Piecewise Linear Frequency Research Articles

Magneto-acousto-electrical tomography using nonlinearly frequency-modulated ultrasound.

Objective. In this study, nonlinearly frequency-modulated (NLFM) ultrasound was applied to magneto-acousto-electrical tomography (MAET) to increase the dynamic range of detection.Approach. Generation of NLFM signals using window function method-based on the principle of stationary phase-and piecewise linear frequency modulation method-based on the genetic algorithm-was discussed. The MAET experiment systems using spike, linearly frequency-modulated (LFM), or NLFM pulse stimulation were constructed, and three groups of MAET experiments on saline agar phantom samples were carried out to verify the performance-respectively the sensitivity, the dynamic range, and the longitudinal resolution of detection-of MAET using NLFM ultrasound in comparison to that using LFM ultrasound. Based on the above experiments, a pork sample was imaged by ultrasound imaging method, spike MAET method, LFM MAET method, and NLFM MAET method, to compare the imaging accuracy.Main results. The experiment results showed that, through sacrificing very little main-lobe width of pulse compression or equivalently the longitudinal resolution, the MAET using NLFM ultrasound achieved higher signal-to-interference ratio (and therefore higher detection sensitivity), lower side-lobe levels of pulse compression (and therefore larger dynamic range of detection), and large anti-interference capability, compared to the MAET using LFM ultrasound.Significance. The applicability of the MAET using NLFM ultrasound was proved in circumferences where sensitivity and dynamic range of detection were mostly important and slightly lower longitudinal resolution of detection was acceptable. The study furthered the scheme of using coded ultrasound excitation toward the clinical application of MAET.

A Novel Range-Azimuth Joint Modulation Scheme for Range Ambiguity Suppression

Range ambiguity is a technical challenge for current spaceborne synthetic aperture radar (SAR) systems. To this end, a novel range-azimuth joint modulation transmission scheme is proposed, and the corresponding imaging processing and performance analysis are detailed. Compared with the azimuth phase coding (APC) technique, this scheme fully exploits the sampling margins of the range and azimuth dimensions, resulting in the range ambiguities experiencing a double suppression effect. Starting from the range-azimuth joint modulation scheme, to obtain the best ambiguity suppression performance, the design of a nonlinear frequency modulation (NLFM) waveform with a continuous piecewise linear instantaneous frequency is formulated and tackled via a MATLAB optimization toolbox. The detailed simulation results based on LuTan-1 (LT-1) parameters illustrate that the proposed methodologies outperform the APC method and provide considerable ambiguity suppression.

Quasi-Orthogonal Waveforms for Ambiguity Suppression in Spaceborne Quad-Pol SAR

This article deals with the synthesis and analysis of quasi-orthogonal nonlinear frequency modulation (NLFM) waveforms to mitigate the impairments of ambiguous returns in quadrature-polarimetric (quad-pol) synthetic aperture radars (SARs). To this end, focusing on signals with a continuous piecewise linear instantaneous frequency, the design of a waveform pair exhibiting both a low cross correlation energy (CCE) and low peak to sidelobe ratios (PSLRs), is considered. To handle the resulting nondeterministic polynomial (NP) hard problem, a coordinate descent (CD) method is employed, where, at each step, the marginal minimization is tackled via a MATLAB optimization toolbox. Hence, transmission/reception schemes jointly capitalizing quasi-orthogonal NLFM waveforms and azimuth phase coding (APC) techniques are proposed to suppress ambiguity interference. Moreover, a systematic framework for the evaluation of the resulting azimuth ambiguity-to-signal ratio (AASR) and range ambiguity-to-signal ratio (RASR) is provided. Finally, detailed simulation experiments based on the LuTan (LT-1) parameters are carried out to verify the practicability and effectiveness of the newly proposed transceiver schemes.

