Classical Time-frequency Analysis Research Articles

LFM signal optimization time-fractional-frequency analysis: Principles, method and application

The classical time-frequency analysis method is not the optimal signal representation method for LFM signal, fractional Fourier transform (FRFT) can represent signal from any fractional domain between time domain and frequency domain. Inspired by this characteristic, an optimization time-fractional-frequency (TFF) analysis method for LFM signal is built in this paper. First, a new simple fractional wavelet transform (FRWT) is proposed using generalized fractional convolution, which can provide joint time and fractional-frequency information of signal. Furthermore, an optimization TFF analysis method based on FRWT is established. It can provide a robust and high-resolution TFF representation for LFM signal, especially for multi-component LFM signal with close or intersecting components. Finally, the FRWT-based TFF analysis method is successfully applied to the parameter estimation of LFM signal. Experimental results show that the FRWT-based parameter estimation method is superior to some existing methods in terms of accuracy and noise robustness.

A Novel Approach for the Characterization of Triangular Modulated Frequency Modulated Continuous Wave Low Probability of Intercept Radar Signals via Application of the Wigner-Ville Distribution

Digital intercept receivers are changing from Fourier-based analysis to classical time-frequency analysis techniques for analyzing low probability of intercept radar signals. This paper presents a novel approach of characterizing low probability of intercept triangular modulated frequency modulated continuous wave radar signals through utilization and direct comparison of the signal processing techniques Wigner-Ville Distribution versus the Reassigned Smooth Pseudo Wigner-Ville Distribution. The following metrics were used for evaluation: percent error of: carrier frequency, modulation bandwidth, modulation period, chirp rate, and time-frequency localization (x and y direction). Also used were: percent detection, lowest signal-to-noise ratio for signal detection, and plot (processing) time. Experimental results demonstrate that overall, the Reassigned Smooth Pseudo Wigner-Ville Distribution signal processing technique produced more accurate characterization metrics than the Wigner-Ville Distribution signal processing technique.

Detection and Parameter Extraction of Low Probability of Intercept Frequency Hopping Signals using the Spectrogram and the Reassigned Spectrogram

Low probability of intercept radar signals, which are often problematic to detect and characterize, have as their goal ‘to see and not be seen’. Digital intercept receivers are currently moving away from Fourier-based analysis and towards classical time-frequency analysis techniques for the purpose of analyzing these low probability of intercept radar signals. Although these classical time-frequency analysis techniques are an improvement over existing Fourier-based techniques, they still suffer from a lack of readability –which can be caused by poor time-frequency localization (such as the spectrogram), which may in turn lead to inaccurate detection and parameter extraction. In this study, the reassignment method, because of its ability to improve time-frequency localization, is proposed as an improved signal analysis technique to address the poor time-frequency localization deficiency of the spectrogram. This paper presents the novel approach of characterizing low probability of intercept frequency hopping radar signals through utilization and direct comparison of the spectrogram versus the reassigned spectrogram.

Low Probability of Intercept Triangular Modulated Frequency Modulated Continuous Wave Signal Characterization Comparison Using the Wigner Ville Distribution and the Choi Williams Distribution

Digital intercept receivers are currently moving away from Fourier-based analysis and towards classical time frequency analysis techniques for the purpose of analyzing low probability of intercept radar signals. This paper presents the novel approach of characterizing low probability of intercept triangular modulated frequency modulated continuous wave radar signals through utilization and direct comparison of the Wigner Ville Distribution versus the Choi Williams Distribution. The following metrics were used for evaluation: percent error of: carrier frequency, modulation bandwidth, modulation period, chirp rate, and time-frequency localization (x and y direction). Also used were: percent detection, lowest signal-to noise ratio for signal detection, and plot (processing) time. Experimental results demonstrate that overall, the Wigner Ville Distribution produced more accurate characterization metrics than the Choi Williams Distribution. An improvement in performance may well translate into an increase in personnel safety.

An Improved Method Based on Time-Frequency Distribution to Detect Time-Varying Interference for GNSS Receivers With Single Antenna

This paper presents a regroup method based on reassigned smoothed pseudo Wigner-Ville distribution (RSPWVD) to detect time-varying interference for global navigation satellite system (GNSS) receivers with a single antenna. In order to prove the effectiveness and superiority of the introduced method, the theoretical analysis and performance simulation has been performed between the proposed method and the classical time-frequency analysis methods. The performance of the proposed method has been accessed by experiments with the real BDS BII signals corrupted by the linear frequency modulation (chirp) interference. The actual performance of experiments has been used to test theoretical analysis by the quantitative metric root mean square error of the instantaneous frequency estimation. The results of experiments depict that the regroup method based on RSPWVD completely eliminates not only cross-term interferences but also end effects and provide better detection performance of time-varying interference compared with the classical time-frequency analysis methods for GNSS receivers with a single antenna.

