It is shown that evoked potential waveforms can be classified into clinically significant patterns in computerised EEG analysis and other medical fields through application of a pattern-recognition technique which is presented. Fourier descriptors are used to characterize each waveform. Since the feature sets of Fourier descriptors contain information about the shape of the waveforms, they are used in the structural stage of the algorithm. In this stage, discriminant analysis is used to design a measure of dissimilarity between pairs of waveforms. Only the resulting interdistance matrix is preserved in the construction of the vector representation, making the dissimilarity measure crucial to the success of the remainder of the procedure. An algorithm using Fourier descriptors as feature vectors and the sum of squared error criterion to indicate improvement in percent of correctly classified waveforms has yielded accuracies of at least 90%.>

LetC(B)denote the binary cyclicANcode with generatorA, whereAB=2^{n} - 1. It is known thatC(B)is equidistant ifBis a prime powerp^{k}, where either2or-2is primitive moduloBprovidedp\equiv 1 \pmod{3}{\rm if} k > 1. It is conjectured that these are the onlyBsuch thatC(B)is equidistant. We have verified this forB < 100 000. Several results are established that further limit the possibilities for counterexamples to the conjecture.

In this correspondence we give a new definition of modular arithmetic weight (relative to any modulusm > 0and any radixr \geq 2), which has two very useful properties, i) It is defined for all integers and is invariant under congruence modulom. ii) It yields a metric for all modulim. In the important casesm = r^n, m = r^n - 1, andm =r^n + 1, it coincides with the modular weight of Rao and Garcia, and thus acts as a proper measure of errors for these moduli. Due to these properties, we are able to obtain conceptually simpler proofs of several known (as well as some new) results on the computation of modular distance in cyclic AN-codes. Along these same lines we introduce the notion of modular-cyclic nonadjacent form (NAF) whenm = r^n - 1. For moduli of this type, we show that every integer has a modular-cyclic NAF; the number of nonzero digits is the modular weight. It is a curious fact that a "modular" version of the well-known Chang/Tsao-Wu algorithm (for computing the NAF) turns out to yield the modular-cyclic NAF directly.

In this correspondence we define a "nonadjacent form" for integers in an arbitrary radixr > 1. This form is proved to be unique, and the arithmetic weight of an integer is shown to be equal to the number of nonzero terms in the form. Two algorithms are presented for the computation of this form. Ifr = 2, our form coincides with the well-known modified binary nonadjacent form.