Two-dimensional Frequency Spectrum Research Articles

Accurate Range Modeling for High-Resolution Spaceborne Synthetic Aperture Radar.

Spaceborne synthetic aperture radar (SAR) is an advanced microwave imaging technology that provides all-weather and all-day target information. However, as spaceborne SAR resolution improves, traditional echo signal models based on airborne SAR design become inadequate due to the curved orbit, Earth rotation, and increased propagation distance. In this study, we propose an accurate range model for high-resolution spaceborne SAR by analyzing motion trajectory and Doppler parameters from the perspective of the space geometry of spaceborne SAR. We evaluate the accuracy of existing range models and propose an advanced equivalent squint range model (AESRM) that accurately fits the actual range history and compensates for high-order term errors by introducing third-order and fourth-order error terms while maintaining the simplicity of the traditional model. The proposed AESRM's concise two-dimensional frequency spectrum form facilitates the design of imaging algorithms. Point target simulations confirm the effectiveness of the proposed AESRM, demonstrating significant improvements in fitting accuracy for range histories characterized by nonlinear trajectories. The developed AESRM provides a robust foundation for designing imaging algorithms and enables higher resolution and more accurate radar imaging.

A novel scheme for determination of vessel heading using airborne magnetic wake scanning

Practical remote vessel detection schemes are switching from the active lidar and sonar based methods to modern passive schemes such as analyzing the geomagnetic anomaly initiated from a moving remote vessel. The detection of a remote vessel and its heading direction has been fully studied in our recently published work through analyzing the two-dimensional frequency spectrum image of the magnetic wake captured by an array of magnetic sensors positioned under the sea surface. Instead of employing the fixed-positioned multi-sensor detection scheme, in this work, we study the heading detection of a remote vessel traveling in shallow/deep water through analyzing the measured magnetic anomaly captured by a single airborne magnetic sensor. After representing mathematical expressions of the captured magnetic wake initiated from the remote vessel, we manage to formulate the Fourier transform of the magnetic wake, and show that the detection of a remote vessel as well as its heading direction can be estimated through detecting the frequency corresponding to the peak amplitude of the spectrum. We show through theoretical and numerical results that the lower the cross-angle between the drone and vessel traveling directions, the more accurate the estimation of the heading angle.

Time-Frequency Characteristics of Acoustic Emission Signals on Water-Bearing Sandstone Specimen Subjected to Conventional Uniaxial Compression

This paper presents an experimental investigation of acoustic emission (AE) time-frequency characteristics of a water-bearing sandstone specimen in a conventional uniaxial compression test. The main achievements are as follows: (1) The violent fluctuation of AE time domain parameters indicates that the water-bearing sandstone specimen is about to be destroyed. This characteristic provides a theoretical basis for predicting the failure of water-bearing rock in engineering practice. (2) In the elastic phase, the AE b value is the lowest but has a sudden increase after falling into the steady crack propagation phase. In the unsteady crack propagation phase, the AE b value is further increased. This characteristic is of great indicative value for predicting the failure of the water-bearing sandstone specimen. (3) The difference of dominant frequency among the three key points is very small, indicating that the crack initiation and propagation of the water-bearing sandstone specimen has a certain stability in the damage and failure process. But, the two-dimensional frequency spectrum structure of AE waveform signals shows that the closer to failure, the more the number of the frequency spectrum structure peaks. (4) The energy of AE signals is mainly concentrated in the first three frequency bands. The closer to failure, the more the energy proportion of the first three frequency bands is reduced; conversely, the energy proportion of the latter five frequency bands is increased, which leads to more complexity of the failure modes of the water-bearing sandstone specimen.

Azimuth-Invariant Motion Compensation and Imaging Chirp Scaling Algorithm for Multiple-Receiver Synthetic Aperture Sonar

To improve the imaging quality of conventional imaging algorithms without motion compensation (MOCO) and the efficiency of point-by-point MOCO algorithms for multiple-receiver synthetic aperture sonar (SAS) with azimuth-invariant six-degree of freedom (DOF) motion errors, an azimuth-invariant MOCO and imaging chirp scaling (CS) algorithm is presented in this paper. Taylor series approximation is used to process the range history in double square root form, while considering the fourth-order and inner terms with respect to the azimuth time. Using the method of series reversion and Fourier transform (FT) properties, the analytical two-dimensional frequency spectrum of the point target response of each receiver is derived. On this basis, the azimuth-invariant MOCO and imaging CS algorithm is proposed for six-DOF motion error compensation and multiple-receiver SAS imaging. Because it considers the azimuth-invariant six-DOF motion errors, the proposed algorithm has better imaging quality than conventional imaging algorithms without MOCO. Additionally, it has a significantly higher efficiency than point-by-point MOCO algorithms because the CS algorithm is a fast FT-based algorithm and does not require interpolation processing. The imaging simulation and experimental results verified the effectiveness and efficiency of the proposed algorithm.