A Frequency Domain Extraction Based Adaptive Joint Time Frequency Decomposition Method of the Maneuvering Target Radar Echo

The maneuvering target echo of high-resolution radar can be expressed as a multicomponent polynomial phase signal (mc-PPS). However, with improvements in radar resolution and increases in the synthetic period, classical time frequency analysis methods cannot satisfy the requirements of maneuvering target radar echo processing. In this paper, a novel frequency domain extraction-based adaptive joint time frequency (FDE-AJTF) decomposition method was proposed with three improvements. First, the maximum frequency spectrum of the phase compensation signal was taken as the fitness function, while the fitness comparison, component extraction, and residual updating were operated in the frequency domain; second, the time window was adopted on the basis function to fit the uncertain signal component time; and third, constant false alarm ratio (CFAR) detection was applied in the component extraction to reduce the ineffective components. Through these means, the stability and speed of phase parameters estimation increased with one domination ignored in the phase parameter estimation, and the accuracy and effectiveness of the signal component extraction performed better with less influence from the estimation errors, clutters, and noises. Finally, these advantages of the FDE-AJTF decomposition method were verified through a comparison with the classical method in simulation and experimental tests.

Low Probability of Intercept Triangular Modulated Frequency Modulated Continuous Wave Signal Characterization Comparison using the Spectrogram and the Scalogram

Digital intercept receivers are currently moving away from Fourier-based analysis and towards classical time-frequency analysis techniques for the purpose of analyzing low probability of intercept radar signals. This paper presents the novel approach of characterizing low probability of intercept frequency modulated continuous wave radar signals through utilization and direct comparison of the Spectrogram versus the Scalogram. Two different triangular modulated frequency modulated continuous wave signals were analyzed. The following metrics were used for evaluation: percent error of: carrier frequency, modulation bandwidth, modulation period, chirp rate, and time-frequency localization (x and y direction). Also used were: percent detection, lowest signal-to-noise ratio for signal detection, and plot (processing) time. Experimental results demonstrate that overall, the Spectrogram produced more accurate characterization metrics than the Scalogram. An improvement in performance may well translate into saved equipment and lives.

A Roth‐type theorem for dense subsets of Rd

Let $1 < p < \infty$, $p\neq 2$. We prove that if $d\geq d_p$ is sufficiently large, and $A\subs\R^d$ is a measurable set of positive upper density then there exists $\la_0=\la_0(A)$ such for all $\la\geq\la_0$ there are $x,y\in\R^d$ such that $\{x,x+y,x+2y\}\subs A$ and $|y|_p=\la$, where $||y||_p=(\sum_i |y_i|^p)^{1/p}$ is the $l^p(\mathbb R^d)$-norm of a point $y=(y_1,\ldots,y_d)\in\R^d$. This means that dense subsets of $\R^d$ contain 3-term progressions of all sufficiently large gaps when the gap size is measured in the $l^p$-metric. This statement is known to be false in the Euclidean $l^2$-metric as well as in the $l^1$ and $\ell^{\infty}$-metrics. One of the goals of this note is to understand this phenomenon. A distinctive feature of the proof is the use of multilinear singular integral operators, widely studied in classical time-frequency analysis, in the estimation of forms counting configurations.

Low Probability of Intercept Frequency Hopping Signal Characterization Comparison using the Spectrogram and the Scalogram

Low probability of intercept radar signals, which are often problematic to detect and characterize, have as their goal ‘to see and not be seen’. Digital intercept receivers are currently moving away from Fourier-based analysis and towards classical time-frequency analysis techniques for the purpose of analyzing these low probability of intercept radar signals. This paper presents the novel approach of characterizing low probability of intercept frequency hopping radar signals through utilization and direct comparison of the Spectrogram versus the Scalogram. Two different frequency hopping low probability of intercept radar signals were analyzed(4-component and 8-component). The following metrics were used for evaluation: percent error of:carrier frequency, modulation bandwidth, modulation period, and time-frequency localization. Also used were: percent detection, lowest signal-to-noise ratio for signal detection, and plot (processing) time. Experimental results demonstrate that overall,theScalogram produced more accurate characterization metrics than the Spectrogram. An improvement in performance may well translate into saved equipment and lives.

Detection and Parameter Extraction of Low Probability of Intercept Radar Signals using the Hough Transform

Digital intercept receivers are currently moving away from Fourier-based analysis and towards classical time-frequency analysis techniques, such as the Wigner-Ville distribution, Choi-Williams distribution, spectrogram, and scalogram, for the purpose of analyzing low probability of intercept radar signals (e.g. triangular modulated frequency modulated continuous wave and frequency shift keying). Although these classical time-frequency techniques are an improvement over the Fourier-based analysis, they still suffer from a lack of readability, due to cross-term interference, and a mediocre performance in low SNR environments. This lack of readability may lead to inaccurate detection and parameter extraction of these radar signals. In this paper, the use of the Hough transform, because of its ability to suppresscross-term interference, separate signals from cross-terms, and perform well in the presence of noise, is proposed as an improved signal analysis technique. With these qualities, the Hough transform has the potential to produce better readability and consequently, more accurate signal detection and parameter extraction metrics.

