Nonlinear Chirp Signal Research Articles

Adaptive sparse estimation of nonlinear chirp signals using Laplace priors.

The identification of nonlinear chirp signals has attracted notable attention in the recent literature, including estimators such as the variational mode decomposition and the nonlinear chirp mode estimator. However, most presented methods fail to process signals with close frequency intervals or depend on user-determined parameters that are often non-trivial to select optimally. In this work, we propose a fully adaptive method, termed the adaptive nonlinear chirp mode estimation. The method decomposes a combined nonlinear chirp signal into its principal modes, accurately representing each mode's time-frequency representation simultaneously. Exploiting the sparsity of the instantaneous amplitudes, the proposed method can produce estimates that are smooth in the sense of being piecewise linear. Furthermore, we analyze the decomposition problem from a Bayesian perspective, using hierarchical Laplace priors to form an efficient implementation, allowing for a fully automatic parameter selection. Numerical simulations and experimental data analysis show the effectiveness and advantages of the proposed method. Notably, the algorithm is found to yield reliable estimates even when encountering signals with crossed modes. The method's practical potential is illustrated on a whale whistle signal.

Photonic time-frequency filter based on the software-defined time-frequency prism.

We propose a microwave photonic 2D time-frequency filter based on a photonic time-frequency prism. A time-varying frequency response is realized by deviating the passband of a 1D ordinary frequency filter in the 2D time-frequency plane. The proposed time-frequency filter features highly reconfigurable frequency-sweeping speed and bandwidth, thanks to the software-defined photonic time-frequency prism. With the proposed technique, separation of multiple linear and nonlinear chirp signals with overlapped spectra is experimentally demonstrated.

Direction Finding for Multiple Wideband Chirp Signal Sources using Blind Signal Separation and Matched Filtering

This paper proposes a new scheme to estimate the direction-of-arrival (DOA) of multiple wideband chirp signals. The proposed scheme comprises three steps: 1) preprocessing of the mixed signal using independent component analysis in order to obtain each wideband chirp signal; 2) matched filtering in order to transform the multiple wideband chirp signals into narrowband signals; and 3) the estimation of final DOAs using the conventional subspace-based method. In order to validate the effectiveness of the proposed scheme, we carried out extensive experiments, including three different scenarios: non-overlapped in the frequency domain, overlapped in the frequency domain, and nonlinear chirp signal cases. From the experimental results, we can conclude that the proposed scheme provides not only accurate results in terms of root-mean-squared error (RMSE), but also the lowest computational complexity compared to the previous methods.

Separation of Phase-Corrupted Multicomponent Nonlinear Chirp Signal

Multi-component nonlinear chirp signals (NCSs) widely exist in microwave remote sensing. In some applications, it is necessary to separate NCSs containing close components in the time-frequency (TF) domain. However, the phase-corrupted data may cause a defocused TF signature and prevent individual component extraction. To solve the problem, the optimization model is developed to reconstruct and decompose multi-component NCSs with phase errors and solved by an alternating iterative algorithm. In each iteration, the individual components, phase errors, and the regularization parameter are updated by the alternating direction method of multipliers, least-square-error criterion, and the matching pursuit principle, respectively. Finally, the effectiveness of the proposed method is verified by simulation and real data examples.

Photonics-Assisted Multi-Band Dual Linear/Nonlinear Chirp Waveform Generation Based on Optical Phase Modulation