Unraveling nonlinear electrophysiologic processes in the human visual system with full dimension spectral analysis

Natural sensory signals have nonlinear structures dynamically composed of the carrier frequencies and the variation of the amplitude (i.e., envelope). How the human brain processes the envelope information is still poorly understood, largely due to the conventional analysis failing to quantify it directly. Here, we used a recently developed method, Holo-Hilbert spectral analysis, and steady-state visually evoked potential collected using electroencephalography (EEG) recordings to investigate how the human visual system processes the envelope of amplitude-modulated signals, in this case with a 14 Hz carrier and a 2 Hz envelope. The EEG results demonstrated that in addition to the fundamental stimulus frequencies, 4 Hz amplitude modulation residing in 14 Hz carrier and a broad range of carrier frequencies covering from 8 to 32 Hz modulated by 2 Hz amplitude modulation are also found in the two-dimensional frequency spectrum, which have not yet been recognized before. The envelope of the stimulus is also found to dominantly modulate the response to the incoming signal. The findings thus reveal that the electrophysiological response to amplitude-modulated stimuli is more complex than could be revealed by, for example, Fourier analysis. This highlights the dynamics of neural processes in the visual system.

An Azimuth Frequency Non-Linear Chirp Scaling (FNCS) Algorithm for TOPS SAR Imaging With High Squint Angle

During the data acquisition of a squint terrain observation by progressive scan (TOPS) synthetic aperture radar (SAR), the steering of the antenna main beam increases the azimuth bandwidth and results in the azimuth signal aliasing in the Doppler domain. Besides, the range curvature and the Doppler frequency modulation (FM) rates after linear range walk correction are azimuth-variant for squint TOPS SAR. These problems may cause some difficulties for the SAR data processing. To deal with the problems, a new imaging algorithm for the squint TOPS SAR is introduced in this paper. After linear range walk correction, the azimuth preprocessing is implemented to achieve the two-dimensional frequency spectrum without aliasing. Then, utilizing a modified chirp scaling algorithm, we complete the range cell migration correction (RCMC) and range compression to the TOPS SAR data without subaperture. Finally, the frequency nonlinear chirp scaling (FNCS) is proposed to correct the variation of the FM rates and the azimuth signal is focused in the Doppler domain via the spectral analysis (SPECAN) method. Both simulation and real data results show the effectiveness of the proposed algorithm.

A novel modified Omega-K algorithm for circular trajectory scanning SAR imaging using series reversion

This article presents a modified Omega-K algorithm for circular trajectory scanning synthetic aperture radar (CTSSAR) imaging. Due to the curvature of circular trajectory, it is difficult to have access to the two-dimensional frequency spectrum for CTSSAR via the principle of stationary phase (POSP), as conventional SAR imaging methods RD and CS. Herein, the analytic point target spectrum is first derived by series reversion and the POSP, based on which a modified Omega-K algorithm is developed to focus data accurately. The accuracy can be controlled by keeping enough terms in the two series expansions so that a well-focused image can be achieved with a proper range approximation. After detailed analyses and experiments, the fourth-order approximation is proved to be the best choice. Furthermore, the computational efficiency is evaluated by comparing the given method with the back projection algorithm and other methods with different approximated orders. The proposed algorithm is verified to be the best one in terms of computational burden. A well-focused image is obtained by simulations, validating the feasibility of the proposed algorithm.

