the temporal distribution of power imbalances is important for two main reasons: the impact on the frequency dynamics of the system in terms of frequency metrics such as minimum instantaneous frequency and maximum absolute rate of change of frequency, and the correct representation of the dynamic behaviour of the system also for complex events such system separation. The work provides an analytical approach for the theoretical study of the frequency dynamics with temporally distributed power imbalances. The analytical approach is then used to examine the impact of multiple disturbances having different magnitudes and time offsets on the typical frequency metrics used to characterize the transient performances of the system. The concepts derived in the work are finally applied to the case of an actual event occurred in the Continental Europe power system, showing the fundamental role of considering temporally distributed power imbalances for a correct and accurate assessment of the dynamics of the system.

Detection of LFM Radar Signals and Chirp Rate Estimation Based on Time-Frequency Rate Distribution.

Linear frequency-modulated (LFM) signals are the most significant example of waveform used in low probability of intercept (LPI) radars, synthetic aperture radars and modern communication systems. Thus, interception and parameter estimation of the signals is one of the challenges in Electronic Support (ES) systems. The methods, which are widely used to accomplish this task are mainly based on transformations from time to time-frequency domain, which concentrate the energy of signals along an instantaneous frequency (IF) line. The most popular examples of such transforms are the short time Fourier transform (STFT) and Wigner-Ville distribution (WVD). However, for LFM waveforms, methods that concentrate signal energy along a line in the time-frequency rate domain may allow to obtain better detection and estimation performance. This type of transformation can be obtained using the cubic phase (CP) function (CPF). In the paper, the detection of LFM waveform and its chirp rate (CR) parameter estimation based on the extended forms of the standard CPF is proposed. The CPF was originally introduced for instantaneous frequency rate (IFR) estimation for quadratic frequency modulated (QFM) signals i.e., cubic phase signals. Summation or multiplication operations on time cross-sections of the CPF allow to formulate the extended forms of the CPF. Based on these forms, detection test statistics and the estimation procedure of LFM signal parameters have been proposed. The widely known estimation methods assure satisfying accuracy for high SNR levels, but for low SNRs the reliable estimation is a challenge. The proposed approach based on joint analysis of detection and estimation characteristics allows to increase the reliability of chirp rate estimates for low SNRs. The results of Monte-Carlo simulation investigations on LFM signal detection and chirp rate estimation evaluated by the mean squared error (MSE) obtained by the proposed methods with comparisons to the Cramer-Rao lower bound (CRLB) are presented.

Time-Frequency Jammer Mitigation Based on Kalman Filter for GNSS Receivers

In this paper, a time-frequency (TF) jammer mitigation algorithm based on a Kalman filter is proposed for global navigation satellite system (GNSS) receivers. A new state-space representation of the received signal is formed considering the rapidly changing characteristics of the jamming signal. Using the instantaneous frequency (IF) and chirp rate estimates obtained by the TF analysis, the proposed algorithm applies a Kalman filter for jamming signal estimation. The estimated jamming signal is then subtracted from the received data to remove the jammer signal. To cope with the time-varying accuracy in the jammer parameter estimates, the methods for adaptively adjusting the process and measurement noise variances using chirp rate estimates are described. Simulations are performed to verify the effectiveness of the proposed method for mitigating various types of jammers. The proposed approach improves the jammer signal removal performance by minimizing the effect of the Kalman filter model mismatch when compared to other techniques reported in the literature.

Local AM/FM Parameters Estimation: Application to Sinusoidal Modeling and Blind Audio Source Separation

This letter extends our recently introduced method which was designed to estimate instantaneous frequency and chirp rate of linearly modulated signals. Indeed, we derive several new estimators related to our previous ones which provide in the time-frequency plane all the signal parameters of the investigated model: amplitude, frequency, and their local modulations (AM/FM). Our estimators are first introduced and compared in terms of statistical efficiency with theoretical bounds and with other state-of-the-art estimators. Then, they are used to improve spectral analysis applied to audio sinusoidal modeling. Finally, they lead to a new source separation technique based on coherent amplitude and frequency modulation that is evaluated on real-world music signals.

Direct Instantaneous Frequency Rate Estimation to Improve the Carrier Estimation Performance in Mars Entry, Descent, and Landing Flight

This paper focuses on the carrier estimation performance improvement in Mars entry, descent, and landing (EDL) flights. Carrier reconstruction could be used for trajectory derivation and Martian atmosphere profile inversion, and is the critical information for mission operations, as it helps determine the flight status of the spacecraft, demodulate the downlink information. The current approach is maximum likelihood estimation based on a two-dimensional (2D) maximum energy search algorithm, which computes the grid energy over all the combinations of frequency cells and frequency rate cells among the search space. Although it has good performance on robust estimation, the frequency estimation accuracy is limited due to the short coherent integration. An instantaneous frequency rate tracking approach based on the cubic phase function (CPF) is proposed that directly estimates the instantaneous frequency rate over the frequency rate cells, followed by the frequency estimation among the frequency cells. A sequential estimation method is introduced to propose the sequential CPF statistics, which uses the a priori Doppler phase information to suppress the noise squaring loss inherent in the standard CPF statistics. Simulations have been made on the released Mars Science Laboratory EDL trajectory for the two approaches, which show that considerable estimation improvement has been achieved for aerobraking flight by the new algorithm.

