Nonlinear Frequency Modulated Signals Research Articles

High-resolution direction finding of non-stationary signals using matching pursuit

One of the main goals of time–frequency (TF) signal representations in non-stationary array processing is to equip multi-antenna receivers with the ability to separate sources in the TF domain prior to direction finding. This permits high-resolution direction-of-arrival (DOA) estimation of individual sources and of more sources than sensors. In this paper, we use linear decomposition of sensor data based on matching pursuit (MP). The leading atoms of the MP, which capture most of the source TF signatures, can be different for different sources and, as such, provide the desired source discrimination. The MP coefficients with high signal-to-noise ratio (SNR) and corresponding to the leading decomposition atoms are used to develop the MP-MUSIC DOA estimation for non-stationary source signals. We demonstrate the source discriminatory capability of the proposed technique using linear FM, nonlinear FM, and other non-stationary signals. Further, we compare MP-MUSIC performance with conventional MUSIC and the time–frequency MUSIC, which incorporates bilinear transforms.

Application of Arbitrary Position and Width Pulse Trains Signals in Ultrasonic Imaging: Correlation Performance Study

Ultrasonic imaging requires both the accuracy and the resolution. Conventional imaging systems use the pulse signals to accomplish the task. But the energy attainable with such signals is limited. Spread spectrum, compressible signals allow to achieve the wide bandwidth even using long durations. Conventional signals do not offer full flexibility or, like nonlinear frequency modulation signals, lack the ease of properties control. We suggest using novel spread spectrum signals generation technique: trains of pulses of arbitrary pulse width and position (APWP). It is expected that APWP should have properties similar to chirp (wide, controllable bandwidth) and both the single pulse (low correlation sidelobes) signals. Study presented here was aimed at evaluating the correlation properties of APWP signals. It indicates that application of APWP signals allows obtaining the properties better or close to those of the conventional signals. It can be concluded that APWP signals offer a new perspective in imaging applications.DOI: http://dx.doi.org/10.5755/j01.eee.19.3.2690

Test

Ultrasonic imaging requires both the accuracy and the resolution. Conventional imaging systems use the pulse signals to accomplish the task. But the energy attainable with such signals is limited. Spread spectrum, compressible signals allow to achieve the wide bandwidth even using long durations. Conventional signals do not offer full flexibility or, like nonlinear frequency modulation signals, lack the ease of properties control. We suggest using novel spread spectrum signals generation technique: trains of pulses of arbitrary pulse width and position (APWP). It is expected that APWP should have properties similar to chirp (wide, controllable bandwidth) and both the single pulse (low correlation sidelobes) signals. Study presented here was aimed at evaluating the correlation properties of APWP signals. It indicates that application of APWP signals allows obtaining the properties better or close to those of the conventional signals. It can be concluded that APWP signals offer a new perspective in imaging applications. DOI: http://dx.doi.org/10.5755/j01.eee.19.3.2690

Sidelobe Reduction in the Pulse-Compression Radar Using Synthesis of NLFM Laws

It is well known that in the pulse-compression radar theory, the sidelobe reduction using synthesis of some proper nonlinear FM (NLFM) laws represents a major research direction. In order to assure the sidelobe suppression, the main objective of this paper is to present an adequate synthesis algorithm of NLFM signals based on stationary phase principle. The achieved experimental results confirm a significant sidelobe reduction (i.e., more than −40 dB) without necessity to apply some weighting techniques. In addition, the analysis of the synthesized NLFM laws by ambiguity function tool is also discussed.

Instantaneous Frequency Estimation Algorithm of Non-linear Frequency Modulation Signal in Low SNR Based on Generalized S-transform

Abstract The Nonlinear Frequency Modulation (NLFM) signals have been gradually used in new radar systems, however its instantaneous frequency (IF) estimation is still a difficult problem. This paper introduces the generalized S-transform to NLFM signals processing fields and proposes a new IF estimation algorithm of NLFM signals in low SNR based on generalized S-transform. Firstly, the timefrequency distribution (TFD) of NLFM signals in low SNR is got by generalized S-transform. Secondly, a time-frequency (TF) filtering processing is executed to the TFD of NLFM signals and the noise is restrained. Finally the TFD spectrum ridges are extracted as IF curves estimation from the filtered TFD of NLFM signals. Simulation results demonstrate that the IF estimation algorithm proposed in this paper has better performances in IF estimating of NLFM signal in low SNR than other existing algorithms.

