Digital Autocorrelation Research Articles

Logarithmic Frequency Waveforms

This article introduces a new class of Doppler-tolerant and estimation-capable radar waveforms called logarithmic frequency waveforms (LFWs). These waveforms are created by mapping the magnitudes, phases, and spacing of good digital radar codes onto a set of carriers defined over a logarithmically warped frequency axis. This mapping preserves the digital code's desirable autocorrelation mainlobe-to-sidelobe ratio when matched filtering is done over the warped frequency variable. The logarithm converts the multiplicative Doppler shift into an additive translation of the code's autocorrelation; thus, the location of the matched filter output's maximum is used to estimate the waveform's Doppler shift. This applies even if the code is neither inherently Doppler tolerant nor Doppler detection capable. We introduce two major classes of LFWs, logarithmic frequency codes, and logarithmic frequency rulers. We numerically illustrate their ambiguity functions and compare their Doppler estimation performance in additive white Gaussian noise against the linear chirp (linear frequency modulated) outfitted with the extended matched filter and the hyperbolic-frequency-modulated waveform.

Geometrical optical transfer function: is it worth calculating?

In this paper, we explore the merit of calculating the geometrical optical transfer function (GOTF) in optical design by comparing the time to calculate it with the time to calculate the diffraction optical transfer function (DOTF). We determine the DOTF by numerical integration of the pupil function autocorrelation (that reduces to an integration of a complex exponential of the aberration difference function), 2D digital autocorrelation of the pupil function, and the Fourier transform (FT) of the point-spread function (PSF); and we determine the GOTF by the FT of the geometrical PSF (that reduces to an integration over the pupil plane of a complex exponential that is a scalar product of the spatial frequency and transverse ray aberration vectors) and the FT of the spot diagram. Our starting point for calculating the DOTF is the wave aberrations of the system in its pupil plane, and the transverse ray aberrations in the image plane for the GOTF. Numerical results for primary aberrations and some typical imaging systems show that the direct numerical integrations are slow, but the GOTF calculation by a FT of the spot diagram is two or even three times slower than the DOTF calculation by an FT of the PSF, depending on the aberration. We conclude that the calculation of GOTF is, at best, an approximation of the DOTF and only for large aberrations; GOTF does not offer any advantage in the optical design process, and hence negates its utility.

Relating wavefront error, apodization, and the optical transfer function: on-axis case: comment.

In a recent paper [J. Opt. Soc. Am. A31, 2476 (2014)JOAOD60740-323210.1364/JOSAA.31.002476], a linear expansion of the optical transfer function (OTF) of an imaging system in which the expansion coefficients are related to its wavefront errors has been developed. It is claimed that the OTF can be calculated quickly by using this approach. We provide instead closed-form basis functions that are not determined recursively. Numerical examples demonstrate that the OTF calculation by a digital autocorrelation of the pupil function is much faster regardless of the wavefront complexity.

Note: Laser Doppler velocimeter using a dual-longitudinal-mode laser source

This paper presents a new laser Doppler technique using a dual-longitudinal-mode He-Ne laser as the laser source. Theoretical analysis shows that the Doppler frequency is proportional with the frequency difference of the two modes. The Doppler frequency in this technique is very low compared with the one in the single-mode laser Doppler technique. The new laser Doppler technique can be used to measure high speed. Experiment results show that the Doppler frequency is only about 82 Hz while the measurement speed reaches 31.4 m∕s. The signal-to-noise ratio of the Doppler signal is improved by the technique of digital filter and digital autocorrelation.