A novel photonic scheme for generating multi-band dual-chirp waveforms with linear or nonlinear chirp rates is proposed via two cascaded polarization modulators (PolMs) paralleled with a phase modulator (PM). The cascaded PolMs produce a flat optical frequency comb (OFC) as a multi-frequency reference light, while the PM is driven by the power-function-type baseband signals to obtain the lightwave with different order phase chirp. The phase-chirped lightwave and the multi-frequency reference lightwave are orthogonally coupled by a polarization beam combiner (PBC) and then recombined via a polarization beam splitter (PBS) to make them in-phase in one output port of the PBS and anti-phase in the other. The two recombined lightwaves are detected by a balanced photodetector (BPD), and the different order dual-chirp signals, covering six bands, can be generated in their differential photocurrent without interference components. Compared with the single-chirp signal of the knife-edge-type ambiguity function, the dual-chirp signal with the peak-saliency-type ambiguity function significantly suppresses sidelobe and shows better range-Doppler resolution performance. With the 1GHz-bandwidth and 102.4ns-duration quadratic baseband driving signal, six-band linear dual-chirp signal, centered at 10, 30, 50, 70, 90 and 110GHz, are generated by simulation, and each linear dual-chirp signal has a bandwidth of 4.1GHz, the pulse compression ratio of 465.45 and the peak-to-sidelobe ratio (PSLR) of 12.8dB. As baseband driving signal has higher (3rd) order power, the six-band nonlinear dual-chirp signals with the same central frequencies can also be generated but with increased bandwidth (6.3GHz) and the improved PSLR (15.51dB). Their autocorrelation functions show that compared with the linear chirp signal, the nonlinear chirp signal has better sidelobe suppression capability, which is improve as the degree of nonlinearity increase.

Comparison of optimisation strategies for the improvement of depth detection capability of Pulse-Compression Thermography

ABSTRACT In Pulse-Compression Thermography, the impulse response of the Sample Under Test is retrieved pixelwise by applying a proper matched filter on the set of acquired thermal images obtained by stimulating the system with a heat source amplitude – modulated by a proper coded signal. Linear frequency-modulated chirp signals and binary codes are the most employed coded excitations, and to improve the detection capability of the technique, a non-linear frequency-modulated chirp signal can be used to deliver more energy to the sample in a frequency range of interest. In this work, we report the application of an exponential chirp to modulate the heating source and we compare it with a standard linear chirp excitation. To do a fair comparison, various windowing functions have been applied on the matched filters to reduce range side lobes, thus enhancing the retrieved impulse response quality. It is shown that the combined use of an exponential chirp and an appropriate matched filter obtained by exploiting the Reactance Transform window provides a faithful reconstruction of the sample impulse response and an enhanced signal-to-noise ratio with respect to the use of linear chirp. This has been demonstrated on a 3D-printed polymethyl methacrylate (PMMA) sample containing 16 flat-bottom holes of different depths.

Modified PWNLFM Signal for Side-Lobe Reduction

Many applications in radar systems require low range side-lobe performance which is achieved by pulse compression processing. Most used chirp signal for this processing is linear frequency modulation (LFM) signal but with a presence of first high side-lobe level. Suppression of this side-lobe requires weighting function causing the reduction in signal to noise ratio at the receiver owing to mismatch loss. Non-linear chirp signals are introduced as a solution and became most practiced signals aimed at reducing side-lobes. In this paper, an overall piece wise non-linear frequency modulation chirp signal is designed by merging two stages, one with linear function and the other with a tangent based non-linear function. Simulation results show significant reduction in the sidelobe level of autocorrelation function when NLFM is generated in this method.

Comparative study between linear and non-linear frequency-modulated pulse-compression thermography.

Pulse-compression thermography is an emerging non-destructive technique whose effectiveness strictly depends on the choice of the coded excitations used to modulate the heating stimulus. In this paper, the features of frequency-modulated coded signals, i.e., chirps, have been tested for imaging thin Teflon defects embedded within a carbon fiber composite specimen. With the aim of maximizing the heat transferred within the sample, the use of several optimized non-linear chirp signals has been also investigated and their defect detection capability compared in terms of the maximum achievable signal-to-noise ratio.

Nonlinear Chirp Mode Decomposition: A Variational Method

Variational mode decomposition (VMD), a recently introduced method for adaptive data analysis, has aroused much attention in various fields. However, the VMD is formulated based on the assumption of narrow-band property of the signal model. To analyze wide-band nonlinear chirp signals (NCSs), we present an alternative method called variational nonlinear chirp mode decomposition (VNCMD). The VNCMD is developed from the fact that a wideband NCS can be transformed to a narrow-band signal by using demodulation techniques. Our decomposition problem is, thus, formulated as an optimal demodulation problem, which is efficiently solved by the alternating direction method of multipliers. Our method can be viewed as a time–frequency filter bank, which concurrently extracts all the signal modes. Some simulated and real data examples are provided showing the effectiveness of the VNCMD in analyzing NCSs containing close or even crossed modes.

