Reciprocals of Binary Power Series

Reciprocal Walsh Series

Abstract-Any basis function of a generalized Fourier series takes on many values in an interval. In contrast, the binary nature of the basis functions of Walsh-Fourier series (WFS) allows them to be considered self-reciprocall except for a finite number of discontinuities. Hence, quotients of linear combinations of Walsh functions may be used to generate series representations of reciprocals of...

A new approach to detect Life threatening cardiac arrhythmias using Sequential spectrum of Electrocardiogram signals

This study evaluates the discriminative power of sequential spectrum analysis of the short-term electrocardiogram (ECG) time series in separating normal and subjects with life threatening arrhythmias like, ventricular tachycardia/fibrillation (VT/VF). The raw ECG time series is transformed into a series of binary symbols and the binary occupancy or relative distribution of mono-sequences (i.e. ...

Variations on computing reciprocals of power series

A new approach to detect Life threatening cardiac arrhythmias using Sequential spectrum of Electrocardiogram signals

This study evaluates the discriminative power of sequential spectrum analysis of the short-term electrocardiogram (ECG) time series in separating normal and subjects with life threatening arrhythmias like, ventricular tachycardia/fibrillation (VT/VF). The raw ECG time series is transformed into a series of binary symbols and the binary occupancy or relative distribution of mono-sequences (i.e. ...

Testing Kak's Conjecture on Binary Reciprocal of Primes and Cryptographic Applications

This note considers reciprocal of primes in binary representation and shows that the conjecture that 0s exceed 1s in most cases continues to hold for primes less than one million. The conjecture has also been tested for ternary representation with similar results. Some applications of this result to cryptography are discussed. Introduction In a note nearly 25 years ago, Kak conjectured [1] that...

Congruences involving the reciprocals of central binomial coefficients

We present several congruences modulo a power of prime p concerning sums of the following type ∑p−1 k=1 m k ( 2k k ) −1 which reveal some interesting connections with the analogous infinite series.