Application of GIS for Evaluation and Design of Watershed Guidelines

We analyse the suitability of Government of India’s 2003 and 2008 common guidelines for prioritising micro-watersheds for restoration. These guidelines attempt to balance the need for improved hydraulic function with poverty alleviation and agricultural productivity. To do so, they provide a set of sub-criteria for prioritising micro-watersheds for treatment. We ranked the microwatersheds in the Kalivelli basin in South India based on these sub-criteria. We then compared the 2003 with the 2008 guidelines using GIS and spatial statistics. Visual inspection of the resulting digital maps and spatial autocorrelation analysis showed that individual sub-criteria within a guideline were highly positively auto correlated. Spatial cross-correlations using Mantels test between sub-criteria in the same guidelines produced negative results however. Very different watersheds would have been selected for treatment using the 2003 vs. the 2008 guidelines. While this could have been evidence that the 2008 guidelines were an improvement over the 2003 guidelines, comparing the planning outcomes did not support this conclusion. We conclude that criteria used to select micro-watersheds for hydrologic treatment should be re-formulated emphasizing efffcient resource use and improved hydraulic function prior to social and economic concerns. Finally, we argue that a combined GIS and spatial analysis approach is amenable to quickly evaluating watershed selection criteria as well as assessing post implementation outcomes.

Research on multipoint layer-type laser Doppler self-velocimeter

An idea of using a multipoint layer-type laser Doppler self-velocimeter (LDV) to offer velocity for the vehicle navigation system was proposed because the accelerometer had the error term generated by overload. The principle of measuring its own velocity with laser Doppler was expounded while a multipoint layer-type LDV was designed, and the Doppler signal was processed by the technique of tracking filter and digital autocorrelation. The result of theory and experiment showed that the multipoint layer-type dual-beam LDV system was suitable for measuring on rough road surfaces when the individual dual-beam LDV was in the status of out of focus. Low-frequency disturbance and some noises were eliminated by the tracking filter, and the residual noise was removed by digital autocorrelator so that the signal-to-noise ratio and the detection sensibility of the system was greatly improved. Comparing to the global position system, the relative accuracy of LDV is ~1.95%.

Cobble cam: grain‐size measurements of sand to boulder from digital photographs and autocorrelation analyses

AbstractA new application of the autocorrelation grain size analysis technique for mixed to coarse sediment settings has been investigated. Photographs of sand‐ to boulder‐sized sediment along the Elwha River delta beach were taken from approximately 1·2 m above the ground surface, and detailed grain size measurements were made from 32 of these sites for calibration and validation. Digital photographs were found to provide accurate estimates of the long and intermediate axes of the surface sediment (r2 > 0·98), but poor estimates of the short axes (r2 = 0·68), suggesting that these short axes were naturally oriented in the vertical dimension. The autocorrelation method was successfully applied resulting in total irreducible error of 14% over a range of mean grain sizes of 1 to 200 mm. Compared with reported edge and object‐detection results, it is noted that the autocorrelation method presented here has lower error and can be applied to a much broader range of mean grain sizes without altering the physical set‐up of the camera (∼200‐fold versus ∼6‐fold). The approach is considerably less sensitive to lighting conditions than object‐detection methods, although autocorrelation estimates do improve when measures are taken to shade sediments from direct sunlight. The effects of wet and dry conditions are also evaluated and discussed. The technique provides an estimate of grain size sorting from the easily calculated autocorrelation standard error, which is correlated with the graphical standard deviation at an r2 of 0·69. The technique is transferable to other sites when calibrated with linear corrections based on photo‐based measurements, as shown by excellent grain‐size analysis results (r2 = 0·97, irreducible error = 16%) from samples from the mixed grain size beaches of Kachemak Bay, Alaska. Thus, a method has been developed to measure mean grain size and sorting properties of coarse sediments. Copyright © 2009 John Wiley & Sons, Ltd.

On-The-Fly Observing System of the Nobeyama 45-m and ASTE 10-m Telescopes

Abstract We have developed a spectral line On-The-Fly (OTF) observing mode for the Nobeyama Radio Observatory 45-m and the Atacama Submillimeter Telescope Experiment 10-m telescopes. Sets of digital autocorrelation spectrometers are available for OTF with heterodyne receivers mounted on the telescopes, including the focal-plane 5$\times$5 array receiver, BEARS, on the 45-m. During OTF observations, the antenna is continuously driven to cover the mapped region rapidly, resulting in a high observing efficiency and accuracy. Pointing of the antenna and readouts from the spectrometer are recorded as fast as 0.1s. In this paper we report on improvements made to the software and instruments, requirements and optimization of observing parameters, the data-reduction process, and verification of the system. It is confirmed that, using optimal parameters, the OTF is about twice as efficient as the conventional position-switch observing method.