STFT With Adaptive Window Width Based on the Chirp Rate

An adaptive time-frequency representation (TFR) with higher energy concentration usually requires higher complexity. Recently, a low-complexity adaptive short-time Fourier transform (ASTFT) based on the chirp rate has been proposed. To enhance the performance, this method is substantially modified in this paper: i) because the wavelet transform used for instantaneous frequency (IF) estimation is not signal-dependent, a low-complexity ASTFT based on a novel concentration measure is addressed; ii) in order to increase robustness to IF estimation error, the principal component analysis (PCA) replaces the difference operator for calculating the chirp rate; and iii) a more robust Gaussian kernel with time-frequency-varying window width is proposed. Simulation results show that our method has higher energy concentration than the other ASTFTs, especially for multicomponent signals and nonlinear FM signals. Also, for IF estimation, our method is superior to many other adaptive TFRs in low signal-to-noise ratio (SNR) environments.

Coded Tissue Superharmonic Imaging: An Analytical Study

Superharmonic imaging (SHI) benefits medical ultrasound imaging in achieving higher spatial and contrast resolution but gives poor signal-to-noise ratio (SNR) and penetration depth that require careful control on excitation power and frequency. In the present work, coded pulsed excitations (linear frequency modulated and nonlinear frequency modulated signals) are used to evaluate the superharmonic field generation and propagation (coded tissue superharmonic imaging). The evaluation includes the study of parameters such as peak side lobe level, beam width, axial level for analyzing SNR and penetration depth. The results for coded tissue SHI are reported in comparison with conventional SHI and with the performance of coded tissue harmonic imaging and fundamental ultrasound imaging.

Spline-Kernelled Chirplet Transform for the Analysis of Signals With Time-Varying Frequency and Its Application

The conventional time-frequency analysis (TFA) methods, including continuous wavelet transform, short-time Fourier transform, and Wigner-Ville distribution, have played important roles in analyzing nonstationary signals. However, they often show less capability in dealing with nonstationary signals with time-varying frequency due to the bad energy concentration in the time-frequency plane. On the other hand, by introducing an extra transform kernel that matches the instantaneous frequency of the signal, parameterized TFA methods show powerful ability in characterizing time-frequency patterns of nonstationary signals with time-varying frequency. In this paper, a novel time-frequency transform, called spline-kernelled chirplet transform (SCT), is proposed. By introducing a frequency-rotate operator and a frequency-shift operator constructed with spline kernel function, the SCT is particularly powerful for the strongly nonlinear frequency-modulated signals. In addition, an effective algorithm is developed to estimate the parameters of transform kernel in the SCT. The capabilities of the SCT and parameter estimation algorithm are validated by their applications for numerical signals and a set of vibration signal collected from a rotor test rig.

A Novel Method of Signal Denoising

Abstract A novel time-frequency technique for linear and nonlinear frequency modulated signal denoising is proposed. The proposed method is based on the principle of Quasi Fourier Transform (QTF). Firstly, we discusses in depth the principles and properties of QFT theoretically. Secondly, by applying the QFT, Multi-component signal with aliasing in frequency domain is separated successfully, and it is readily to de-noise for linear or nonlinear frequency modulated signals with white or 1/f noise. Thirdly, related issues such as the resolution and the effect of noise are studied. The simulation results show that QFT is an efficient tool to extract effectively useful signals from buried in the noise.

