Sinc Function Interpolation Research Articles

High Wideband Digital Oscilloscope Design

In most test applications, acquisition and analysis involving simultaneous processing of analog and digital signals. However, the bandwidth of most mainstream digital oscilloscopes is limited to 100 MHz, which is unable to meet the testing needs of high-frequency signals in complex electronic systems [1], and therefore, high-bandwidth digital oscilloscopes have emerged. Based on this background, this paper designs a digital oscilloscope hardware platform with high bandwidth by integrating FPGA and ARM technologies, aiming to meet the rigorous testing requirements of modern electronic systems. The FPGA module is based on the xc7s75fgga676 chip, which is mainly responsible for ADC control, data processing and frequency measurement functions. AM5708 is selected as the ARM module to realize the trigger, time base, amplitude and automatic setting functions of the oscilloscope. In order to ensure the accuracy and fidelity of waveform changes, the Sinc function interpolation method is used. This design further improves the acquisition bandwidth and processing speed on the basis of traditional MSO (Mixed Signal Oscilloscope) oscilloscopes, which is of great significance for the acquisition and processing of high-speed signals.

Evaluation of reaction rate of thermogravimetric analysis data using periodic sinc function interpolation

AbstractThe periodic sinc function interpolation offers a compelling solution to address the issue of noise in the analysis of thermogravimetric analysis (TGA) data, thereby enhancing the outcomes of differential techniques such as the Friedman isoconversional method. In this study, we introduce a novel approach that leverages the periodic sinc function interpolation to directly obtain smooth reaction rates from TGA data, eliminating the reliance on numerical differentiation methods. The efficacy of this method has been confirmed through its application to noisy experimental data derived from the thermal decomposition of various polymers, showcasing its robustness. Readers are provided with the corresponding code for Gnu Octave, serving as a free alternative to MATLAB. Additionally, the activation energies calculated from the experimental data using both the Friedman method and periodic sinc function interpolation closely align with those determined by the integral Vyazovkin method, emphasizing the validity and reliability of this new approach.

ISAR Imaging for Maneuvering Targets via Fast Rotation Parameter Estimation

In inverse synthetic aperture radar (ISAR) imaging of maneuvering targets, traditional high-order phase compensation methods are usually limited by the heavy computational burden of parameter estimation, making it hard to apply in real-time cases. In this letter, an efficient ISAR motion compensation method is proposed based on fast parameter estimation. A novel analytic expression of the image entropy is derived with the help of a compensation matrix based on sinc function interpolation, which can eliminate the high-order phase term. Hence, the parameter estimation is transformed to an optimization problem where the gradient descent algorithm can be adopted to accelerate the computation speed. Compared with other recently proposed methods, our method is superior in high robustness and low computing cost. Experiments with simulated and real data have verified that without affecting the image quality, the computing time of our method can be reduced to about 1/4 of the traditional search algorithm.

Fast Generation of Deceptive Jamming Signal Against Spaceborne SAR Based on Spatial Frequency Domain Interpolation

This article proposes a novel method for the generation of the deceptive jamming signal against spaceborne SAR, which can calculate the jammer’s frequency response (JFR) efficiently. The first advantage of this algorithm is that the real-time computational complexity is independent of the number of fake scattering units, so it is particularly suitable for generating scenes containing a large number of scatterers. Besides, the imaging quality of fake targets is also improved significantly, especially in the case of squint geometries. First, using the Taylor series expansion and approximations, we derive the recurrence relationship of the slant range between the adjacent pulse repetition intervals. Based on this relationship, the JFR at each azimuth time is mapped to a special spatial spectrum, which is the 2-D Fourier transform along the range and azimuth dimensions of the JFR matrix at the time of the first pulse arrival. Therefore, after the initial JFR is calculated, the subsequent JFRs can be quickly obtained by sinc function interpolation. Then, the validity and effective region of this algorithm are estimated by the theoretical analysis of the slant range error. The simulation results and a computational complexity analysis verify that the algorithm demonstrates superior performance in terms of imaging quality and efficiency.

Numerical simulation for a class of predator\u2013prey system with homogeneous Neumann boundary condition based on a sinc function interpolation method

For the nonlinear predator–prey system (PPS), although a variety of numerical methods have been proposed, such as the difference method, the finite element method, and so on, but the efficient numerical method has always been the direction that scholars strive to pursue. Based on this question, a sinc function interpolation method is proposed for a class of PPS. Numerical simulations of a class of PPS with complex dynamical behaviors are performed. Time series plots and phase diagrams of a class of PPS without self-diffusion are shown. The pattern is obtained by setting up different initial conditions and the parameters in the system according to Turing bifurcation condition. The numerical simulation results have a good agreement with theoretical results. Simulation results show the effectiveness of the method.