Mesospheric doppler wind measurements from Aura Microwave Limb Sounder (MLS)

This paper describes a microwave limb technique for measuring Doppler wind in the Earth’s mesosphere. The research algorithm has been applied to Aura Microwave Limb Sounder (MLS) 118.75 GHz measurements where the O 2 Zeeman lines are resolved by a digital autocorrelation spectrometer. A precision of ∼17 m/s for the line-of-sight (LOS) wind is achieved at 80–92 km, which corresponds to radiometric noise during 1/6 s integration time. The LOS winds from Aura MLS are mostly in the meridional direction at low- and mid-latitudes with vertical resolution of ∼8 km. This microwave Doppler technique has potential to obtain useful winds down to ∼40 km of the Earth’s atmosphere if measurements from other MLS frequencies (near H 2O, O 3, and CO lines) are used. Initial analyses show that the MLS winds from the 118.75 GHz measurements agree well with the TIDI (Thermosphere Ionosphere Mesosphere Energetics and Dynamics Doppler Interferometer) winds for the perturbations induced by a strong quasi 2-day wave (QTDW) in January 2005. Time series of MLS winds reveal many interesting climatological and planetary wave features, including the diurnal, semidiurnal tides, and the QTDW. Interactions between the tides and the QTDW are clearly evident, indicating possible large tidal structural changes after the QTDW events dissipate.

Thermal Hydraulic Criteria for Base-Triggered Vapor Explosion

Spontaneous vapor explosion can occur when a layer of high temperature molten material is deposited on a pool of water or on a moist floor. This is called a base-triggered vapor explosion. In order to clarify the micro-mechanism of base-triggered vapor explosions, an experimental apparatus was designed and constructed to observe the base-triggered vapor explosion from the bottom upwards. This experimental apparatus also allowed detailed observation of the microscopic behavior at the interface between the molten material and the water. The experiments used U-Alloy95 as a simulant material. As a result, it was found that water was trapped between molten material and the floor when the molten material droplet was released into the water and covered the floor. Particle imaging velocimetry (PIV) analysis and the digital auto-correlation method were applied to the observation images to evaluate the behavior of the molten material. The upward blowout velocity of the molten material was measured from the images observed from the side of the test section and the ratio of the kinetic energy to the thermal energy of the molten material was estimated from the blowout velocity.

Theoretical Design of Fibre-Based Digital Autocorrelator forCompletely Characterizing Ultrashort Pulses

A new idea to design fibre-based digital autocorrelation technique forcompletely characterizing ultrashort pulses is presented. Feasibilityof the design is demonstrated by theory. The technique is found topromise minimized optical alignment requirements, compactconfiguration, high time resolution, and short measurement time.

우주전파 관측용 400MHz 대역 자기 상관분광기 설계 및 제작

This paper is the research and development including the system design and the prototype system building of the 400MHz wide-band digital autocorrelation spectrometer system for radio astronomy observation, which will be used as back-end signal processing unit of the Dual channel SIS receiver at Taeduk Radio Astronomy Observatory. So in this paper, we performed development of the high speed digitizing sampler, the circular memory buffer, and the correlator module for the 400MHz wide-band digital autocorrelator. This developed system will be use at TRAO after the housing and some calibration.

The high resolution versatile digital spectrometer of HIFI-HSO

We present a versatile digital autocorrelation spectrometer designed to suit the needs of HIFI, the sub-millimeter heterodyne instrument of the ESAs HSO satellite. This spectrometer will offer a set of four observing modes with different “on-line resolution/total bandwidth” combinations. An original architecture, based on mixed gallium arsenide and silicon technologies, allowed us to realize a 512 channel, low-power consumption and high speed correlation module. We give some details on the optimization of the design (quantization scheme, readout format) performed to fit the HSO-HIFI requirements. We also describe an approach to distortion correction which takes into account the non-rigorous adjustment of the comparison thresholds of the spectrometer’s analog to digital converter. Up to now, the efficiency of a spectrometer has been described as depending only on the quantization scheme used. In this paper, we show that the efficiency varies within the spectrum and we introduce the “spectral efficiency”, which is connected to the input signal band shape.

