Low Time-bandwidth Product Research Articles

Evaluation of the Prolate Spheroidal Wavefunctions via a Discrete-Time Fourier Transform Based Approach

Computation of prolate spheroidal wavefunctions (PSWFs) is notoriously difficult and time consuming. This paper applies operator theory to the discrete Fourier transform (DFT) to address the problem of computing PSWFs. The problem is turned into an infinite dimensional matrix operator eigenvalue problem, which we recognize as being the definition of the DPSSs. Truncation of the infinite matrix leads to a finite dimensional matrix eigenvalue problem which in turn yields what is known as the Slepian basis. These discrete-valued Slepian basis vectors can then be used as (approximately) discrete time evaluations of the PSWFs. Taking an inverse Fourier transform further demonstrates that continuous PSWFs can be reconstructed from the Slepian basis. The feasibility of this approach is shown via theoretical derivations followed by simulations to consider practical aspects. Simulations demonstrate that the level of errors between the reconstructed Slepian basis approach and true PSWFs are low when the orders of the eigenvectors are low but can become large when the orders of the eigenvectors are high. Accuracy can be increased by increasing the number of points used to generate the Slepian basis. Users need to balance accuracy with computational cost. For large time-bandwidth product PSWFs, the number of Slepian basis points required increases for a reconstruction to reach the same error as for low time-bandwidth products. However, when the time-bandwidth products increase and reach maximum concentration, the required number of points to achieve a given error level achieves steady state values. Furthermore, this method of reconstructing the PSWF from the Slepian basis can be more accurate when compared to the Shannon sampling approach and traditional quadrature approach for large time-bandwidth products. Finally, since the Slepian basis represents the (approximate) sampled values of PSWFs, when the number of points is sufficiently large, the reconstruction process can be omitted entirely so that the Slepian vectors can be used directly, without a reconstruction step.

Assessing the Effectiveness of Generalized Likelihood Ratio Test Detector Schemes in Seismic Event Detection and the Avoidance of Nontarget Signals

ABSTRACT Cross-correlation techniques have played a long-standing and pivotal role in seismic event monitoring. However, the performance of correlation-based detectors is challenged by nuisance seismicity, or nontarget signals. Such detections are a problem when the mission is to automatically map events to the correct source region. Using aftershocks of the 2014 Mw 6.0 South Napa, California, earthquake, we demonstrate the effectiveness of utilizing a dynamic correlation processor framework in a generalized likelihood ratio test (GLRT) detector configuration to minimize nontarget detections. A GLRT maximizes a detection statistic with respect to one or more unknown parameters. In this case, the detection statistic is a template signal match against the waveform in a window sliding over a data stream, and the unknown parameter is an index variable indicating group membership of the template event or events. Detected events are assigned to the event group that yields the largest detection statistic. Our results show that a GLRT detector will outperform a suite of independently operating correlation and subspace detectors in terms of having a lower nontarget detection rate at a given missed detection rate. We also show that a GLRT detector composed of a few high-rank subspace detectors has a slightly higher nontarget detection rate, but a significantly lower missed detection rate, than a GLRT detector composed of many low-rank subspace detectors. The high-rank GLRT configuration produced impressive results even with marginal data (single channel, single station, and very low time bandwidth product), which bodes well for the utility of building efficient aftershock classification systems and global monitoring systems at larger scales. However, future work is required to assess performance at the regional scale and to assess the performance of the system at detecting target events not used in the detector template creation.

Minimum TR radiofrequency-pulse design for rapid gradient echo sequences.

A framework to design radiofrequency (RF) pulses specifically to minimize the TR of gradient echo sequences is presented, subject to hardware and physiological constraints. Single-band and multiband (MB) RF pulses can be reduced in duration using variable-rate selective excitation (VERSE) VERSE for a range of flip angles; however, minimum-duration pulses do not guarantee minimum TR because these can lead to a high specific absorption rate (SAR). The optimal RF pulse is found by meeting spatial encoding, peripheral nerve stimulation (PNS) and SAR constraints. A TR reduction for a range of designs is achieved and an application of this in an MB cardiac balanced steady-state free-precession (bSSFP) experiment is presented. Gradient imperfections and their imaging effects are also considered. Sequence TR with low-time bandwidth product (TBP) pulses, as used in bSSFP, was reduced up to 14%, and the TR when using high TBP pulses, as used in slab-selective imaging, was reduced by up to 72%. A breath-hold cardiac exam was reduced by 46% using both MB and the TR-optimal framework. The importance of RF-based correction of gradient imperfections is demonstrated. PNS was not a practical limitation. The TR-optimal framework designs RF pulses for a range of pulse parameters, specifically to minimize sequence TR.