The Design of Nonlinear Chirp Based on the DSP Builder Technique

This paper, by analyzing the function Chirp, studies the software design and realization of the function. It offers a design plan based on the nonlinear Chirp signal of DSP Builder technique and designs the signal generator of the nonlinear Chirp based on the design flow of Matlab/Simulink/DSP Builder/Quartusll. It also conducts simulation verification using the development software Matlab/Simulink and Quartusll, proving that the design can well realize the signal source Chirp. The experiment proves that the DSP Builder technique can modify the starting frequency, bandwidth and the frequency resolution of linear frequency modulation signals by changing the programming parameters. The method is proved to be simple in designing, convenient in modification, low in cost and it doesn’t involve any programming; therefore, it is easy to realize.

Excitation Waveform Design for Lamb Wave Pulse Compression.

Most ultrasonic guided wave methods focus on tone burst excitation to reduce the effect of dispersion so as to facilitate signal interpretation. However, the resolution of the output cannot attain a very high value because time duration of the excitation waveform cannot be very small. To overcome this limitation, a pulse compression technique is introduced to Lamb wave propagation to achieve a δ-like correlation so as to obtain a high resolution for inspection. Ideal δ-like correlation is impossible as only a finite frequency bandwidth can propagate. The primary purpose of this paper is to design a proper excitation waveform for Lamb wave pulse compression, which shortens the correlation as close as possible to a δ function. To achieve this purpose, the performance of some typical signals is discussed in pulse compression, which include linear chirp (L-Chirp) signal, nonlinear chirp (NL-Chirp) signal, Barker code (BC), and Golay complementary code (GCC). In addition, how the excitation frequency range influences inspection resolution is investigated. A strategy for the frequency range determination is established subsequently. Finally, an experiment is carried out on an aluminum plate where these typical signals are used as excitations at different frequency ranges. The quantitative comparisons of the pulse compression responses validate the theoretical findings. By utilizing the experimental data, the improvement of pulse compression in resolution compared with tone burst excitation is also validated, and the robustness of the waveform design method to inaccuracies in the dispersion compensation is discussed as well.

Underwater Acoustic Communication Using Nonlinear Chirp Signal

This paper presents an underwater acoustic communication with nonlinear chirp modulation. The information is carried by the carrier amplitude, frequency or phase in the most common underwater acoustic communications. However, the proposed method includes the information within frequency variation of carrier wave for a symbol. Especially, as carrier wave the hyperbolic frequency modulated signal, one of the nonlinear chirp signal, is used and it is robust in the Doppler channel. The proposed method was analyzed and compared to conventional method by simulation. When the doppler shift existed, the error probability of the proposed method is reduced by 5~12 % than conventional method with linear frequency modulated signal. Sea trial was performed to analyze the performance of the proposed method.

Filtering in Time-Frequency Domain using STFrFT

The Fractional Fourier Transform is a generalized form of Fourier Transform, which can be interpreted as a rotation by angle α in time-frequency plane or decomposition of signals in terms of chirps. However it fails in locating Fractional Fourier Domain Frequency contents. Short-time FRFT variants are suitable for analysis of multicomponent and nonlinear chirp signals with improved time-frequency resolution. Short-Time FRFT is the simultaneous representation of, combination of the time and FRFD-frequency information. Filtering in the fractional domain separates the noise and the highly concentrated signal. Filtering results depict that the results in fractional domain give better results. The timefrequency representation in fractional domain is useful tool for various applications like filtering of chirp signals. Simulations are performed on MATLAB platform.