A NEW IMAGING ALGORITHM FOR GEOSYNCHRONOUS SAR BASED ON THE FIFTH-ORDER DOPPLER PARAMETERS

This paper proposes a new imaging algorithm based on a novel accurate range model to process the data acquired by Geosynchronous-Earth-orbital Synthetic Aperture Radar (Geo-SAR). The new range model, called DRM-5, is obtained from the 1{5th order Doppler parameters of spaceborne SAR. It is employed to describe the slant range of Geo-SAR during the super-long integration time. Furthermore, the two-dimensional frequency spectrum of point targets based on the new range model is derived and analyzed. An advanced Frequency Domain Algorithm (FDA) based on DRM-5 is proposed to process the data of stripmap mode Geo-SAR. The varied Doppler parameters in the cross-azimuth direction are considered in the new imaging algorithm, and the space-varied range-azimuth coupling phase term is compensated through data blocking. A simulation experiment is performed to verify the e-ciency and superiority of the new algorithm, and the results show that it has a good efiect on an L- band stripmap mode Geo-SAR system with azimuth resolution around 5m and 300km range swath.

AN IMPROVED NONLINEAR CHIRP SCALING ALGORITHM BASED ON CURVED TRAJECTORY IN GEOSYNCHRONOUS SAR

Geosynchronous synthetic aperture radar (GEO SAR) has the characteristics of long aperture time and large imaging area. Therefore, the conventional imaging algorithm in Low Earth Orbit (LEO) SAR loses efiect. In this paper, based on curved trajectory model under an ideal acquisition and not considering some acquisition perturbations (atmosphere, orbital deviations), an accurate two-dimensional frequency spectrum is analytically obtained via series reversion principle and high order Taylor expansion. Then, an improved Nonlinear Chirp Scaling (NCS) algorithm is proposed in GEO SAR, which includes novel range migration correction factor, coupling phase compensation factor, NCS factor and azimuth compression function. Finally, the correctness of the proposed NCS algorithm is verifled via imaging results of point array targets and area targets.

Two-dimensional Fourier spectroscopy applied to electron-phonon correlations in quantum well intersubband systems

Two-dimensional photon echo spectroscopy allows one to track relaxation and correlation processes in optically excited nanostructures. We analyze such spectra for intersubband transitions in an $n$-doped GaAs/Al${}_{0.35}$Ga${}_{0.65}$As single quantum well. Focusing on electron-longitudinal optical phonon interaction in a non-Markovian treatment, the carrier dynamics in the conduction subbands are investigated in the low density regime. Our results provide detailed information about the temporal evolution of electron-phonon correlations in the two-dimensional frequency spectrum.

Omega-K Algorithm for Bistatic SAR With Arbitrary Geometry Configuration

Compared to the common monostatic synthetic aperture radar (SAR), the bistatic SAR data are more challenging to process because of their complicated flight geometry. Although several bistatic SAR image formation algorithms have been presented, most of them are only able to handle azimuth-invariant bistatic configuration where the transmitter and receiver platforms are moving in parallel tracks with identical velocities. This paper proposes an Omega-K algorithm to handle a general case of bistatic SAR data. The two-dimensional frequency spectrum expression derived by the method of series reversion is rewritten to a new form with explicit geometric significance. Based on this new frequency spectrum expression, the frequency mapping function can be derived by making use of the multivariable Taylor's theorem. After data mapping operation, the coupling between the range and azimuth can be eliminated, and the final focused image can be obtained using FFT technology. Numerical simulations are performed to validate the proposed algorithm.

KASCADE measurements of energy spectra for elemental groups of cosmic rays: Results and open problems

A composition analysis of KASCADE air shower data is performed by means of unfolding the two-dimensional frequency spectrum of electron and muon numbers. Aim of the analysis is the determination of energy spectra for elemental groups representing the chemical composition of primary cosmic rays. Since such an analysis depends crucially on simulations of air showers the two different hadronic interaction models QGSJet and SIBYLL are used for their generation. The resulting primary energy spectra show that the knee in the all particle spectrum is due to a steepening of the spectra of light elements but, also, that neither of the two simulation sets is able to describe the measured data consistently over the whole energy range with discrepancies appearing in different energy regions.

Solar granulation. The frequency spectrum of photo spheric brightness at long spatial wave lengths.

