Nonlinear Frequency Modulated Signals Research Articles

Design of a High-Power Nanosecond Electromagnetic Pulse Radiation System for Verifying Spaceborne Detectors

The Spaceborne Global Lightning Location Network (SGLLN) serves the purpose of identifying transient lightning events occurring beneath the ionosphere, playing a significant role in detecting and warning of disaster weather events. To ensure the effective functioning of the wideband electromagnetic pulse detector, which is a crucial component of the SGLLN, it must be tested and verified with specific signals. However, the inherent randomness and unpredictability of lightning occurrences pose challenges to this requirement. Consequently, a high-power electromagnetic pulse radiation system with a 20 m aperture reflector is designed. This system is capable of emitting nanosecond electromagnetic pulse signals under pre-set spatial and temporal conditions, providing a controlled environment for assessing the detection capabilities of SGLLN. In the design phase, an exponentially TEM feed antenna has been designed firstly based on the principle of high-gain radiation. The feed antenna adopts a pulser-integrated design to mitigate insulation risks, and it is equipped with an asymmetric protective loading to reduce reflected energy by 85.7%. Moreover, an innovative assessment method for gain loss, based on the principle of Love’s equivalence, is proposed to quantify the impact of feed antenna on the radiation field. During the experimental phase, a specialized E-field sensor is used in the far-field experiment at a distance of 400 m. The measurements indicate that at this distance, the signal has a peak field strength of 2.2 kV/m, a rise time of 1.9 ns, and a pulse half-width of 2.5 ns. Additionally, the beamwidth in the time domain is less than 10°. At an altitude of 500 km, the spaceborne detector records a signal with a peak field strength of approximately 10 mV/m. Particularly, this signal transformed into a nonlinear frequency-modulated signal in the microsecond range across its frequency spectrum, which is consistent with the law of radio wave propagation in the ionosphere. This study offers a stable and robust radiation source for verifying spaceborne detectors and establishes an empirical foundation for investigating the impact of the ionosphere on signal propagation characteristics.

Separation of signal and harmonics in non-explosive seismic prospecting with amplitude and nonlinear frequency-modulated signals

When vibroseis oscillations are excited, along with the main signal, harmonics are generated. They travel into the Earth and, like the main signal, interact with the target reflectors. Harmonics have a wider than that of the main signal frequency band, so they can be used to increase the resolution of the seismic data. To do this, the signal-related data should be separated from the harmonic-related data. This problem can be successfully solved by the previously proposed optimization recursive filtering algorithm, which, however, was developed only for linearly frequency-modulated signals. In this work, the algorithm is generalized to the case of amplitude modulation and nonlinear frequency modulation. Examples of application of the technique to increase the resolution of real vibroseis data are given.

Modeling of harmonics of amplitude and nonlinear frequency-modulated signals

In vibroseismic data, nonlinear signal distortions called harmonics are usually present. The previously proposed method of separating the signal and its harmonics makes it possible to improve the quality of the initial data, as well as to obtain additional information about the geological structure of the earth interior. One of the limitations of the proposed methodology is its initial development for linear frequency-modulated signals. A new method of prediction of harmonics that allows non-linear frequency modulation as well as amplitude variation is proposed.

Optimal compactness of fractional Fourier domain characterizes frequency modulated signals

The Fourier transform (FT) is a mathematical tool widely used in signal processing applications; however, it presents limitations when dealing with non-stationary time series. By considering the fractional powers of the FT operator, a generalized version is obtained known as the fractional FT. This transformation allows free rotations of the time–frequency plane that can be exploited for processing frequency modulated signals. This work addresses the problem of characterizing noisy, multicomponent, and non-linear frequency modulated signals through a proper order of the fractional FT, whose kernel consists of a chirp with linear frequency modulation. The estimation of the optimal fractional FT order obeys a strategy that includes the quantification of the compactness of fractional Fourier domains and the search for the order that leads to the most compact domain. For this purpose, five compactness measures are assessed in combination with four different optimization algorithms. Numerical experiments are performed on synthetic signals, generated under distinct frequency modulation conditions, and on real acoustic signals. The results reveal that the spectral second moment and the spectral entropy provide robust and reliable measures of the compactness of the fractional Fourier domain. These metrics enable an effective computation of the optimal fractional order that describes the frequency modulation content of the underlying signal. The optimization algorithms assessed in this study yield similar estimations of the optimal fractional order, yet the coarse-to-fine algorithm is more efficient in terms of computation time, followed by the particle swarm optimization algorithm. Moreover, it is verified that the strategy can be adopted for extracting dynamical information of the frequency modulation content from synthetic signals with multiple linear and non-linear components and from real acoustic data, e.g., bat and bird recordings. The extensive assessment of the signal processing strategy based on the fractional FT outlined in this work provides relevant information for exploring further applications with time series captured when studying complex and non-stationary processes, such as biological, medical, or economic systems.