A Mitigation of Multipath Ranging Error Using Non-linear Chirp Signal

While the chirp signal is extensively used in radar and sonar systems for target decision in wireless communication systems, it has not been widely used for positioning in indoor environments. Recently, the IEEE 802.15.4a standard has adopted the chirp spread spectrum (CSS) as an underlying technique for low-power and low-complexity precise localization. Chirp signal based ranging solutions have been established and deployed but their ranging performance has not been analyzed in multipath environments. This paper presents a ranging performance analysis of a chirp signal and suggests a method to suppress multipath error by using a type of non-linear chirp signal. Multipath ranging performance is evaluated using a conventional linear chirp signal and the proposed non-linear chirp signal. We verify the feasibility of both methods using two-ray multipath model simulation. Our results demonstrate that the proposed non-linear chirp signal can successfully suppress the multipath error.

Coded tissue harmonic imaging with nonlinear chirp signals

Coded tissue harmonic imaging with pulse inversion (CTHI-PI) based on a linear chirp signal can improve the signal-to-noise ratio with minimizing the peak range sidelobe level (PRSL), which is the main advantage over CTHI with bandpass filtering (CTHI-BF). However, the CTHI-PI technique could suffer from motion artifacts due to decreasing frame rate caused by two firings of opposite phase signals for each scanline. In this paper, a new CTHI method based on a nonlinear chirp signal (CTHI-NC) is presented, which can improve the separation of fundamental and harmonic components without sacrificing frame rate. The nonlinear chirp signal is designed to minimize the PRSL value by optimizing its frequency sweep rate and time duration. The performance of the CTHI-NC method was evaluated by measuring the PRSL and mainlobe width after compression. From the in vitro experiments, the CTHI-NC provided the PRSL of −40.6 dB and the mainlobe width of 2.1 μs for the transmit quadratic nonlinear chirp signal with the center frequency of 2.1 MHz, the fractional bandwidth at −6 dB of 0.6 and the time duration of 15 μs. These results indicate that the proposed method could be used for improving frame rates in CTHI while providing comparable image quality to CTHI-PI.

A 77 GHz 90 nm CMOS Transceiver for FMCW Radar Applications

The first 77 GHz frequency modulated continuous wave (FMCW) radar transceiver IC with an accurate FMCW chirp signal generator using a 90 nm CMOS process is presented. To realize accurate FMCW radar system in CMOS, a PLL synthesizer based FMCW generator with chirp smoothing technique that is able to output linear FMCW frequency chirp using a nonlinear reference chirp signal supplied from a low spec/cost digital-oriented frequency reference is applied. The fabricated IC consists of an LNA, a down-conversion mixer with an output buffer, a driver amplifier, a power amplifier with power combiner, an LO distributer and an FMCW synthesizer. The measured FMCW signal from the proposed FMCW generator achieves 93 kHz frequency error (nonlinearity) at the 77 GHz chip signal. Radar performance of the IC has less than 1% ranging error from 1 m to 8 m distance from the measurement in a laboratory. These results show the transceiver achieves a fundamental function for radar applications with 520 mW power consumptions.

Feature Extraction From Underwater Signals Using Time-Frequency Warping Operators

Processing marine-mammal signals for passive oceanic acoustic tomography or species classification and monitoring are problems that have recently attracted attention in scientific literature. For these purposes, it is necessary to use a method which could be able to extract the useful information about the processed data, knowing that the underwater environment is highly nonstationary. In this context, time-frequency (TF) or time-scale methods constitute a potential approach. Practically, it has been observed that the majority of TF structures of the marine-mammal signals are highly nonlinear. This fact affects dramatically the performances achieved by the Cohen's class methods, these methods being efficient in the presence of linear TF structures. Fortunately, thanks to the warping operator principle, it is possible to generate other class of time-frequency representations (TFRs). The new TFRs may analyze nonlinear chirp signals better than Cohen's class does. In spite of its mathematical elegance, this principle is limited in real applications by two major elements. First, as we will see, its implementation leads to a considerable growth of the signal length. Consequently, from operational point of view, this principle is limited to short synthetic signals. Second, the design of a single warping operator can be inappropriate if the analyzed signal is multicomponent. Furthermore, the choice of "adapted" warping operator becomes a problem when the signal components have different TF behaviors. In this paper, we propose a processing method of marine-mammal signals, well adapted to a real passive underwater context. The method tries to overcome the two aforementioned limitations. Also, the first step consists in data size reducing by the detection of the TF regions of interests (ROIs). Furthermore, in each ROI, a technique which combines some typical warping operators is used. The result is an analytical characterization of the instantaneous frequency laws (IFLs) of signal components. The simulations on real underwater data show the performances of this method in comparison with classical ones