Design of an Optimal Piece-Wise Spline Wigner-Ville Distribution for TFD Performance Evaluation and Comparison

This paper proposes a new performance evaluation process for time-frequency distributions (TFD) by designing a reference optimal TFD and novel accuracy and resolution measures. The motivation comes from the need for a TFD performance evaluation method that is objective, capable of quantifying the TFD accuracy and resolution, can determine the performance difference among different TFDs, and suitable for signals with an arbitrary number of components, instantaneous frequency and amplitude. We formulate the proposed optimal TFD, namely the piece-wise spline Wigner-Ville distribution (PW-WVD), by decomposing a standard non-stationary signal model using piece-wise linear frequency modulated (LFM) basis and by exploiting the Wigner-Ville distribution optimality for LFM signals. We compare the designed PW-WVD to conventional optimal TFDs and show that the former is more suitable to serve as a reference for TFD performance evaluation. Using the PW-WVD we derive TFD accuracy and resolution measures, compare them to conventional approaches, and analyze their sensitivity to form a TFD selection criteria. We evaluate the accuracy and resolution of twelve different TFDs and develop precise TFD selection strategies with or without prior information on the signal parameters. Results indicate that the compact kernel distribution is the best performing TFD given no prior information on the signal parameters and different TFDs must be selected upon the availability of prior information.

New Chaotic Oscillator Derived from Class C Single Transistor-Based Amplifier

This paper describes a new autonomous deterministic chaotic dynamical system having a single unstable saddle-spiral fixed point. A mathematical model originates in the fundamental structure of the class C amplifier. Evolution of robust strange attractors is conditioned by a bilateral nature of bipolar transistor with local polynomial or piecewise linear feedforward transconductance and high frequency of operation. Numerical analysis is supported by experimental verification and both results prove that chaos is neither a numerical artifact nor a long transient behaviour. Also, good accordance between theory and measurement has been observed.

CDMA-MIMO Radar With the Tansec Waveform

This work addresses code division multiple access (CDMA) implementation of automotive multiple-input multiple-output (MIMO) radars. The tansec frequency modulation (TSFM) is proposed as a single intracoding scheme for CDMA-MIMO radars. The properties of the TSFM coding family are analyzed and two novel codeword selection algorithms are proposed. The TSFM is compared to a variety of coding families by evaluating their autocorrelation and cross-correlation properties. The considered coding families are based on phase coding: Hadamard, Gold, optimal peak to sidelobe; and frequency coding: piecewise linear frequency modulated. Properties of the coding families are analyzed with a variety of novel criteria, which are especially useful for CDMA-MIMO radars. The performance of the CDMA-MIMO radar with different coding families is evaluated via simulations of practical multitarget automotive scenarios. It is shown that the frequency-based TSFM coding family outperforms the other considered coding families in terms of their cross-correlation properties.

Photonic chirp rates estimator for piecewise linear frequency modulated waveforms based on photonic self-fractional Fourier transform

This paper reports a photonic chirp rates estimator for the piecewise linear frequency modulated waveforms (PLFMWs). The estimator is based on the photonic self-fractional Fourier transform (FrFT) by utilizing the input PLFMW as the transform kernel. In this way, the self-FrFT operation can be finished with short latency time and the chirp rates of all LFM sub-pulses can be retrieved according to their fractional frequencies. In experiment, the chirp rates estimation of a four-stage PLFMW is performed. The measurement range from -964.47 GHz/µs to 50.76 GHz/µs with resolution of 0.0518 GHz/µs is demonstrated for the experimental system. And the absolute measurement error within ±0.06 GHz/µs and the relative measurement error less than 2% is also obtained.

Performance Analysis of NLFM Signals with Doppler Effect and Background Noise

This paper focuses on the study of effect of background noise and Doppler Effect on various Nonlinear Frequency Modulation (NLFM) waveforms designed using two stage piece-wise and three stage piece-wise linear and non linear functions. The background noise investigated is Additive White Gaussian Noise (AWGN). Simulations are carried out for different target speeds ranging from 100 to 5000km/hour to study Doppler Effect. The simulations are carried out using Matlab software. Among the waveforms designed, the NLFM function designed using two piece-wise Linear Frequency Modulation (LFM) is observed to be Doppler tolerant and also not affected by noise, as the SNR changes from -20 to 20 dB the peak side-lobe level (PSL) of this signal is around -34.84 dB.