view Abstract Citations References Co-Reads Similar Papers Volume Content Graphics Metrics Export Citation NASA/ADS Solar granulation. The frequency spectrum of photo spheric brightness at long spatial wave lengths. Wlérick, Gérard Abstract A very good photograph of solar granulation taken by Dr. W. A. Miller at Rocky Point, Long Island, N. Y., has been analyzed. The aperture of the telescope was 4.5 inches and the plate Kodak 548 GH. As no colored filter was used, the plate was impressed by radiations from the interval 3600-5650A. With the microphotometer of the High Altitude Observatory tracings were made along two linear paths whose total length corresponds to 1,140,000 km on the sun. The statistical analysis was similar to that made by Frenkiel and Schwarzschild (1955) and by Uberoi (1955) for solar granulation photographs taken at Mount Wilson with a ~-inch aperture in a narr9w wavelength interval centered around 58oo A. It consisted of the computation of the autocorrelation function of brightness, of the one-dimensional frequency spectrum and of the two-dimensional frequency spectrum. A correction was applied for the finite resolution of the telescope due to diffraction and chromatic aberration. The results indicate that in the range of spatial wave lengths from 87,000 km to 3140 km, wave numbers from 7.2 X 10-I km-0 to 2 X io-3 km-0, the two-dimensional frequency spectrum P (k) is of the low frequency type, i.e., the average energy per unit frequency decreases with frequency. The results thus differ from those of Frenkiel and Schwarzschild and of Uberoi who found with Mount Wilson photographs that the frequency spectrum was nearly constant in the range from 30,000 to 2000 km, wave numbers from 2 X io-4 km-0 to 3 10-I km-0. The difference implies that more energy resides in larger scale granular structure for the shorter wave-length images used by Miller and indicates the importance of homogeneous granule studies simultaneously at several colors. The help of Miss Sabine Hirsch for the computation is gratefully acknowledged. This work was supported by the Radio Corporation of America and the Geophysics Research Directorate, Air Force Cambridge Research Center. Frenkiel, F. N. and Schwarzschild, M. 1955, Ap. J. 121, 216. Uberoi, M. S. 1955, Ap. J. 122, 466. High Altitude Observatory, Boulder, Colo. Publication: The Astronomical Journal Pub Date: 1957 DOI: 10.1086/107592 Bibcode: 1957AJ.....62Q..39W full text sources ADS |

A theory of the origin of microseisms

In the past it has been considered unlikely that ocean waves are capable of generating microseismic oscillations of the sea bed over areas of deep water, since the decrease of the pressure variations with depth is exponential, according to the first-order theory generally used. However, it was recently shown by Miche that in the second approximation to the standing wave there is a second-order pressure variation which is not attenuated with depth and which must therefore ultimately predominate over the first-order pressure variations. In §§ 2 and 3 of the present paper the general conditions under which second-order pressure variations of this latter type will occur are considered. It is shown that in an infinite wave train there is in general a second-order pressure variation at infinite depth which is applied equally over the whole fluid and is associated with no particle motion. In the case of two progressive waves of the same wave-length travelling in opposite directions this pressure variation is proportional to the product of the (first-order) amplitudes of the two waves and is of twice their frequency. The pressure variation at infinite depth is found to be closely related to changes in the potential energy of the wave train as a whole. By introducing the two-dimensional frequency spectrum of the motion it is shown that in the general case variations in the mean pressure over a wide area only occur when the spectrum contains wave groups of the same wave-length travelling in opposite directions. (These are called opposite wave groups.) In § 4 the effect of the compressibility of the water is considered by evaluating the motion of an opposite pair of waves in a heavy compressible fluid to the second order of approximation. In place of the pressure variation at infinite depth, waves of compression are set up, and there is resonance between the bottom and the free surface when the depth of water is about (1/2n+ 1/4) times the length of a compression wave (nbeing an integer). The motion in a surface layer whose thickness is of the order of the length of a Stokes wave is otherwise unaffected by the compressibility. Section 5 is devoted to the question whether the second-order pressure variations in surface waves are capable of generating microseisms of the observed order of magnitude. By considering the displacement of the sea bed due to a concentrated force at the upper surface of the water it is shown that the effect of resonance will be to increase the disturbance by a factor of the order of 5 over its value in shallow water. The results of §§ 3 and 4 are used to derive an expression for the vertical displacement of the ground in terms of the frequency characteristics of the waves. The displacement from a storm area of 1000 sq.km, is estimated to be of the order of 6.5μ at a distance of 2000 km. Ocean waves may therefore be the cause of microseisms, provided that there is interference between groups of waves of the same frequency travelling in opposite directions. Suitable conditions of wave interference may occur at the centre of a cyclonic depression or possibly if there is wave reflexion from a coast. In the latter case the microseisms are likely to be smaller, except perhaps locally. Confirmation of the present theory is provided by the observations of Bernard and Deacon, who discovered independently that the period of the microseisms is in many cases about half that of the ocean waves associated with them.