Effective reduction of sidelobes in pulse compression radars using NLFM signal processing approaches

Pulse compression techniques are widely used in modern radar systems to enhance range resolution and detection capability. As signal design is one of the basic factors of an efficient radar system, the problem of designing a radar signal with good characteristics using pulse compression is addressed in this paper. A linear frequency modulated (LFM) waveform has been widely used for conventional radars. However, it has a higher sidelobe level which makes the detection of weak targets very difficult in presence of strong targets returns and as a result the problem of masking occurs. In order to get suppressed sidelobes of radar matched filter output as well as preserve the main lobe resolution and level to overcome the problem of masking, nonlinear frequency modulated (NLFM) signals are used in modern radars. In this paper, we will introduce two different approaches to design an optimized NLFM signal which is characterized by optimized sidelobe level (SLL). The first is the exponential piecewise linear function (EPWL) which is the modification of piecewise linear (PWL) functions relying on an exponential predistortioning function. The second is the odd-term polynomial approximation (OTPA) in which the generation of NLFM signal depends only on odd-powered terms of the polynomial function. Furthermore, the simulation results of autocorrelation functions (ACF) of the proposed signals show its superiority over the traditional LFM signals and significantly enhancement compared to the recent background work. The Doppler sensitivity of the designed signals has been evaluated, revealing that the first approach offers Doppler tolerance and is suitable for surveillance radar systems, while the second approach with a lower sidelobe level is used in applications such as Synthetic Aperture Radar (SAR). Finally, the ambiguity function of the designed signals has been measured to illustrate the effect of the Doppler effect relative to different velocities.

Smart Jamming Against SAR Based on Nonlinear Frequency-Modulated Signal

The traditional methods of jamming against synthetic aperture radar (SAR), which are implemented based on linear frequency-modulated (LFM) signals, are currently unable to meet the needs of electronic countermeasures. Compared with the LFM signal, the frequency of the nonlinear frequency-modulated (NLFM) signal varies nonlinearly with time. Because of this time-frequency structure, the NLFM signal is naturally mismatched with the linear matched filter of SAR; thus, a stronger and more flexible jamming effect is produced. In this paper, the NLFM signal is used in the SAR jamming field for the first time, and a smart jamming method against SAR based on the NLFM signal is proposed, which can produce the following two jamming effects: barrage and deceptive. First, the shaping factor is defined to generate the expected NLFM signal. The shaping factor controls the jamming range in the fast time direction for barrage jamming. For deceptive jamming, a jamming method involving piecewise weighting is proposed. The shaping factor is used to control the defocusing degree of false targets. Subsequently, the pulse compression results of the jamming signal are deduced, and the influence of different parameters on the jamming effect is theoretically analyzed. Experimental results based on simulation show that the method can control the jamming range and effect in the fast time direction while achieving a flexible deceptive jamming effect.

A Novel MIMO-SAR Echo Separation Solution for Reducing the System Complexity: Spectrum Preprocessing and Segment Synthesis

The problem of echo separation using digital beamforming (DBF) on receive for multiple-input multiple-output (MIMO) synthetic aperture radar (SAR) is of notable importance to allow for practical systems. Regrettably, current DBF-MIMO-SAR schemes, such as the short-term shift-orthogonal (STSO) scheme, are computationally cumbersome, increasing the required hardware complexity. To alleviate this problem, we here propose an improved echo separation solution for realizing a low-cost MIMO-SAR system. We detail a generic waveform design scheme as well as optimized monostatic radar waveforms (e.g., nonlinear frequency modulation (NLFM) signal) showing how these can be directly adopted in the proposed scheme to improve the imaging performance. The proposed scheme enables the number of the interference segments generated by unmatched waveforms to be halved by the use of the fast time spectrum preprocessing and segment synthesis, dramatically simplifying the array configuration and reduces the system complexity. By exploiting inter-pulse phase coding techniques, the proposed method can provide a reconfigurable waveform transmitting scheme, allowing the system resources in range frequency, elevation space, and Doppler domains to be jointly exploited for the separation of aliased signal returns. The proposed scheme is evaluated using extensive numerical and measured data sets, demonstrating the feasibility and potential of the proposed method for resource-limited spaceborne/airborne MIMO-SAR systems.

