We proposed a description and coding method of Chinese characters using their structural features. In this paper, we propose a pattern generation method of Chinese characters as an application of the description and coding method. In the method, the generation process of a character can be regarded as a derivation process of sentence which expresses the character, then a Chinese character can be generated iteratively not depending on the numbers of its components and also generated in various shapes by changing some parameters needed for the generation. We can get natural shapes of characters by choosing adequate values of parameters. Many applications using this pattern generation method are considered.

The algorithm for the fast Walsh-Hadamard transform (FWT) derived from the Walsh-Paley function provides fast and simple processors which calculate the i-th Walsh transform Fi (i0, 1, , 2n1) of the natural-, dyadic-, and sequency-ordered Walsh-Hadamard transforms respectively according to control signals. This processor needs only 22n1 adder-subtractors (A/S) and is n times as fast as the one of the iterative type with n iterations. The characteristics of FWT with the term T resemble that of the assembly of digital filters. The digital filter representing FWT can be analyzed with z-transform and its transfer function is described as a simple function of z. The 3 dB bandwidth calculated by FWT is almost constant (about 0.85/T) for n2, 3, ...,10. All the Walsh transform Fi can be calculated by the processor with n2n A/S, while the processor using delay lines needs only 22n1 A/S. The improved processor with delay lines deals with successive data and calculates all the Walsh transform or the Walsh spectrograms at the same time. These processors are effective for the recognition of speech and the analysis of signals.

A formula for the variations in vertex-potentials caused by an increase of an edge-weight is derived using topological methods. This formula can be expressed in terms of the increase of the weight and the potential differences between two vertices joined by the edge with respect to three ordered vertex-pairs in the original network before the weight is increased.