A method and apparatus are provided for interpolating a first set of multi-dimensional sample values from a second set of multi-dimensional sample values. The method includes the steps of determining a set of relationships between a second sampling space from which the second set of samples are obtained and a first sampling space into which the first set of samples are interpolated and calculating a partial Fourier transform of the second set of samples. The method further includes the steps of ...

A multidimensional puzzle. The puzzle includes a plurality of three-dimensional first object pieces having a contoured front surface. The object pieces are each representative of a thing with the contoured front surface having a shape identified with the thing represented by the object piece. A background defines a plurality of recesses each shaped to receive one of the object pieces with the contoured surface projecting from the recess. The background includes a plurality of second pieces. The ...

The yield of fully substituted, multidimensional aromatic hubs in the condensation of hydroxyl and acid halide functionalities is improved by adding a thallium catalyst, such as thallium ethoxide (Tl-OC.sub.2 H.sub.5), in the solvent.

Phase and amplitude modulation of single or multiple pulses and/or dual polarizations are used in a digital communications system which transmits multidimensional codes. Four dimensional code transmission is specifically disclosed, although the scheme may be extended to eight-dimensional and even 16-dimensional code transmission. The four-dimensional codes are constructed by mapping a digital word into two two-dimensional plane as two sets of x and y coordinates. Signals proportional to these x ...

A multibeam structure measures displacement of one or more response elements to detect multiple components of applied force. The flexible beams are each coupled to a response element which may be displaced by a force arising from linear acceleration, angular acceleration, fluid flow, electric/magnetic/gravitational fields, and others sources. The displacement of the response element is detected with a variety of sensing methods including capacitive and piezoresistive sensing.

A method and arrangement for decoding n-dimensional codes in which the alphabet of codewords is selected from the points of a lattice comprised of a union of cosets of the lattice D.sub.n, the latter being comprised of those n-dimensional integer-valued-coordinate points which have a predetermined parity.

An n-dimensional channel code is used in a data transmission system. The alphabet of codewords (data symbols) comprises a subset of points of a selected coset of a selected lattice. The alphabet includes at least one point of the coset whose norm (signal energy) is greater than at least one other point of the coset which is excluded from the alphabet.

A decorative element typically constructed of paperboard coated with metallic foil and including a base of geometric form and a number of side panels extending away from the base at an angle so that a reflection of the base is apparent on the side panels and/or the reverse. Any designs incorporated on the base or side panels are also reflected providing a pleasing overall effect.

A memory array associated with a display can be accessed in either one of two substantially orthogonal directions. The memory array is structured so that it may be accessed, such as for reading or writing, in either the horizontal or vertical direction. Pel position representations in the array are arranged so that vertically sequential pel positions in a given column are represented by data in sequential memory modules rather than by data in the same memory module. Likewise, horizontally sequen...

A switching network that utilizes at least three degrees of freedom, time, wavelength and space. In one embodiment that involves point-to-point switching, each space channel between an input and an output is assigned a time slot and wavelength coordinate characteristic of the output and the input transmitter and output receiver are tuned to the appropriate time and wavelength coordinates and selective switching is used to complete the space channel between the input and output. In another embodi...