A213 ベーストリガ蒸気爆発現象に関する研究

Spontaneous vapor explosion can occur when a layer of the high temperature molten material lies on the water pool or on the moisture floor. This is so-called base-triggered vapor explosion. This base-triggered vapor explosion is supposed to occur in the case of a severe accident in various facilities. It is very important to clarify the base-triggered vapor explosion from the viewpoints of the prediction and the prevention of the vapor explosion. In order to evaluate the behavior of the base-triggered vapor explosion, the experimental apparatus is designed and constructed. The experiments using U-Alloy95 as a simulating substance are conducted. Consequently, the behavior of the molten material can be observed in detail with this experimental apparatus. The digital auto-correlation method and PIV are also applied to the visual observation data obtained on the experiments in order to evaluate the velocity distribution of the molten material. Based on the velocity, the pressure at the vapor explosion is also evaluated.

Development of the SRAO 1024-Channel Digital Auto-Correlator

We developed a 1024-channel digital auto-correlation spectrometer for the Seoul Radio Astronomy Observatory (hereafter the SRAO-1KACS). The SRAO-1KACS has two main modules: the IF-to-baseband converter (IFBC) module and the 1024-channel auto-correlator (1KACR) module. The input frequency range of the IFBC module is from 1.5 to 1.55 GHz with a dynamic range of −4 ∼ +3 dBm. The 1KACR module performs calculations of auto-correlation coefficients by the ‘accumulation and modulo-2-counting method’ in 3-level configuration. The system is controlled by a Linux-based personal computer. The SRAO-1KACS provides 3 different observational modes: 50, 25, and 12.5 MHz bandwidth modes. The channel losses are 20%, 12%, and 8% for each bandwidth mode, respectively. Various tests were executed including lab tests and astronomical tests. Lab tests were performed for a 1.5625MHz sinusoidal wave input and for a white noise source. We also executed astronomical tests in 12CO J=1−0 emission line at 115.2712 GHz, which showed that SRAO-1KACS can be used at astronomical observatories.

400MHz 광대역 디지털 자기상관분광기 설계연구

본 연구에서는 전파천문 관측연구 분야에서 외부은하의 스펙트럼 선 관측연구와 특정 전파원의 조사 관측을 위해서 필요한 광대역 디지털 자기상관분광기 시스템을 연구 개발하기 위 한 설계 연구를 수행하였다. 본 연구에서 설계되는 자기상관분광기는 기존의 시스템과는 달리 신호 입력에 대한 입력전력의 동적 범위와 입력 주파수 범위를 확대하여 어떤 시스템의 전파 분광기로도 자유롭게 사용할 수 있도록 하였다. 또한 신호의 샘플링 방식 또한 일반의 신호 검출기와는 다르게 aliasing 샘플링 방식을 사용하여, 대역 손실을 최소화하고 있으며, 상관기를 통과한 신호에 대해서는 전용의 DSP소자를 이용하여, 적분 및 퓨리에 변환 등을 하드웨어적으로 처리하도록 하여 그 신호 처리속도를 빠르게 설계하여, 최근에 많은 연구가 진행되는 우주전파 관측연구인 “On the fly”방식 등의 측정 방식을 지원할 수 있도록 설계하였다. In this paper, we performed the design study of a wide-band digital autocorrelation spectrometer for the observation study of an extra-galaxy's spectral lines and the survey research of the special radio sources in field of the radio astronomy observational research. The autocorrelation spectrometer designed in this paper can be used to their spectrometer of any system because this spectrometer has a wide dynamic power and frequency range properties. In this system we use the aliasing sampling method to minimize the band loss. For the output signal of the correlator we can increase the signal processing speed using by a special DSP chip, the integration and the FFT using hardware, so this spectrometer can support the newest developed technique for the radio astronomy observation so called “On the fly” method.

