Interval Arithmetic based Adaptive Filtering Technique for Removal of Noise in Audio Signal

Active noise cancellation is one of the fundamental problems in acoustic signal processing. The proposed work focuses on the enhancement of audio signal quality by cancelling the noise using interval analysis (arithmetic). An adaptive filters basically works on the concept of optimal weight calculations which is an optimization problem. This optimization problem can be more effectively solved using interval analysis. Interval analysis gives the boundary of the weight co officiants. Using interval Newton method, the weight co officiants are found. This algorithm is tested for noise cancellation of speech signal. The three adaptive filters algorithm used for comparison with the obtained results are Least Mean Square (LMS), Recursive Mean Square (RMS) filters and Kernel based filters. It is observed that the parameters mean square error is very less. The speed of convergence and signal to noise ratio is improved as compared to kernel methods. But processing time is very high and computational cost is doubled, as interval data includes infimum and supremum values. This algorithm can be used in noise cancelling headphones.

Numerical Study of Multiple Attractors in the Parallel Inductor–Capacitor–Memristor Circuit

Dynamical phenomena in the parallel inductor–capacitor–memristor circuit are studied numerically. A systematic search for coexisting attractors is carried out. The existence of multiple attractors is observed and bifurcation diagrams are constructed. Basins of attraction are computed. The coexistence of attractors is proved using interval analysis tools. The existence of periodic attractors is confirmed by applying the interval Newton method to prove the existence of stable periodic orbits of an associated return map. For numerically observed chaotic attractors the existence of attractors is proved by constructing trapping regions enclosing chaotic trajectories of the return map. The existence of topological chaos is proved using the method of covering relations.