Peak Side Lobe Reduction analysis of NLFM and Improved NLFM Radar signal

Signal design is an important component for good performance of radar systems. Here, the problem of determining a good radar signal with the objective of minimizing autocorrelation sidelobes is addressed. Linear Frequency Modulated signal (LFM) is frequently used pulse compression waveform. But using LFM makes it necessary to use weighting techniques in order to reduce the side lobes which considerably decrease the SNR. At the radar receiver, the LFM signal results in first side lobe of -13dB corresponding to the main lobe. This may reduce the resultant SNR usually by 1 or 2dB. In this paper, an attempt is done to design a radar signal to attain low autocorrelation Peak Side Lobe Ratio (PSLR) which exhibits high SNR and high range resolution. In order to maintain high SNR and to get suppressed side lobes of the signal, one can use Non-Linear Frequency Modulation (NLFM). A NLFM signal is designed for different time sweeps called as Improved NLFM. In Improved NLFM the total time sweep and bandwidth are divided into Two Stage and Tri-Stage sweeps NLFM. The quality of the overall best radar signal is assessed through the parameter PSLR for different values of BT. From this analysis, it is found that the tri stage NLFM gives the low PSLR up to -17.62dB. Simulation results shows the reduction in the sidelobe level from LFM to NLFM and in Improved two and Tri-Stage NLFM.

Nonlinear Frequency-Modulated Waveforms Modeling and Optimization for Radar Applications

Conventional radars commonly use a linear frequency-modulated (LFM) waveform as the transmitted signal. The LFM radar is a simple system, but its impulse-response function produces a −13.25 dB sidelobe, which in turn can make the detection of weak targets difficult by drowning out adjacent weak target information with the sidelobe of a strong target. To overcome this challenge, this paper presents a modeling and optimization method for non-linear frequency-modulated (NLFM) waveforms. Firstly, the time-frequency relationship model of the NLFM signal was combined by using the Legendre polynomial. Next, the signal was optimized by using a bio-inspired method, known as the Firefly algorithm. Finally, the numerical results show that the advantages of the proposed NLFM waveform include high resolution and high sensitivity, as well as ultra-low sidelobes without the loss of the signal-to-noise ratio (SNR). To the authors’ knowledge, this is the first study to use NLFM signals for target-velocity improvement measurements. Importantly, the results show that mitigating the sidelobe of the radar waveform can significantly improve the accuracy of the velocity measurements.

Estimation and Classification of NLFM Signals Based on the Time-Chirp Representation.

A new approach to the estimation and classification of nonlinear frequency modulated (NLFM) signals is presented in the paper. These problems are crucial in electronic reconnaissance systems whose role is to indicate what signals are being received and recognized by the intercepting receiver. NLFM signals offer a variety of useful properties not available for signals with linear frequency modulation (LFM). In particular, NLFM signals can ensure the desired reduction of sidelobes of an autocorrelation (AC) function and desired power spectral density (PSD); therefore, such signals are more frequently used in modern radar and echolocation systems. Due to their nonlinear properties, the discussed signals are difficult to recognize and therefore require sophisticated methods of analysis, estimation and classification. NLFM signals with frequency content varying with time are mainly analyzed by time-frequency algorithms. However, the methods presented in the paper belong to time-chirp domain, which is relatively rarely cited in the literature. It is proposed to use polynomial approximations of nonlinear frequency and phase functions describing signals. This allows for applying the cubic phase function (CPF) as an estimator of phase polynomial coefficients. Originally, the CPF involved only third-order nonlinearities of the phase function. The extension of the CPF using nonuniform sampling is used to analyse the higher order polynomial phase. In this paper, a sixth order polynomial is considered. It is proposed to estimate the instantaneous frequency using a polynomial with coefficients calculated from the coefficients of the phase polynomial obtained by CPF. The determined coefficients also constitute the set of distinctive features for a classification task. The proposed CPF-based classification method was examined for three common NLFM signals and one LFM signal. Two types of neural network classifiers: learning vector quantization (LVQ) and multilayer perceptron (MLP) are considered for such defined classification problem. The performance of both the estimation and classification processes was analyzed using Monte Carlo simulation studies for different SNRs. The results of the simulation research revealed good estimation performance and error-free classification for the SNR range encountered in practical applications.