Numerical Solution of a Class of Predator-Prey Systems with Complex Dynamics Characters Based on a Sinc Function Interpolation Collocation Method

Although many kinds of numerical methods have been announced for the predator-prey system, simple and efficient methods have always been the direction that scholars strive to pursue. Based on this problem, in this paper, a new interpolation collocation method is proposed for a class of predator-prey systems with complex dynamics characters. Some complex dynamics characters and pattern formations are shown by using this new approach, and the results have a good agreement with theoretical results. Simulation results show the effectiveness of the method.

Performance Analysis of Accurate Time Delay and Its Influence on Sonar Beam Formation

The time delay accuracy affects the processing performance of the sonar signals. This paper studies the implementation principles of such accurate time delay methods as linear interpolation method, Sinc function interpolation method, Lagrange interpolation method and Farrow filter method and investigates the performance of different accurate time delay methods by simulation as well as the influence of accurate time delay on beam formation. The research results show the images of accurate time delay will be smoother, and lower in side lobe and less in false peak than that of conventional time delay. But both of them have the same beam width.

Improve the Simulations of Near-Inertial Internal Waves in the Ocean General Circulation Models

AbstractThe near-inertial wind work and near-inertial internal waves (NIWs) in the ocean have been extensively studied using ocean general circulation models (OGCMs) forced by 6-hourly winds or wind stress obtained from atmospheric reanalysis data. However, the OGCMs interpolate the reanalysis winds or wind stress linearly onto each time step, which partially filters out the wind stress variance in the near-inertial band. In this study, the influence of the linear interpolation on the near-inertial wind work and NIWs is quantified using an eddy-resolving (°) primitive equation ocean model. In addition, a new interpolation method is proposed—the sinc-function interpolation—that overcomes the shortages of the linear interpolation.It is found that the linear interpolation of 6-hourly winds significantly underestimates the near-inertial wind work and NIWs at the midlatitudes. The underestimation of the near-inertial wind work and near-inertial kinetic energy is proportional to the loss of near-inertial wind stress variance due to the linear interpolation. This further weakens the diapycnal mixing in the ocean due to the reduced near-inertial shear variance. Compared to the linear interpolation, the sinc-function interpolation retains all the wind stress variance in the near-inertial band and yields correct magnitudes for the near-inertial wind work and NIWs at the midlatitudes.

Simulation of Dynamic EADs Jamming Performance against Tracking Radar in Presence of Airborne Platform

We propose a numerical scheme to simulate the time-domain echo signals at tracking radar for a realistic scenario where an EAD (expendable active decoy) and an airborne target are both in dynamic states. On various scenarios where the target takes different maneuvers, the trajectories of the EAD ejected from the target are accurately calculated by solving 6-DOF (Degreeof-Freedom) equations of the motion for the EAD. At each sampling time of the echo signal, the locations of the EAD and the target are assumed to be fixed. Thus, the echo power from the EAD can be simply calculated by using the Friis transmission formula. The returned power from the target can be computed based on the pre-calculated scattering matrix of the target. In this paper, an IPO (iterative physical optics) method is used to construct the scattering matrix database of the target. The sinc function-interpolation formulation (sampling theorem) is applied to compute the scattering at any incidence angle from the database. A simulator is developed based on the proposed scheme to estimate the echo signals, which can consider the movement of the airborne target and EAD, also the scattering of the target and the RF specifications of the EAD. For applications, we consider the detection probability of the target in the presence of the EAD based on Monte Carlo simulation.

AREA EFFICIENT FRACTIONAL SAMPLE RATE CONVERSION ARCHITECTURE FOR SOFTWARE DEFINED RADIOS

The modern software defined radios (SDRs) use complex signal processing algorithms to realize efficient wireless communication schemes. Several such algorithms require a specific symbol to sample ratio to be maintained. In this context the fractional rate converter (FRC) becomes a crucial block in the receiver part of SDR. The paper presents an area optimized dynamic FRC block, for low power SDR applications. The limitations of conventional cascaded interpolator and decimator architecture for FRC are also presented. Extending the SINC function interpolation based architecture; towards high area optimization and providing run time configuration with time register are presented. The area and speed analysis are carried with Xilinx FPGA synthesis tools. Only 15% area occupancy with maximum clock speed of 133 MHz are reported on Spartan-6 Lx45 Field Programmable Gate Array (FPGA).