A fast time-frequency multi-window analysis using a tuning directional kernel

In this paper, a novel approach for time-frequency analysis and detection, based on the chirplet transform and dedicated to non-stationary as well as multi-component signals, is presented. Its main purpose is the estimation of spectral energy, instantaneous frequency (IF), spectral delay (SD), and chirp rate (CR) with a high time-frequency resolution (separation ability) achieved by adaptive fitting of the transform kernel. We propose two efficient implementations of this idea, which allow to use the fast Fourier transform (FFT). In the first one, referred to as “self-tuning”, a previously proposed CR estimation is used for a local fitting of the chirplet kernel over time. For this purpose, we use the CR associated with the dominant (prominent) component. In the second one, we define a new measure for evaluating at each time-frequency point, how the used analyzing window is matched to the signal. This measure is defined as the absolute difference between the estimated CR and the CR parameter associated to the used analysis window. Our method is able to produce combined time-frequency distributions of the spectral energy, IF, SD, and CR. They are obtained using several classical chirplet transforms with analysis windows of various CRs. The compositions are made by finding the lowest fitting measure for every time-frequency points over all transforms. Finally, we assess the robustness of the methods by a detection application and time-frequency localization, both in the presence of high additive white Gaussian noise (additive white Gaussian noise (AWGN)) as well as we present many time-frequency (TF) images of synthetic and real-world signals.

Autonomous radar pulse modulation classification using modulation components analysis

An autonomous method for recognizing radar pulse modulations based on modulation components analysis is introduced in this paper. Unlike the conventional automatic modulation classification methods which extract modulation features based on a list of known patterns, this proposed method classifies modulations by the existence of basic modulation components including continuous frequency modulations, discrete frequency codes and discrete phase codes in an autonomous way. A feasible way to realize this method is using the features of abrupt changes in the instantaneous frequency rate curve which derived by the short-term general representation of phase derivative. This method is suitable not only for the basic radar modulations but also for complicated and hybrid modulations. The theoretical result and two experiments demonstrate the effectiveness of the proposed method.

The instantaneous frequency rate spectrogram

An accelerogram of the instantaneous phase of signal components referred to as an instantaneous frequency rate spectrogram (IFRS) is presented as a joint time-frequency distribution. The distribution is directly obtained by processing the short-time Fourier transform (STFT) locally. A novel approach to amplitude demodulation based upon the reassignment method is introduced as a useful by-product. Additionally, an estimator of energy density versus the instantaneous frequency rate (IFR) is proposed and referred to as the IFR profile. The energy density is estimated based upon both the classical energy spectrogram and the IFRS smoothened by the median filter. Moreover, the impact of an analyzing window width, additive white Gaussian noise and observation time is tested. Finally, the introduced method is used for the analysis of the acoustic emission of an automotive engine. The recording of the engine of a Lamborghini Gallardo is analyzed as an example.

A self-consistent model for the saturation dynamics of the vortex shedding around the mean flow in the unstable cylinder wake

The supercritical instability leading to the Bénard-von Karman vortex street in a cylinder wake is a well known example of supercritical Hopf bifurcation: the steady solution becomes linearly unstable and saturates into a periodic limit cycle. Nonetheless, a simplified physical formulation accurately predicting the transition dynamics of the saturation process is lacking. Building upon our previous work, we present here a simple self-consistent model that provides a clear description of the saturation mechanism in a quasi-steady manner by means of coupling the instantaneous mean flow with its most unstable eigenmode and its instantaneous amplitude through the Reynolds stress. The system is coupled for different oscillation amplitudes, providing an instantaneous mean flow as function of an equivalent time. A transient physical picture is described, wherein a harmonic perturbation grows and changes in amplitude, frequency, and structure due to the modification of the mean flow by the Reynolds stress forcing, saturating when the flow is marginally stable. Comparisons with direct numerical simulations show an accurate prediction of the instantaneous amplitude, frequency, and growth rate, as well as the saturated mean flow, the oscillation amplitude, frequency, and the resulting mean Reynolds stresses.