Research of Mobile Underwater Acoustic Communication of M-Ary Combining FDM and Piecewise-LFM

Aiming at the countering doppler shift, a mobile underwater acoustic communication scheme of M-ary via FDM-PLFM is proposed. The cross-correlation between piecewise linear frequency modulation(PLFM) and traditional LFM signal is analyzed based on the cross-correlation function. Combining with frequency division multiplexing(FDM), the spectrum utilization of traditional underwater acoustic LFM communication scheme is improved. With the underwater acoustic LFM communication scheme, the new scheme does not require the doppler frequency shift compensation at the low doppler shift. The simulation results show that the present scheme has lower bit error rate than that for the traditional underwater acoustic M-ary LFM communication method under higher data rate conditions.

Transmit beampattern design for coherent FDA by piecewise LFM waveform

In transmit beampattern design, it is desirable to maximize the power around locations of interest. Multiple-input multiple-output (MIMO) radar transmits orthogonal waveforms, which is hardly achievable in practical applications. Moreover, the constant modulus constraint and the computational burden limit the system performance. In this paper, we propose an effective piecewise linear frequency modulation (PLFM) waveform for coherent frequency diverse array (FDA) radar to synthesize the desired transmit beampattern. By deriving the relationship between the beam direction and the transmit signal frequency, we find that different sub-band of transmitted signal corresponds to different angular sector. With the relationship between frequency band and mainlobe of beampattern, the beampattern synthesis is transformed into the design of waveform spectrum which is realized by designing the PLFM waveform in this paper. Compared with the state-of-the-art technique, the proposed PLFM waveform in coherent FDA enjoys the advantage of the constant modulus, low sidelobe level and reduced computation complexity. In addition, the multi-dimensional ambiguity function and the transmit beampattern response are derived to examine the properties. Numerical results are presented to validate the effectiveness of the proposed method.

Bode Plots Revisited: a Software System for Automated Generation of Piecewise Linear Frequency Response Plots

The paper presents an algorithm for automatic generation of piecewise linear Bode plots. The algorithm is complete in the sense it covers for all posible locations of poles and zeros of transfer functions, including unstable poles and poles and zeroes at the imaginary axis. The starting transfer function is factored into a canonical form, and thirteen elementary transfer function types are defined by their canonical forms. The thirteen elementary transfer function types are shown to be derived from just five generic transfer function types, and piecewise linear Bode plots are defined and depicted for all five of the generic types. For all thirteen elementary transfer function types the nodes they introduce in the piecewise linear plots are specified, as well as the algorithms how they affect the node altitudes. Finally, a three stage algorithm that produces both the Bode plots and the exact numerically computed frequency response plots is described. The algorithm is implemented in a command line based program, illustrated in a filter example, and future work directions are indicated, aiming a graphical user interface and integration of the program to a linear system symbolic analysis software suite.

Refining the ambiguity domain characteristics of non-stationary signals for improved time–frequency analysis: Test case of multidirectional and multicomponent piecewise LFM and HFM signals

This paper aims at providing a more accurate description of the ambiguity domain characteristics of a piecewise multicomponent non-stationary signals with focus on piece-wise linear frequency modulated (LFM) (PW-LFM) signal and a mixed LFM and hyperbolic FM (HFM). The main motivation comes from the observed PW-LFM nature of several real life signals. It is essential that the characteristics of these types of signals be taken into account for the design of high resolution Time–Frequency Distributions (TFDs) and therefore to improve the application and interpretation of time–frequency signal analysis and processing. In this paper the ambiguity function (AF) of a general PW-LFM signal is derived exactly and then analyzed to deduce important properties. The precise location and behavior of both auto-terms and cross-terms of a general piecewise LFM signal can be deduced from its AF. Numerical simulations using different types of test signals confirm the analytical derivations. An extension of the PW-LFM test signal is also presented by using HFM signals. For such signals, the exact analytical expression of auto-terms is given as well as the expression of cross-terms between HFM and LFM. The results obtained can be used in future studies to design more advanced quadratic time–frequency distributions (QTFDs) that exhibit improved properties in terms of resolution and accuracy.

