First-order Interpolation Research Articles

Approximate FM Demodulation Using Zero Crossings

This paper deals with approximate methods for demodulating FM signals using their zero crossings. A first-order (linear) interpolation method is devised and analyzed. Computer programs were then prepared to compare this first-order interpolator to the more usual zero-order interpolator. Higher order interpolation is briefly discussed, and the results of using a second-order interpolator are compared to those using the lower order methods.

Atmospheric corrections to satellite radiometric data over rugged terrain

Radiometric measurements from satellites in the solar portion of the electromagnetic spectrum can be converted to measurements of surface exitance. Over rugged terrain, the satellite image must be precisely registered to a terrain data set. For small areas a first-order polynomial interpolation scheme is generally satisfactory for the geometric rectification. If there are saturated pixels, a nearest-neighbor procedure is used for the interpolated satellite radiance numbers; otherwise a cubic-convolution algorithm is used. Path radiance and path transmittance are calculated with a simple spectral model, which requires an estimate of the water vapor and aerosol content of the atmosphere.

Doubly Curved Membrane Shell Finite Element

The formulation and testing of a high-order doubly curved membrane shell finite element is presented. Specialized for application to shells of revolution, the element is defined by lines of principal curvature and allows a third-order mapping of the meridian. The in-plane displacement assumptions are complete bicubic. The functions are represented by products of one-dimensional first-order Hermite interpolation functions. The transverse displacement assumption is bilinear. Mixed displacement derivatives are condensed from the element stiffness matrix forming an element with 28 degrees-of-freedom. An eigenvalue analysis performed on the element stiffness matrix indicates that three rigid body modes are implicitly included. These three rigid body modes, the two in-plane translations and the rotation about the shell normal, are sufficient to produce excellent convergence characteristics in analyzing membrane shells, regardless of the shell's Gaussian curvature.

Operation of multivariable function generators

The multivariable function generator (MVFG) is a multiport device which, given a set of continuous bounded analog inputs at time t, produces estimates for a set of bounded outputs after a processing time delay Δt u. The transfer characteristics of the MVFG can be both arbitrary and nonlinear and are specified by defining the output variables at a finite number of coordinate points. The operation of the device described in this paper is based on first-order interpolation techniques and combines the flexibility of digital processing with the continuity and speed of analog processing. The speed and accuracy of the device result from its distributed-processor archi tecture in which several independent operations proceed concurrently. Sources of errors and tech niques for minimizing their effects are discussed.

A rectangular laminated anisotropic shallow thin shell finite element

This report contains the details of the development of the stiffness matrix for a rectangular laminated anisotropic shallow thin shell finite element. The derivation is done under linear thin shell assumptions. Expressing the assumed displacement state over the middle surface of the shell as products of one-dimensional first-order Hermite interpolation polynomials, it is possible to insure that the displacement state for the assembled set of such elements, to be geometrically admissible. Monotonic convergence of the total potential energy is therefore possible as the modelling is successively refined. The element is systematically evaluated for its performance considering various examples for which analytical or other solutions are available.

High Order Rectangular Shallow Shell Finite Element

The stiffness matrix for a high order shallow shell finite element is presented explicitly. The element is of rectangular plan and possesses three constant radii of curvature: two principal ones and a twist one. Each of the three displacement functions is assumed as the product of one-dimensional, first-order Hermite interpolation formulas. An eigenvalue analysis performed on the element stiffness matrix shows that the six rigid-body displacements are included. Convergence studies are carried out for a cylindrical shell, a translational shell with two constant principal radii of curvature, and a hyperbolic paraboloidal shell with a constant twist radius of curvature. Excellent agreements are found when comparing the present results with the alternative series and finite difference solutions. A review of the previously developed shell finite elements shows that the present element is highly efficient in terms of convergence rate or computational effort.

Buffer Design for Data Compression Systems

Design of the output buffer is one of the most important tasks in implementing an adaptive data compression system. Upon proper design of the buffer including such parameters as size, inputoutput data rates, and occupancy control, rests the overall compression efficiency and error performance of the system. The binomial distribution is used to derive an exact model for a synchronous buffer. The Poisson distribution, which provides a reasonable model for a high-speed asynchronous buffer, is shown to yield an error greater than 10 percent in required buffer length for synchronous buffers. Design requirements such as probabilities of overflow and underflow, buffer length, and average buffer fill are derived as functions of compression ratio φ and the ratio of input-output transmission rates C . It is shown that the buffer queuing behavior is a function of the ratio \rho = C/\phi , as well as C and φ independently. The derived results indicate that restricting buffer overflow by increasing the buffer size is inefficient. Control is suggested in which the aperture of the compression algorithm is changed to control the buffer fill. The design requirements are determined for the zero-order predictor and the first-order interpolator with two degrees of freedom. Using the buffer equations derived and the compression ratio-aperture relationship, the design of a buffer is described. It is shown that doubling the aperture with a resultant doubling in rms error reduces the buffer probability of overflow by a factor of 100.

Finite deflection structural analysis using plate and shell discreteelements.

An analysis capability for predicting the nonlinear behavior of elastic structural systems that can be adequately idealized with rectangular plate and cylindrical shell discrete elements is reported. The displacement patterns in each element are approximated in terms of products of one-dimension al, first-order Hermite interpolation polynomials and undetermined nodal displacement parameters. Geometric admissibility of the displacement state for an assembled set of these discrete elements can be readily assured. Incorporation of geometric nonlinearities in the strain-displacement relations permits the prediction of finite displacements. For example, elastic postbuckling behavior can be analyzed using this method. The option to impose a prescribed end-shortening and then determine the boundary-force distribution required to maintain the resulting displacement pattern is a valuable feature of this capability. Numerical solutions are obtained by direct minimization of the total potential energy. The elastic postbuckling behavior of a flat-plate panel and a cylindrical shell panel are presented as examples. The applicability of these discrete elements to predicting the elastic postbuckling behavior of integrally stiffened plate and cylindrical shell panels is provided by the assumed element displacement patterns.

A cylindrical shell discrete element.

The development of the stiffness and consistent mass matrices for a finite cylindrical shell element is reported. The derivation of these matrices is based upon linear behavior and thin-shell assumptions. Expressing the assumed displacement state over the middle surface of the cylindrical shell element as products of one-dimensional, first-order Hermite interpolation formulas, it is possible to insure that the displacement state for the assembled set of cylindrical elements is geometrically admissible. Mono tonic convergence of the total potential energy is therefore assured as the modeling is successively refined, since the assumed displacement pattern satisfies the admissibility requirements in the statement of the principle of minimum potential energy. A numerical example is included to demonstrate the effectiveness of this cylindrical shell discrete element.