Time-Domain Joint Parameter Estimation of Chirp Signal Based on SVR

Parameter estimation of chirp signal, such as instantaneous frequency (IF), instantaneous frequency rate (IFR), and initial phase (IP), arises in many applications of signal processing. During the phase-based parameter estimation, a phase unwrapping process is needed to recover the phase information correctly and impact the estimation performance remarkably. Therefore, we introduce support vector regression (SVR) to predict the variation trend of instantaneous phase and unwrap phases efficiently. Even though with that being the case, errors still exist in phase unwrapping process because of its ambiguous phase characteristic. Furthermore, we propose an SVR-based joint estimation algorithm and make it immune to these error phases by means of setting the SVR's parameters properly. Our results show that, compared with the other three algorithms of chirp signal, not only does the proposed one maintain quality capabilities at low frequencies, but also improves accuracy at high frequencies and decreases the impact with the initial phase.

A New Estimation Method of Instantaneous Frequency Rate for Multicomponent Polynomial Phase Signal

该文在分数阶傅里叶(FRFT)计算分解的基础上，讨论了其某些步骤在信号检测中的冗余，提出了一种简化的分数阶傅里叶算法(RFRFT)，详细讨论了它的几种重要性质，并结合一次相位差分法提出了乘积性RFRFT(PRFRFT)算法，实现了mc-PPS的瞬时频率变化率(IFR)估计。同时借助角度变换提高了RFRFT识别参数的分辨率。该方法运算量小，易于实现。仿真结果证实了该方法能够有效地抑制噪声和交叉项，可以适应低信噪比环境。

An adaptive Generalized S-transform for instantaneous frequency estimation

The Generalized S-transform (GST) applied in Instantaneous Frequency (IF) estimation is addressed in this paper. The analytical model for IF estimation error using the GST is established, which reveals that the estimation bias is determined directly by two variables: the standard deviation of the Gaussian window and the Instantaneous Frequency Rate (IFR) of the test signal. Based on the mathematical model, performance of the GST as an IF estimator is analyzed by three steps. Firstly, the time-varying expression for IF estimation Relative Error (RE) using the GST is derived. Secondly, the relationships between the RE and the signal’s frequency characters are found. Thirdly, the effects of the window parameters on the RE are discussed. Consequently, a novel Adaptive Generalized S-transform (AGST) is developed, in which the window parameters are automatically adjusted in order to process signals with fast changing frequency characters. The proposed method is evaluated through several kinds of test signals to show its efficiency in IF estimation.

Instantaneous frequency rate estimation of multi-component LMF signals based on LPFT

Instantaneous frequency rate estimation of multi-component LMF signals based on LPFT

Time-frequency rate distributions with complex-lag argument

A general form of the Nth order complex-lag time-frequency rate distribution is proposed. A few interesting special cases are considered and analysed. The proposed approach can arbitrarily reduce the spread factor. Hence, it provides a high concentration even for signals with fast varying instantaneous frequency rate.

Performance of Instantaneous Frequency Rate Estimation Using High-Order Phase Function

<para xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> The high-order phase function (HPF) is a useful tool to estimate the instantaneous frequency rate (IFR) of a signal with a polynomial phase. In this paper, the asymptotic bias and variance of the IFR estimate using the HPF are derived in closed-forms for the polynomial phase signal with an arbitrary order. The Cramér-Rao bounds (CRBs) for IFR estimation, in both exact and asymptotic forms, are obtained and compared with the asymptotic mean-square error (MSE) of the HPF-based IFR estimator. Simulations are provided to verify our theoretical results. </para>

Instantaneous Frequency Rate Estimation for High-Order Polynomial-Phase Signals

Instantaneous frequency rate (IFR) estimation for high-order polynomial phase signals (PPSs) is considered. Specifically, an IFR estimator with only a second-order nonlinearity is proposed. The asymptotic mean-squared error (MSE) of the proposed IFR estimator is obtained via a multivariate first-order perturbation analysis. Our results show that the proposed estimator yields a smaller MSE and a lower signal-to-noise ratio (SNR) threshold than a popular IFR estimator involving higher nonlinearity. The proposed IFR estimator is also extended to estimate the phase parameters of a PPS. Numerical studies are presented to illustrate the performance of the proposed estimator.

A new technique for instantaneous frequency rate estimation

This letter introduces a two-dimensional bilinear mapping operator referred to as the cubic phase (CP) function. For first-, second-, or third-order polynomial phase signals, the energy of the CP function is concentrated along the frequency rate law of the signal. The function, thus, has an interpretation as a time-frequency rate representation. The peaks of the CP function yield unbiased estimates of the instantaneous (angular) frequency rate (IFR) and, hence, can be used as the basis for an IFR estimation algorithm. The letter defines an IFR estimation algorithm and theoretically analyzes it. The estimation is seen to be asymptotically optimal at the center of the data record for high signal-to-noise ratios. Simulations are provided to verify the theoretical claims.