Real-time, high velocity-resolution color Doppler optical coherence tomography

Color Doppler optical coherence tomography (CDOCT) is a noninvasive optical imaging technique for micrometer-scale physiological flow mapping simultaneously with morphological optical coherence tomography imaging. We have developed a novel CDOCT signal-processing strategy capable of imaging physiological flow rates at 8 frames/s. Our new strategy features hardware-implemented digital autocorrelation across subsequent scans, permitting us to measure 300-Hz-8-kHz Doppler shifts upon signals of 0.6-MHz bandwidth. The performance of the CDOCT system was demonstrated in a flow phantom and in vivo in Xenopus laevis.

Early Detection of Fatigue Damage Through Ultrasonic Non-Destructive Evaluation—Part II: Experimental

Abstract Ultrasonic wave velocities (longitudinal and transverse waves) and the attenuation coefficient were used to investigate damage of aluminum 7075-T651 before and after progressive stages of fatigue. Repeated observations under controlled conditions allied to digital signal acquisition, autocorrelation, and regression were used to estimate small velocity and attenuation changes. Although comparatively small uncertainties were observed, the feasibility of utilizing the velocity of ultrasonic waves as a fatigue monitor was not substantiated under actual research conditions. However, careful measurements of the ultrasonic attenuation parameter demonstrated its potential to provide an early assessment of damage during fatigue. Part I of this work discussed the theoretical approach and described the fatigue testing procedures adopted in this investigation. This is a presentation and discussion of the experimental results.

Barrel swirl breakdown in spark-ignition engines: Insights from particle image velocimetry measurements

Particle image velocimetry (PIV) has been used here to study the formation and breakdown of barrel swirl (‘tumble’) in a production geometry, four-stroke, four-valve, motored, spark-ignition, optically accessed internal combustion (IC) engine. The barrel swirl ratio (BSR) of the cylinder head could be enhanced by means of a port face inducer gasket so that the flow processes taking place at low and high swirl ratios could be investigated conveniently. Double-exposed images from planes both parallel and perpendicular to the cylinder axis were recorded at selected crank angles through the induction and compression strokes at a motored engine speed of 1000 r/min, with a wide open throttle, for both high and low BSR cases. The recorded images were interrogated by digital autocorrelation to give two-dimensional maps of instantaneous velocity. In both high and low BSR cases, a barrel or tumbling vortex motion is generated during induction, which is shown to persist throughout the majority of the compression stroke. The details of barrel swirl formation during induction and its subsequent modification during compression, however, differ strongly between the two cases. These differences can be explained qualitatively in terms of two main events; the first being competition during induction between vortices of unequal strength and the second being competition between the large-scale swirl motion and the local flow field generated by piston motion during compression. In the low barrel swirl case, significant dissipation occurs owing to these interactions and consequently the large-scale motion exhibits lower mean velocities and undergoes significant distortion. In the case of high BSR, the competition effects are minimized and a single ordered vertical vortex exhibiting high velocity magnitudes is observed to avoid piston induced distortion. It then moves into the apex of the pent roof combustion chamber where it survives as a single ordered vortex until at least 40° crank angle (CA) before top dead centre (TDC). Limitations and developments of the PIV technique are discussed.

Particle image velocimetry analysis of IC engine in-cylinder flows

This paper discusses the use of particle image velocimetry for measuring in-cylinder flows in multi-valve IC engines. The techniques and their limitations are discussed with special reference to the study of large-scale flow structures in a four valve optical IC engine exhibiting significant barrel swirl. Examples of velocity vector maps derived by digital autocorrelation are presented for a range of crank angles through the induction and compression strokes from both horizontal and vertical measurement planes. The evident strengths and limitations of the current technique for in-cylinder applications are discussed with respect to spatial resolution, velocity gradients and dynamic range. Recent developments for overcoming the limitations are also reviewed.