A new feature for the classification of non-stationary signals based on the direction of signal energy in the time–frequency domain

The detection of seizure activity in electroencephalogram (EEG) segments is very important for the classification and localization of epileptic seizures. The evolution of a seizure in an EEG usually appears as a train of non-uniformly spaced spikes and/or as piecewise linear frequency modulated signals. If a seizure is present, then the energy of the EEG is concentrated along the time axis and the frequency axis in the time–frequency plane. However, in the absence of a seizure, the energy of the EEG signal is uniformly distributed along all directions in the time–frequency plane. Based on this observation, we propose a new approach for the detection of a seizure. In this paper, we develop a new feature that exploits the direction of the energy of the signal in the time–frequency domain to distinguish between seizures and non-seizures in an EEG. Our experimental results indicate the superiority of the proposed approach over other conventional time–frequency approaches; for example, the proposed feature set achieves a classification accuracy of 98.25% by only using five features.

Detection of low-velocity and floating small targets in sea clutter via income-reference particle filters

In this paper, an adaptive composite generalized likelihood ratio test (GLRT) detector using the forward-backward income-reference particle filter (FB-IRPF) for signal estimation is proposed to detect low-velocity and floating small targets in high-resolution sea clutter. In integration duration of the order of seconds, target returns with nonlinear Doppler modulation and amplitude slow fluctuation are parameterized by a piecewise linear frequency modulated (PW-LFM) model equipped by a two-dimensional dynamic system of unknown statistics. Correspondingly, temporal nonstationary sea clutter time series is modelled into a piecewise spherical invariant random vector (PW-SIRV) sequences. By introducing the optimal test statistic at each piece as the user-defined cost and embedding it into the route of the forward-backward cost-reference particle filter (FB-CRPF), the FB-IRPF is developed to estimate the state sequence of a PW-LFM signal and to integrate its income at all the pieces. Using the integrated income as the test statistic, the adaptive composite GLRT is derived. It is compared with the fractal-based detector and tri-feature-based detector in a recognized sea clutter dataset for small target detection. The results show that the proposed detector attains better overall detection performance and is complementary with the tri-feature-based detector to some extent.

An Improved Design of High-Resolution Quadratic Time–Frequency Distributions for the Analysis of Nonstationary Multicomponent Signals Using Directional Compact Kernels

This paper presents a new advanced methodology for designing high resolution time–frequency distributions (TFDs) of multicomponent nonstationary signals that can be approximated using piece-wise linear frequency modulated (PW-LFM) signals. Most previous kernel design methods assumed that signals auto-terms are mostly centered around the origin of the $(\nu,\tau)$ ambiguity domain while signal cross-terms are mostly away from the origin. This study uses a multicomponent test signal for which each component is modeled as a PW-LFM signal; it finds that the above assumption is a very rough approximation of the location of the auto-terms energy and cross-terms energy in the ambiguity domain and it is only valid for signals that are well separated in the $(t,f)$ domain. A refined investigation led to improved specifications for separating cross-terms from auto-terms in the $(\nu,\tau)$ ambiguity domain. The resulting approach first represents the signal in the ambiguity domain, and then applies a multidirectional signal dependent compact kernel that accounts for the direction of the auto-terms energy. The resulting multidirectional distribution (MDD) approach proves to be more effective than classical methods like extended modified B distribution, S-method, or compact kernel distribution in terms of auto-terms resolution and cross-terms suppression. Results on simulated and real data validate the improved performance of the MDD, showing up to 8% gain as compared to more standard state-of-the-art TFDs.