Analysis of Low Probability of Intercept Radar Signals Using the Reassignment Method

Digital intercept receivers are currently moving towards classical time-frequency analysis techniques for analyzing low probability of intercept radar signals. Although these techniques are an improvement over existing Fourier-based techniques, they still suffer from a lack of readability, due to poor time-frequency localization and cross-term interference, which may lead to inaccurate detection and parameter extraction. In this study, the reassignment method, because of its ability to smooth out cross-term interference and improve time-frequency localization, is proposed as an improved signal analysis technique to address these deficiencies. Simulations are presented that compare time-frequency representations of the classical time-frequency techniques with those of the reassignment method. Four different low probability of intercept waveforms are analyzed (two frequency modulated continuous wave waveforms and two frequency shift keying waveforms). The following metrics are used for analysis evaluation: Percent detection, number of cross-term false positives, lowest signal-to-noise ratio for signal detection, processing time, percent error of: Carrier frequency, modulation bandwidth, modulation period, time-frequency localization (x and y direction) and chirp rate. Experimental results demonstrate that the ‘squeezing’ and ‘smoothing’ qualities of the reassignment method improve readability over the classical time-frequency analysis techniques and consequently, provide more accurate signal detection and parameter extraction in all but one of the metrics categories.

Fractional Differential Analysis for Texture of Digital Image

This paper discusses the capabilities of the fractional differential approach for the detection of textural features in two-dimensional digital images and the involved Lateral Inhibition Principle, and fractional differential masks and algorithms of digital image. Firstly, the kinetic physical meaning of fractional differential and the relationship between fractional calculus and classical time-frequency analysis and the separability of two-dimensional fractional calculus on certain conditions are deduced. Secondly, the difference between two Gaussians receptive fields for fractional differential of digital image involved signal processing and biologic vision nerve model is discussed. An analysis of its Mach band is also included. Thirdly, the implements and parameters of eight n × n fractional differential masks, which are mutual central symmetric, on negative x-coordinate, positive x-coordinate, negative y-coordinate, positive y-coordinate, left lower diagonal, left upper diagonal, right lower diagonal, right upper diagonal respectively are discussed. Lastly, the numerical implementation algorithms of fractional differential mask for digital image are discussed. Numerical experiments show that the textural details enhance capabilities of fractional differential-based texture operator and are better than that of integral differential based one for rich-grained digital images.

The Study of Tool Wear and Breakage Based on the Characteristic Analysis of Acoustic Spectrum

Tool monitoring is an important factor to restrict the improvement of production efficiency, machining quality and automation level. The monitoring of the tool wear and breakage conditions on YCM-V116B machining center was studied, and the acquired milling sound signals were analyzed in detail. By means of the classical time-frequency analysis, it was discovered that the wear sound had its own characteristic frequency band, and the frequency component within the frequency band would change according to the change of wear conditions. So that the frequency component within the frequency band will be a good indicator to monitor the tool wear conditions excellently. On the other hand, the tool breakage sound is a random signal that a transient change in amplitude is produced probably when tool breaks. The tool breakage conditions can be detected exactly by the advantages of wavelet decomposition techniques. The analysis implies that the sound generated during the machining process can be used to monitor tool conditions, which provides a new approach to the sound applications in tool monitoring domain.

Instantaneous frequency decomposition: An application to spectrally sparse sounds with fast frequency modulations

Classical time-frequency analysis is based on the amplitude responses of bandpass filters, discarding phase information. Instantaneous frequency analysis, in contrast, is based on the derivatives of these phases. This method of frequency calculation is of interest for its high precision and for reasons of similarity to cochlear encoding of sound. This article describes a methodology for high resolution analysis of sparse sounds, based on instantaneous frequencies. In this method, a comparison between tonotopic and instantaneous frequency information is introduced to select filter positions that are well matched to the signal. Second, a cross-check that compares frequency estimates from neighboring channels is used to optimize filter bandwidth, and to signal the quality of the analysis. These cross-checks lead to an optimal time-frequency representation without requiring any prior information about the signal. When applied to a signal that is sufficiently sparse, the method decomposes the signal into separate time-frequency contours that are tracked with high precision. Alternatively, if the signal is spectrally too dense, neighboring channels generate inconsistent estimates-a feature that allows the method to assess its own validity in particular contexts. Similar optimization principles may be present in cochlear encoding.

Separability, positivity, and minimum uncertainty in time–frequency energy distributions

Gaussian signals play a very special role in classical time–frequency analysis because they are solutions of apparently unrelated problems such as minimum uncertainty, and positivity and separability of Wigner–Ville distributions. We investigate here some of the logical connections which exist between these different features, and we discuss some examples and counterexamples of their extension to more general joint distributions within Cohen’s class and the affine class.