Power-Independent Microwave Instantaneous Frequency Measurement Based on Combination of Brillouin Gain and Loss Spectra

Photonics-assisted microwave instantaneous frequency measurement (IFM) is considered as a promising technique for detecting an unknown radio-frequency (RF) signal, which has advantages of broad frequency measurement range and fast processing speed. Up to date, there is no photonics-assisted IFM system that can essentially measure an unknown RF signal time-frequency information with power fluctuating seriously. Moreover, the measurement accuracy and frequency modulation recognition are not as good as those of traditional electronic methods. Here, we propose an IFM scheme based on the combination of Brillouin gain spectrum (BGS) and Brillouin loss spectrum (BLS), which is RF-power-independent with high measurement efficiency. The combination of BGS and BLS to construct the amplitude comparison function (ACF) can reduce the influence of RF signal power fluctuation within 21.27 dB by single-shot measuring. When an appropriate frequency interval with frequency domain monotonous power of microwave comb signal is modulated on the pump lightwave, the IFM accuracy of the unknown signal reaches about 1 MHz. After the initial calibration of the system, it can recognize the time-frequency variation of single tone signal, linear frequency modulated signal (LFM), nonlinear frequency modulated signal (NLFM), and Costas signal. This scheme will help to promote the application of the IFM in the field of spectrum reconnaissance and reception.

Vibrational resonance by using a real-time scale transformation method

Vibrational resonance (VR) shows great advantages in signal enhancement. Nonlinear frequency modulated (NLFM) signals widely exist in various fields, so it is of great significance to enhance a NLFM signal. However, for the complex NLFM signal, where its instantaneous frequency of the signal varies nonlinearly, the traditional VR method is no longer applicable. To solve this problem, a rescaled VR method by a real-time scale transformation method is proposed. Its basic principle is to use the real-time scale coefficient and auxiliary signal parameters to match a NLFM signal in a nonlinear system. The corresponding numerical simulation is carried out to process three kinds of typical NLFM signals. The results manifest the excellent performance of the proposed method for the signal enhancement of NLFM signals. The method can process NLFM signals with an arbitrary frequency variation. Consequently, it has certain theoretical and practical values in some fields.

Instantaneous Frequency Estimation of Nonlinear FM Radar Signal Based on Multi-Scale Chirplet Path

Instantaneous frequency is an important parameter to non-linear frequency modulated (NLFM) signal in low probability intercept (LPI) radar. For electronic intelligence, it is very important to accurately estimate instantaneous frequency of NLFM signal. A multi-scale chirplet path pursuit (MCPP) method and its improved method are proposed for electronic intelligence systems to estimate instantaneous frequency of NLFM radar signal in this paper. Firstly, signal duration is divided into a set of dynamic time interval, multi-scale chirplet basis function is established on each time interval simultaneously. And then, projection coefficient in each dynamic interval is calculated basing on chirplet basis functions. And then, chirplet basis functions which have the largest projection coefficient with the analysis signal in each time interval are connected by path pursuit algorithm. Rough estimation of instantaneous frequency will be achieved by connecting the linear frequency of those chirplet basis functions. At last, to solve the problem that instantaneous frequency curve is not smooth for the impact of noise and chirplet errors, least square fitting method is used to further improve estimation accuracy. Experimental results show that, proposed improved MCPP algorithm is suitable for the instantaneous frequency of the NLFM radar signal at low SNR. Compared with time-frequency analysis method, it has higher estimation accuracy. Proposed method can also be applied to the instantaneous frequencies estimation of other NLFM signal without prior knowledge, such as seismic signals and fault diagnosis signals.

Optimal resonance response of nonlinear system excited by nonlinear frequency modulation signal