Double-characters detection of nonlinear frequency modulated signals based on FRFT

In many practical applications, signals to be detected are unknown nonlinear frequency modulated (FM) and are corrupted by strong noise. The phase histories of the nonlinear FM signals are assumed to be unknown smooth functions of time, which are usually poorly modeled or cannot be modeled at all by a small number of parameters. Because of the lack of phase model, a nonparametric detection method is proposed based on successive fractional Fourier transform and double-characters detection. The detection process goes in three steps. First, an image is constructed by the fractional Fourier transforms of successive angles in one period. Then, the threshold procedure is utilized to transform the image into a binary image. After the multiple median filtering, the binary image is refined where the isolated noise pixels are removed. Finally, two complementary features are extracted from the refined image, and a double-characters detector is proposed to decide whether the target is present or not. The simulation experiments to three polynomial phase signals with different orders and a sinusoidal phase signal show that the proposed detection method is effective and robust.

Nonparametric detection of frequency modulated signals using fractional Fourier transform

A detection scheme for unknown nonlinear frequency modulated signals in white Gaussian noise is developed using the fractional Fourier transform and two-dimensional order-statistic filter. The simulation experiment and comparison with other methods available are shown, and the effectiveness of the proposed method is reported.

Nonlinear Frequency Modulated Signal Design

The signal time–frequency structure designing is the important problem of radar system solution optimisation. The radar ambiguity function is the very useful signal characteristic that enables to know the signal potential possibilities. The effective numerical methods of the radar ambiguity function calculation give possibility for synthesis of the radar signal having expected features. The synthesis method concerning the nonlinear frequency modulation radar signal is presented in the paper. For the radar ambiguity function calculation the Zak transform is used in the method. The nonlinear frequency modulation signal model was described in which application limitations were taken into account. Examples of simulation research results are presented as a comment of the considerations.

SIDELOBES REDUCTION USING SIMPLE TWO AND TRI-STAGES NON LINEAR FREQUENCY MODULATION (NLFM)

The Linear Frequency Modulation (LFM) waveform is the most commonly and extensively used signal in practical radar system. However a compressed LFM signal at the receiver will produce the flrst sidelobe at a level of i13dB to the peak of the main lobe. A weighting function is needed to apply in order to reduce the sidelobes. However, the penalty of mismatch loss is clearly evident. It may reduce output SNR, typically by 1 to 2dB. Every single dB of additional SNR can have great efiects in reducing false alarm rates in target detection applications. In an efiort to achieve low autocorrelation sidelobe level without applying weighting function, Non-Linear Frequency Modulation (NLFM) signal has been investigated. This paper describes the sidelobe reduction techniques using simple two-stage FM waveform, modifled two-stage FM waveform and tri-stage FM waveform. Simulation results of the proposed NLFM signal are presented. Sidelobe reduction of more than i19dB can be achieved by this design without any weighting technique applied.

Designing Waveforms for Temporal Encoding Using a Frequency Sampling Method

In this paper a method for designing waveforms for temporal encoding in medical ultrasound imaging is described. The method is based on least squares optimization and is used to design nonlinear frequency modulated signals for synthetic transmit aperture imaging. By using the proposed design method, the amplitude spectrum of the transmitted waveform can be optimized, such that most of the energy is transmitted where the transducer has large amplification. To test the design method, a waveform was designed for a BK8804 linear array transducer. The resulting nonlinear frequency modulated waveform was compared to a linear frequency modulated signal with amplitude tapering, previously used in clinical studies for synthetic transmit aperture imaging. The latter had a relatively flat spectrum which implied that the waveform tried to excite all frequencies including ones with low amplification. The proposed waveform, on the other hand, was designed so that only frequencies where the transducer had a large amplification were excited. Hereby, unnecessary heating of the transducer could be avoided and the signal-to-noise ratio could be increased. The experimental ultrasound scanner RASMUS was used to evaluate the method experimentally. Due to the careful waveform design optimized for the transducer at hand, a theoretic gain in signal-to-noise ratio of 4.9 dB compared to the reference excitation was found, even though the energy of the nonlinear frequency modulated signal was 71% of the energy of the reference signal. This was supported by a signal-to-noise ratio measurement and comparison in penetration depth, where an increase of 1 cm was found in favor for the proposed waveform. Axial and lateral resolutions at full-width half-maximum were compared in a water phantom at depths of 42, 62, 82, and 102 mm. The axial resolutions of the nonlinear frequency modulated signal were 0.62, 0.69, 0.60, and 0.60 mm, respectively. The corresponding axial resolutions for the reference waveform were 0.58, 0.65, 0.62, and 0.60 mm, respectively. The compression properties of the matched filter (mismatched filter for the linear frequency modulated signal) were tested for both waveforms in simulation with respect to the Doppler frequency shift occurring when probing moving objects. It was concluded that the Doppler effect of moving targets does not significantly degrade the filtered output. Finally, in vivo measurements are shown for both methods, wherein the common carotid artery on a 27-year-old healthy male was scanned.

