Quantitative analysis of the reconstruction performance of interpolants

The analysis presented provides a quantitative measure of the reconstruction or interpolation performance of linear, shift-invariant interpolants. The performance criterion is the mean square error of the difference between the sampled and reconstructed functions. The analysis is applicable to reconstruction algorithms used in image processing and to many types of splines used in numerical analysis and computer graphics. When formulated in the frequency domain, the mean square error clearly separates the contribution of the interpolation method from the contribution of the sampled data. The equations provide a rational basis for selecting an optimal interpolant; that is, one which minimizes the mean square error. The analysis has been applied to a selection of frequently used data splines and reconstruction algorithms: parametric cubic and quintic Hermite splines, exponential and nu splines (including the special case of the cubic spline), parametric cubic convolution, Keys' fourth-order cubic, and a cubic with a discontinuous first derivative. The emphasis in this paper is on the image-dependent case in which no a priori knowledge of the frequency spectrum of the sampled function is assumed

Ground Measurements of the Shock-Wave Noise from Airplanes in Level Flight at Mach Numbers to 1.4 and at Altitudes to 45000 Feet

Time histories of noise pressures near ground level were measured during flight tests of fighter-type airplanes over fairly flat, partly wooded terrain in the e Mach number range between 1.13 and 1.4 and at altitudes from 25,000 to 45,000 feet. Atmospheric soundings and radar tracking studies were made for correlation with the measured noise data. The measured and calculated values of the pressure rise across the shock wave were generally in good agreement. There is a tendency for the theory to overestimate the pressure at locations remote from the track and to underestimate the pressures for conditions of high tailwind at altitude. The measured values of ground-reflection factor averaged about 1.8 f or the surface tested as compared to a theoretical value of 2.0. P o booms were measured in all cases. The observers also generally reported two booms; although, in some cases, only one boom was reported. The shock-wave noise associated with some of the flight tests was judged to be objectionable by ground observers, and in one case the cracking of a plate-glass store window was correlated in time with the passage of the airplane at an altitude of 25,000 feet