Nonlinear frequency modulation (NLFM) signal is widely used in radar, communication and signal processing. The response of nonlinear system excited by this kind of signal has rich information. At the same time, enhancing different types of signals by resonance phenomenon has unique advantages in the field of signal processing. Compared with other signal processing methods, such as empirical mode decomposition, variational mode decomposition, wavelet transform, signal filtering, etc., this kind of method can not only enhance the signal, but also effectively suppress the interference noise. Therefore, it has certain significance to study the nonlinear system optimal response excited by different NLFM signals and enhance the NLFM signal through resonance phenomenon. In this paper, what is mainly studied is the nonlinear system resonance phenomenon excited by different NLFM signals, which is different from in previous studies. Firstly, a real-time scale transformation method is proposed to process the NLFM signals, and its basic principle is to match different NLFM signals by real-time scale coefficients and system parameters. The signal frequency at each time corresponds to the coefficients with different scales and system parameters, thereby realizing the optimal resonance response at each time. In order to describe the optimal resonance response excited by the NLFM signal more accurately, unlike the traditional spectral amplification factor, the real-time spectral amplification factor is introduced as an evaluation index. Then, the influence of system parameters on the optimal system resonance response is discussed, and the optimal resonance region is obtained, which means that the optimal resonance response can be achieved by selecting the parameters in a reasonable range. This method not only greatly enhances the signal characteristics, but also maintains the continuity of signal time-frequency characteristics. Finally, the real-time scale transformation method is compared with the general scale transformation method, showing the superiority of the proposed method in processing NLFM signal. The method and the results of this paper show some potential in dealing with complex NLFM, which provides a reference for NLFM signal enhancement and detection, and has a certain practical significance in signal enhancement. Furthermore, the relevant influence law of the system optimal response excited by the NLFM signal is given, which has a certain reference value for studying the system dynamic behavior under different signal excitations.

An Extended Model of Ionospheric Dispersion Effects for Nonlinear Frequency Modulation Signal and Correction Method

Nonlinear frequency modulation (NLFM) signal can construct the signal’s power spectral density to reduce sidelobes without loss of signal-to-noise ratio. LuTan-1 (LT-1) is an L-band spaceborne synthetic aperture radar mission which is launched in the beginning of 2022, and a high-precision NLFM signal generator is developed in LT-1. However, the existing model, i.e., the traditional frozen ionosphere model, can not accurately describe ionospheric dispersion effects faced by the NLFM signal due to the non-linear characteristic of the instantaneous frequency. Thus, an extended model is established in this paper to describe ionospheric dispersion effects of the NLFM signal. Then, the differences of ionospheric dispersion effects on the NLFM and linear frequency modulation signals are compared. Afterwards, a method that embedded into the focusing procedure is proposed, which aims to eliminate ionospheric dispersion effects for the NLFM signal. Finally, the hardware-in-the-loop simulations of point targets and distributed targets are performed to verify the proposed method. The method proposed in this paper is used in the ground processing system of LT-1.

Structural Instantaneous Frequency Identification Based on the Fractional Fourier Transform

In order to identify the instantaneous frequency of time-varying signals, this paper derives the theoretical relationship between the frequency in a signal and rotational angle α in a fractional Fourier transform. It is demonstrated that the fractional Fourier transform is actually an algorithm of ordinary Fourier transform combined with telescopic translation window. A general expression of signal instantaneous frequency in the fractional Fourier domain is thereafter formulated so that structural instantaneous frequency can be extracted accordingly. The feasibility and reliability of proposed method is verified by a simulated nonlinear frequency modulation signal and a numerical example of a three-degree-of-freedom damped time-varying structure system. The results show that the proposed method is in good agreement with the theoretical values and the method has a certain degree of anti-noise capability. Subsequently, the proposed method is capable of identifying the instantaneous frequency of time-varying structures.

Low Correlation Interference OFDM-NLFM Waveform Design for MIMO Radar Based on Alternating Optimization.

The OFDM chirp signal is suitable for MIMO radar applications due to its large time-bandwidth product, constant time-domain, and almost constant frequency-domain modulus. Particularly, by introducing the time-frequency structure of the non-linear frequency modulation (NLFM) signal into the design of an OFDM chirp waveform, a new OFDM-NLFM waveform with low peak auto-correlation sidelobe ratio (PASR) and peak cross-correlation ratio (PCCR) is obtained. IN-OFDM is the OFDM-NLFM waveform set currently with the lowest PASR and PCCR. Here we construct the optimization model of the OFDM-NLFM waveform set with the objective function being the maximum of the PASR and PCCR. Further, this paper proposes an OFDM-NLFM waveform set design algorithm inspired by alternating optimization. We implement the proposed algorithm by the alternate execution of two sub-algorithms. First, we keep both the sub-chirp sequence code matrix and sub-chirp rate plus and minus (PM) code matrix unchanged and use the particle swarm optimization (PSO) algorithm to obtain the optimal parameters of the NLFM signal’s time-frequency structure (NLFM parameters). Next, we keep current optimal NLFM parameters unchanged, and optimize the sub-chirp sequence code matrix and sub-chirp rate PM code matrix using the block coordinate descent (BCD) algorithm. The above two sub-algorithms are alternately executed until the objective function converges to the optimal solution. The results show that the PASR and PCCR of the obtained OFDM-NLFM waveform set are about 5 dB lower than that of the IN-OFDM.