Optimal Amplitude Weighting for Near-field Passive Source Localization

In this paper, an optimal amplitude weight expression is derived and presented in closed form. The minimal error variance for location estimation of a near-field source signal that has a low time-bandwidth product is also presented. A noniterative method to calculate and apply weights is proposed to yield more robust estimation results at a lower calculational cost when compared to the traditional iterative method. Besides a theoretical evaluation, the proposed algorithm is also verified through Monte Carlo simulation. The weight expression derived also optimizes the system signal-to-noise ratio (SNR), hence it can be applied to improve the performance of any estimator/detector that utilizes the energy in the sum of sensor output signals.

Observation of Harmonic-Mode-Locking in a Mode-Locked InAs/InP-Based Quantum-Dash Laser With CW Optical Injection

We report tunable harmonic mode-locking in continuous-wave (CW) optically injected InAs/InP quantum-dash lasers emitting at 1.56 μm. The frequency of generated microwave pulses is twice the laser's self-mode-locked frequency. Autocorrelation traces show Gaussian pulses with low time-bandwidth product ( ≈0.6). Mapping of the dynamics shows that this coherent microwave oscillation (MWO) region has maximum locking range ≈600 MHz (≈5 pm). Measurement of the optical linewidth of each individual mode at this regime shows strong narrowing relative to free running values by two orders of magnitude. The RF linewidth of the generated signal is ≈160 kHz confirming the coherence among the optical modes and low timing jitter.

Formation of low time-bandwidth product, single-sided exponential optical pulses in free-electron laser oscillators

The detailed shape of picosecond optical pulses from a free-electron laser (FEL) oscillator has been studied for various cavity detunings. For large values of the cavity detuning the optical pulse develops an exponential leading edge, with a time constant proportional to the applied cavity detuning and the quality factor of the resonator. This behavior has been observed at two separate FELs that have completely different resonator layouts and electron beam characteristics, and using different methods of optical pulse length measurement. The optical pulses have a full width at half maximum time-bandwidth product Deltat(FWHM)Deltaf(FWHM) of 0.2-0.3. The results presented here can be used to predict the optical pulse length and corresponding minimum spectral width that can be generated in a FEL pumped by short electron bunches. This is important for the design of new infrared free-electron laser user facilities, which need to make a balanced choice between short pulses for high temporal resolution and narrow bandwidth for linear and nonlinear spectroscopy.

On resolving 2M-1 narrow-band signals with an M sensor uniform linear array

The problem of determining the maximum number of narrowband signals whose parameters can be estimated with a linear array of M equally spaced sensors is examined. While this number previously has been taken to be M-1 when the signals are mutually uncorrelated, it is shown how to estimate directions and amplitudes for as many as 2M-1 signals. This over twofold increase is accomplished by retaining snapshot-to-snapshot phase information usually lost in algorithms based on spatial correlation matrices. The approach uses length 2M real signal vectors rather than the usual M complex vectors. It is shown that 2M of these real vectors are linearly independent with probability one, and, thus, in the presence of additive white noise, the parameters of 2M-1 signals can be estimated. An algorithm for determining directions and amplitudes is presented. Because of the algorithm's computational complexity, its application is limited to small M and low time-bandwidth products.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Sidelobe Suppression in Low and High Time-Bandwidth Products of Linear FM Pulse Compression Filters

The peak sidelobe suppression of unweighed linear FM surface acoustic wave filters limits the dynamic range of pulse compression systems. Using a discrete inverse Fourier transform "sampling technique" and complex Fresnel integral algorithms, this paper extends previous results of other authors from a time-bandwidth product of 50 up to the high value of 720. In the present work, the weighting is applied in the frequency domain, employing an external Hamming weighting function. The output waveforms are determined for different sampling rates. The results show that a peak sidelobe suppression of -38 dB from the main Iobe is achieved for high time-bandwidth product (TB = 720) at a sampling rate of 512 with broadening in the main lobe, while it is -41 dB for a low time-bandwidth product of TB = 50. Also, the paper contains charts showing the sidelobe suppression of unweighed and Hamming externally weighted linear FM pulse compression filters at different values of time-bandwidth products TB (50,100,250,370,510,720) with different central frequencies, dispersion times, and bandwidths B. The skirt steepness, sidelobe ripple rejection, Gibbs ripples of the wave spectrum, reduction of the insertion loss, and suppression of Fresnel ripples are also compared.

Effect of Fresnel ripples on sidelobe suppression in low time-bandwidth product linear FM pulse compression

Effect of Fresnel ripples on sidelobe suppression in low time-bandwidth product linear FM pulse compression

The Calculation of the Statistical Properties of the Synchronization Times in a PN Spread Spectrum System for Minimized Acquisition Time Designs

This paper presents a method to calculate the mean acquisition time and the mean time to lose lack in a pseudonoise (PN) spread spectrum system. In addition, all the desired statistical moments of these synchronization times can be evaluated. The theory is applied to optimize the acquisition process in a system with a low time-bandwidth product of the synchronization detector. The results demonstrate the dependence of the synchronization times on the information signal and permit optimum design of the synchronization detector.