Instantaneous frequency estimation of nonlinear frequency-modulated signals in the presence of multiplicative and additive noise

This paper addresses the problem of estimating the instantaneous frequency (IF) of monocomponent nonlinear, not necessarily polynomial, frequency modulated (FM) signals affected by stationary multiplicative and additive noise. Both noise processes are assumed to be complex circular Gaussian and independent. The peak of the polynomial Wigner-Ville distribution (PWVD) is proposed here as an IF estimator. We derive analytical expressions for the bias and asymptotic variance of the estimator and propose an algorithm to select the optimal window length to resolve the bias-variance tradeoff in the IF estimation. Simulation results are presented to confirm the theoretical results.

A new estimation technique for high-resolution bathymetry

A new technique for depth estimation in airborne laser bathymetry is proposed. The technique involves the transmission of a nonlinear frequency-modulated signal, the detection of the signal reflected by the ocean, and its processing using an appropriate matched filter. On the basis of this technique, a new airborne laser bathymeter could be designed that would offer improved resolution between the signal components reflected by the surface and bottom of the ocean, which would translate into improved accuracy of depth measurement.

Analysis of nonlinear FM signals by pattern recognition of their time-frequency representation

The aim is to propose a method for detection and parameter estimation of nonlinear FM signals, mono- or multicomponent, embedded in white Gaussian noise. The proposed approach consists in mapping the signal into the time-frequency plane by a time-frequency distribution with reassignment, and then in applying a pattern recognition technique, like the Hough transform, to the time-frequency representation to recognize specific shapes. The advantages of this method over the conventional maximum likelihood estimator are (1) a simpler implementation, because it reduces the dimension of the search space and (2) a consistent attenuation of the interference terms between different components of a signal or between signal and noise.

Polynomial Wigner-Ville distributions and their relationship to time-varying higher order spectra

The Wigner-Ville distribution (WVD) has optimal energy concentration for linear frequency modulated (FM) signals. This paper presents a generalization of the WVD in order to effectively process nonlinear polynomial FM signals. A class of polynomial WVD's (PWVD's) that give optimal concentration in the time-frequency plane for FM signals with a modulation law of arbitrary polynomial form are defined. A class of polynomial time-frequency distributions (PTFD's) are also defined, based on the class of PWVD's. The optimal energy concentration of the PWVD enables it to be used for estimation of the instantaneous frequency (IF) of polynomial FM signals. Finally, a link between PWVD's and time-varying higher order spectra (TVHOS) is established. Just as the expected value of the WVD of a nonstationary random signal is the time-varying power spectrum, the expected values of the PWVD's have interpretations as reduced TVHOS. >

Estimation of instantaneous frequency using the discrete Wigner distribution

Analytical expressions for the performance of the discrete Wigner distribution (DWD) in estimating the instantaneous frequency of linear frequency modulated signals in additive white noise are derived and verified using simulation. It is shown that the DWD peak provides an optimal estimate at high input signal-to-noise ratios. The applicability of these results to the general case of nonlinear FM signals is discussed.

Method of measuring nonlinear FM signal distortion in generators and receivers

Method of measuring nonlinear FM signal distortion in generators and receivers