The effect of sampling rate and anti-aliasing filters on high-frequency response spectra

The most commonly used intensity measure in ground-motion prediction equations is the pseudo-absolute response spectral acceleration (PSA), for response periods from 0.01 to 10 s (or frequencies from 0.1 to 100 Hz). PSAs are often derived from recorded ground motions, and these motions are usually filtered to remove high and low frequencies before the PSAs are computed. In this article we are only concerned with the removal of high frequencies. In modern digital recordings, this filtering corresponds at least to an anti-aliasing filter applied before conversion to digital values. Additional high-cut filtering is sometimes applied both to digital and to analog records to reduce high-frequency noise. Potential errors on the short-period (high-frequency) response spectral values are expected if the true ground motion has significant energy at frequencies above that of the anti-aliasing filter. This is especially important for areas where the instrumental sample rate and the associated anti-aliasing filter corner frequency (above which significant energy in the time series is removed) are low relative to the frequencies contained in the true ground motions. A ground-motion simulation study was conducted to investigate these effects and to develop guidance for defining the usable bandwidth for high-frequency PSA. The primary conclusion is that if the ratio of the maximum Fourier acceleration spectrum (FAS) to the FAS at a frequency $$f_{saa} $$ corresponding to the start of the anti-aliasing filter is more than about 10, then PSA for frequencies above $$f_{saa} $$ should be little affected by the recording process, because the ground-motion frequencies that control the response spectra will be less than $$f_{saa} $$ . A second topic of this article concerns the resampling of the digital acceleration time series to a higher sample rate often used in the computation of short-period PSA. We confirm previous findings that sinc-function interpolation is preferred to the standard practice of using linear time interpolation for the resampling.

Emission Spectral Tomography Reconstruction Based on Maximum Entropy Interpolation

To improve the performance of optical computed tomography (OpCT) reconstruction in the case of limited projection views, maximum entropy (ME) algorithms were proposed and can achieve better results than traditional ones. However, in the discrete iterative process of ME, the variables of the iterative function are continuous. Hence, interpolation methods ought to be used to improve the precision of the iterative function values. Here, a sinc function interpolation approach was adopted in ME algorithm (SINCME) and its reconstruction results for OpCT with limited views were studied using four typical phantoms. Compared results with ME without interpolation, traditional medical CT back-projection algorithm (BP), and iterative algorithm algebraic reconstruction technique (ART) showed that the SINCME algorithm achieved the best reconstruction results. In an experiment of emission spectral tomography reconstruction, SINCME was also adopted to calculate the three-dimensional distribution of physical parameters of a candle flame. The studies of both algorithm and experiment demonstrated that SINCME met the demand of limited-view OpCT reconstruction.

Proposal of an A/D Converter Clipping Noise Suppression Technique for High-Sensitivity Carrier-Sensing of Cognitive Radio Transceiver

A technique for suppressing the clipping noise of an analogue-to-digital converter (ADC) is proposed to realize a cognitive radio transceiver that offers high sensitivity carrier-sensing. When a large bandwidth cognitive radio transceiver performs carrier-sensing, it must receive a radio wave that includes many primary user transmissions. The radio wave may have high peak-to-average power ratio (PAPR) and clipping noise may be generated. Clipping noise becomes an obstacle to the achievement of high-sensitivity carrier-sensing. In the proposed technique, the original values of the samples clipped by an ADC are estimated by interpolation. Polynomial spline interpolation to the clipped signal is performed in the first step, and then SINC function interpolation is applied to the spline interpolated signal. The performance was evaluated using the signals with various PAPR. It has been found that suppression performance has a dependency on the number of samples clipped at once rather than on PAPR. Although there is an upper limit for the number of samples clipped at once that can be compensated with high accuracy, about 20dB suppression of clipping noise was achieved with the medium degree of clipping.

Optical Joint Transform Encryption Using Binary Phase Difference Key Mask

This study describes optical encryption based on joint transform correlator architectures using a binary phase difference key mask, designed by discrete sinc function interpolation. The key mask has the required properties of space-limited and phase-mostly spectrum for accurate image recovery. Gray-level image encryption and decryption performance measures are discussed as well.

Optimal key mask design for optical encryption based on joint transform correlator architecture

We examine perfect recovery in the optical encryption system based on joint transform correlator architecture, which requires the key mask to be space-limited and phase-only in the frequency domain. Accordingly, a discrete sinc function interpolation is used to generate a binary phase difference mask for image encryption and decryption. Furthermore, the optimal binary phase difference mask is derived from the interpolation process best approximating the ideal sinc function interpolation. The simulation results confirm better recovery of the decrypted image for applying the proposed key masks to the optical encryption system. Especially, the optimal binary phase difference mask significantly enhances the recovery performance.