Piecewise-Linear Frequency Shifting Algorithm for Frequency Resolution Enhancement in Digital Hearing Aids

In human hearing, frequency resolution is a term used to determine how well the ear can separate and distinguish two sounds that are close in frequency. This capability of breaking speech sounds into various frequency components plays a key role in processing and understanding speech information. In this paper, a piecewise-linear frequency shifting algorithm for digital hearing aids is proposed. The algorithm specifically aims at improving the frequency resolution capability. In the first step, frequency discrimination thresholds are processed by a computer testing software. Then, the input signal is parsed through the proposed piecewise-linear frequency shifting algorithm, which comprises of linearly stretching and compressing the frequency content at different frequency ranges. Experimental results showed that by using the proposed frequency shifting algorithm, the separation of formant tracks was increased in the stretching region and slightly squeezed in the adjacent compression region. Subjective assessment on six hearing-impaired persons with V-shaped audiograms demonstrated that nearly a 10% improvement of speech discrimination score was achieved for monosyllabic word lists tested in a quiet acoustic setting. In addition, the speech reception threshold was also improved by 2~8 dB when disyllabic word listswere tested in a noisy acoustic scenario.

Piecewise LFM waveform for MIMO radar

To separate the received signals in a multiple-input multiple-output (MIMO) radar, the transmitted signals should be orthogonal or have a low cross-correlation level. Some other properties, such as low autocorrelation sidelobes, high range resolution, and good Doppler tolerance are also desired. However, they are difficult to achieve simultaneously. In general, an improved criterion is at the cost of another degraded one. In this paper, we propose a piecewise linear frequency modulation (PLFM) waveform for the MIMO radar. The transmitted signals are pulse trains, including diversified subpulses, which are divided into three segments with controllable durations and bandwidths. The duration sequence of the second segment is obtained by the genetic algorithm to optimize the cross correlation. Theoretical analyses and numerical results are presented to illustrate the properties of the proposed PLFM waveform. Compared with the polyphase coding and the discrete frequency coding waveforms, the PLFM waveform has a lower cross-correlation level and higher degrees of freedom. The relationship of the bandwidths among different segments can be used to adjust the sidelobe peak and the main lobe width of the autocorrelation function.

Integrating speaker-nonspecific timbre transformation to an HNM-based speech synthesis scheme

In this article, a speech signal synthesis scheme based on harmonic-plus-noise model (HNM) is extended to provide the function of speaker-nonspecific timbre transformation. To transform synthetic speech's timbre, we have developed a formant-based frequency mapping method called piece-wise linear frequency mapping (PLFM). Additionally, a commonly adopted method is frequency axis scaling (FAS). Both methods have been integrated into the HNM-based signal synthesis scheme, and a real-time speech synthesis system has been implemented according to this scheme. Using the speech files synthesized, perception tests are conducted. The results show that the proposed scheme can indeed transform the source timbre of a female adult into the timbre of a male adult, boy, or girl. In addition, the method PLFM is shown to be better than FAS in obtaining more masculine timbre.

Sparse Detection in the Chirplet Transform: Application to FMCW Radar Signals

This paper aims to detect and characterize a signal coming from frequency modulation continuous wave radars. The radar signals are made of piecewise linear frequency modulations. The maximum chirplet transform (MCT), a simplification of the chirplet transform is proposed. A detection of the relevant maximum chirplets is proposed based on iterative masking, an iterative detection followed by window subtraction that does not require the recomputation of the spectrum. This detection is designed to provide a sparse subset of maximum chirplet coefficients. The chirplets are then gathered into linear chirps whose starting time, length, and chirprate are estimated. These chirps are then gathered again back into the different frequency modulation continuous wave signals, ready to be classified. An illustration is provided on synthetic data.

Newborn EEG Seizure Detection Using Time-Frequency Matched Filtering

Abstract Background: The analysis of Electroencephalography (EEG) signals acquired from epileptic babies shows that seizures can be modeled as piecewise linear frequency modulated (LFM) signals. This fact motivated the use of time-frequency matched filters (TFMFs) for seizure detection in newborn EEG. A TFMF is characterized by a unique test statistic, which is found based on the time-frequency (TF) correlation between the signal under analysis and a template. The test statistic is compared with a threshold to determine the presence or absence of the template in the signal under analysis. Objectives: We present two seizure detection algorithms based on the general class of TFMFs and an improved algorithm in the ambiguity domain and evaluate their performance using real EEG signals. Methods: The method includes the following stages: Based on TF analysis of newborn EEG, we create a template set containing M piecewise LFM signals with L pieces and slopes. We define test statistics based on the TF correlation...