Some algebraic aspects of signal processing

Signal Processing Aspects of Signal

Acoustic signal extraction and identiication in the underwater environment is best achieved by adaptive methods as the signals encountered are generally non-stationary and corrupted by unpredictable noise sources, such as man-made noise, biological and seismic noises. While classical methods often fail in such an environment, the recent use of mul-tiresolution methods like the adaptive wavelet ...

Algebraic Signal Processing Theory

This paper presents an algebraic theory of linear signal processing. At the core of algebraic signal processing is the concept of a linear signal model defined as a triple (A,M,Φ), where familiar concepts like the filter space and the signal space are cast as an algebra A and a module M, respectively, and Φ generalizes the concept of the z-transform to bijective linear mappings from a vector sp...

Some Algebraic Aspects of Morse Code Sequences

1 Morse code polynomials Morse code sequences are finite sequences of dots (•) and dashes (−). If a dot has length 1 and a dash has length 2 then the number of all such sequences of total length n−1 is the Fibonacci number Fn, which is defined as the sequence of numbers satisfying the recursion Fn = Fn−1 + Fn−2 with initial conditions F0 = 0 and F1 = 1. If a dash is assumed to have length j, j≥...

Algebraic Signal Processing: Modeling and subband Analysis

Traditional linear signal processing is based on viewing signals as sequences or functions in time that flow in one direction, from past through present into future. Somewhat surprisingly, the assumption that the most basic operation that can be performed on a signal is a time shift, or “delay,” is sufficient to derive many relevant signal processing concepts, including spectrum, Fourier transf...

Aspects of Signal Processing in Noisy Neurons