Anti-aliasing by interpolation in pre-stack wave-equation migration

Spatial aliasing is an important issue in seismic migration. In this paper, we discuss anti-aliasing schemes in the wavefield continuation which is a wave-equation-based migration method. We describe the difference in interpolation applied pre and post the imaging condition, and compare the effectiveness of the linear interpolation and the sinc function interpolation. Our conclusion is that a five-sample sinc function interpolation applied before the imaging condition is an optimal anti-aliasing scheme according to theoretical and application analysis. We then apply the 3D Born approximation pre-stack depth migration method with optimal anti-aliasing interpolation to a 80 km2 seismic dataset. The migration result shows that the method we propose is better than a conventional wave equation method (not applied anti-spatial aliasing) in the definition of reflection events.

40300 New applications for dry coupling probes : Splitt, G. Non-Destructive Testing, Proceedings of the 4th European Conference, London (United Kingdom), 13–17 Sep. 1987. Vol. 4, pp. 2300–2304. Edited By J.M. Farley and R.W. Nichols. Pergamon Press, 1988

We examine perfect recovery in the optical encryption system based on joint transform correlator architecture, which requires the key mask to be space-limited and phase-only in the frequency domain. Accordingly, a discrete sinc function interpolation is used to generate a binary phase difference mask for image encryption and decryption. Furthermore, the optimal binary phase difference mask is derived from the interpolation process best approximating the ideal sinc function interpolation. The simulation results confirm better recovery of the decrypted image for applying the proposed key masks to the optical encryption system. Especially, the optimal binary phase difference mask significantly enhances the recovery performance.

Efficient sinc function interpolation technique for center padded data

An efficient zooming FFT (fast Fourier transform) algorithm that allows center padding sinc function interpolation of 2-D images is presented. This algorithm avoids the phase shifts that would be introduced if the efficient Skinner interpolation method is used. Output pruning is incorporated to allow efficient determination of a zoomed subimage. Time savings of more than 50% can be achieved. Example images illustrating the use of the algorithm in conjunction with zooming and ARMA (autoregressive moving average) modeling of data are given.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

The use of band-selectable digital filtering in magnetic resonance image enhancement.

Manipulation of the data describing two-dimensional magnetic resonance (MR) images can be used to zoom an image, decrease image noise and artifacts by modeling, or emphasize object edges in the field of view. In this paper, a two-dimensional band-selectable digital filtering (2D-BSDF) technique is detailed. This can be used to decrease the computational burden and increase algorithm stability associated with such data manipulation. Many display devices have the ability of expanding an image by pixel or linear interpolation. Application of the efficient zooming fast Fourier transformation algorithms provides a superior quality sinc-function interpolated image. In 2D-BSDF, the ideal rectangular windows used in sinc-function interpolation are replaced by windows with a more gradual roll-off. This gradual roll-off results in a slight degradation of the image edges but substantially reduces the computation time. Modeling of MRI data has been attempted to remove noise and artifacts from the image. These algorithms are computationally expensive and frequently unstable because of the high model orders required. The 2D-BSDF can be used to prepare a reduced data set, without loss of information. A lower order model may be applied to the subset and computation times approaching that required for normal fast Fourier transform algorithms result. The absence of noise and signal from objects outside the region of interest can considerably enhance the stability of the modeling algorithms. The use of BSDF is equally applicable when used in association with the modeling of 2D NMR spectroscopy data or with edge enhancement or any other data manipulation of magnetic resonance imaging images. In this paper an explanation of 1D-BSDF is provided and an algorithm for 2D-BSDF is developed. A comparison of filter designs and computational times is given when applying the technique to zooming and modeling of MR images. Images from medical MRI data are provided.

Three-Dimensional Plane Pass Filtering as a Regridding and Interpolation Technique: ABSTRACT

Efficient and accurate interpretation of dense irregular 2-D seismic data is an ongoing problem in virtually every exploration area. Developing interpolation algorithms which would create pseudo 3-D volumes from sparse 2-D data could allow a geophysicist an efficient means of interpreting the broad geologic features in an area. An interpolation algorithm which uses the 3-D nature of the irregular 2-D data can be developed which is analogous to sinc function interpolation in 1-D. A Gaussian 3-D plane pass filter is demonstrated to produce reasonable interpolated results within the pass region of the filter. This particular technique has the built-in flexibility of allowing the geophysicist to choose a broad pass volume which essentially regrids existing data with very litt e interpolation or allows the choice of a narrow pass volume to interpolate those spatial frequencies which are not aliased by the irregular sampling of the input data. End_of_Article - Last_Page 461------------