Short-time fractional Fourier methods for the time-frequency representation of chirp signals.

The fractional Fourier transform (FrFT) provides a valuable tool for the analysis of linear chirp signals. This paper develops two short-time FrFT variants which are suited to the analysis of multicomponent and nonlinear chirp signals. Outputs have similar properties to the short-time Fourier transform (STFT) but show improved time-frequency resolution. The FrFT is a parameterized transform with parameter, a, related to chirp rate. The two short-time implementations differ in how the value of a is chosen. In the first, a global optimization procedure selects one value of a with reference to the entire signal. In the second, a values are selected independently for each windowed section. Comparative variance measures based on the Gaussian function are given and are shown to be consistent with the uncertainty principle in fractional domains. For appropriately chosen FrFT orders, the derived fractional domain uncertainty relationship is minimized for Gaussian windowed linear chirp signals. The two short-time FrFT algorithms have complementary strengths demonstrated by time-frequency representations for a multicomponent bat chirp, a highly nonlinear quadratic chirp, and an output pulse from a finite-difference sonar model with dispersive change. These representations illustrate the improvements obtained in using FrFT based algorithms compared to the STFT.

Short-time fractional Fourier methods for signal representation in the time-frequency plane

The analysis of multicomponent chirp signals is of interest in sonar, geophysical, bioacoustic, ultrasonic, and radar applications. This paper examines the interpretation of the fractional Fourier transform (FrFT) of such signals in terms of their representation in the time-frequency plane. The FrFT has been shown to be of value in analyzing and filtering linear chirp signals with various characteristics. The desirability of a short-time variant has been suggested by several authors and this paper introduces new short-time fractional Fourier methods for the piecewise description and parameterization of nonlinear chirp signals. Understanding of a signal’s FrFT as the projection of the joint time-frequency distribution onto a line at angle α to the time axis permits development of these short-time methods. Parameter α provides a means for transform optimization with reference to the entire signal or on a windowed basis. While providing much improved time-frequency resolution over the spectrogram, these techniques do not suffer from cross-term interference seen in Wigner distributions and related methods. Representation of highly nonlinear chirps in the time-frequency plane is demonstrated through analysis of a variety of signals including bat and dolphin chirps, heart sounds, and synthetic signals constructed to highlight particular differences between the techniques.

Extraction of the aortic and pulmonary components of the second heart sound using a nonlinear transient chirp signal model

The objective of this paper is to adapt and validate a nonlinear transient chirp signal modeling approach for the analysis and synthesis of overlapping aortic (A2) and pulmonary (P2) components of the second heart sound (S2). The approach is based on the time-frequency representation of multicomponent signals for estimating and reconstructing the instantaneous phase and amplitude functions of each component. To evaluate the accuracy of the approach, a simulated S2 with A2 and P2 components having different overlapping intervals (5-30 ms) was synthesized. The simulation results show that the technique is very effective for extracting the two components, even in the presence of noise (-15 dB). The normalized root-mean-squared error between the original A2 and P2 components and their reconstructed versions varied between 1% and 6%, proportionally to the duration of the overlapping interval, and it increased by less than 2% in the presence of noise. The validated technique was then applied to S2 components recorded in pigs under normal or high pulmonary artery pressures. The results show that this approach can successfully isolate and extract overlapping A2 and P2 components from successive S2 recordings obtained from different heartbeats of the same animal as well from different animals.