This paper examines the matrix data re-order requirements of a variety of polynomial transform 2D convolution methods which can be employed to efficiently accommodate large field problems. The results indicate that several power-of-2 length polynomial transform methods developed by Nussbaumer allow one to totally avoid the row-column data corner-turn commonly encountered in Fourier Transform 2D convolution methods, while also providing significantly reduced computational complexity. Execution time comparison with an FFT reference base is made assuming the use of general register and array processor units and use of recently developed matrix-transpose methods by Eklundh and Ari to support 2D Fourier Transform corner-turn requirements. These results demonstrate a 2-4 times throughput performance improvement for use of the polynomial transform method in place of the 2D Fourier Transform approach to circularly convolve large 2D fields in the range 1024×1024 to 8192×8192.

This paper describes a spectral method for rotating matrix form digital image data in a cartesian-coordinate organized array processor structure. The major elements of the method include: 1) an initial three step number-theoretic-transform (NTT) procedure to implement appropriate column and row data translations, and 2) a final non-spectral translation step within adjacent pixel groups. Digital array image data may be rotated about a selected pivot point through an arbitrary angle within the range ±45°. A comparison of the spectral method execution time with a non-spectral implementation indicates that the new method can provide a performance improvement factor of up to 5 depending upon the magnitude of the rotation angle and pixel word size.

An improved bound on the number of low-weight sequences that may be generated by L-step observable autonomous finite-state machines is derived. An upper and lower bound on the range of L for this same class of machines is also developed.

A static ferrite storage readout technique is described which utilizes microwave transmission phenomena rather than voltage induction to achieve readout. Reversible, rotational impulse switching is used to effect nondestructive interrogation of a small toroidal core which is coupled to a strip-type ``sense line.'' The core coupled to the stripline causes an electrically controllable discontinuity in the transmission line. The change of stripline transmission characteristics during interrogation, in turn, is dependent upon the remnant state of the core. Detection of a microwave signal transmitted through the stripline yields a bipolar signal which may be used to identify the remnant state of the core. The microwave readout technique which utilizes an XN-band signal permits readout of information in an extremely short duration of time. Experimental results are given to demonstrate readout in as little time as 3 nanoseconds. Utilization of the technique for readout of information from a mass memory configuration is potentially possible.

Logic circuits composed of NOR or NAND elements are now being used extensively in digital systems, mainly because of their economy; one type of element may be used throughout an entire circuit. Assuming that the basic decision to use such "universal" elements has been made, the main design objective will usually be to produce either the fastest or the most economical circuit possible. The fastest NAND circuits, i.e., ones having a minimum number of levels of logic, are obtained by rewriting the minimum-OR polynomial (as obtained by the Quine-McCluskey method) in terms of the NAND connective, yielding a three-level logic (two-level if complemented inputs are available) e.g., where * represents the NAND connective. Similarly the minimum-AND polynomial may be written in terms of the NOR connective. Circuits obtained in this way are often also minimal with respect to the number of logic elements required.