Millimeter-level resolution through-the-wall radar imaging enabled by an optically injected semiconductor laser.

Millimeter-level resolution through-the-wall radar (TWR) imaging is demonstrated using a broadband nonlinear frequency-modulated (NLFM) signal that is generated by an optically injected semiconductor laser. The proposed system uses period-one dynamics of a semiconductor laser, together with an optical frequency downconversion technique to generate NLFM signals, which addresses the problem of traditional period-one oscillation not being able to generate broadband signals in the low-frequency region. In the experiment, an NLFM signal having a broad bandwidth of 18.5 GHz (1.5-20 GHz) is generated with a corresponding radar range resolution of 8.1 mm. Using this signal, TWR imaging is demonstrated, in which the use of the NLFM signal achieves good side-lobe suppression during pulse compression, and a modified back projection imaging algorithm with sub-aperture weighting is proposed to improve the imaging quality.

Staring Spotlight SAR with Nonlinear Frequency Modulation Signal and Azimuth Non-Uniform Sampling for Low Sidelobe Imaging

In synthetic aperture radar (SAR) imaging, geometric resolution, sidelobe level (SLL) and signal-to-noise ratio (SNR) are the most important parameters for measuring the SAR image quality. The staring spotlight mode continuously transmits signals to a fixed area by steering the azimuth beam to acquire azimuth high geometric resolution, and its two-dimensional (2D) impulse response with the low SLL is usually obtained from the 2D weighted power spectral density (PSD) by the selected weighting window function. However, this results in the SNR reduction due to 2D amplitude window weighting. In this paper, the staring spotlight SAR with nonlinear frequency modulation (NLFM) signal and azimuth non-uniform sampling (ANUS) is proposed to obtain high geometric resolution SAR images with the low SLL and almost without any SNR reduction. The NLFM signal obtains non-equal interval frequency sampling points under uniform time sampling by adjusting the instantaneous chirp rate. Its corresponding PSD is similar to the weighting window function, and its pulse compression result without amplitude window weighting has low sidelobes. To obtain a similar Doppler frequency distribution for low sidelobe imaging in azimuth, the received SAR echoes are designed to be non-uniformly sampled in azimuth, in which the sampling sequence is dense in middle and sparse in both ends, and azimuth compression result with window weighting would also have low sidelobes. According to the echo model of the proposed imaging mode, both the back projection algorithm (BPA) and range migration algorithm (RMA) are modified and presented to handle the raw data of the proposed imaging mode. Both imaging results on simulated targets and experimental real SAR data processing results of a ground-based radar validate the proposed low sidelobe imaging mode.

Roll angular rate extraction based on modified spline-kernelled chirplet transform

The roll angular rate is much crucial for the guidance and control of the projectile. Yet the high-speed rotation of the projectile brings severe challenges to the direct measurement of the roll angular rate. Nevertheless, the radial magnetometer signal is modulated by the high-speed rotation, thus the roll angular rate can be achieved by extracting the instantaneous frequency of the radial magnetometer signal. The objective of this study is to find out a precise instantaneous frequency extraction method to obtain an accurate roll angular rate. To reach this goal, a modified spline-kernelled chirplet transform (MSCT) algorithm is proposed in this paper. Due to the nonlinear frequency modulation characteristics of the radial magnetometer signal, the existing time-frequency analysis methods in literature cannot obtain an excellent energy concentration in the time-frequency plane, thereby leading to a terrible instantaneous frequency extraction accuracy. However, the MSCT can overcome the problem of bad energy concentration by replacing the short-time Fourier transform operator with the Chirp Z-transform operator based on the original spline-kernelled chirplet transform. The introduction of Chirp Z-transform can improve the construction accuracy of the transform kernel. Since the construction accuracy of the transform kernel determines the concentration of time-frequency distribution, the MSCT can obtain a more precise instantaneous frequency. The performance of the MSCT was evaluated by a series of numerical simulations, high-speed turntable experiments, and real flight tests. The evaluation results show that the MSCT has an excellent ability to process the nonlinear frequency modulation signal, and can accurately extract the roll angular rate for the high spinning projectiles.