THE APPLICATION OF FRACTIONAL CALCULUS TO NOISE SIMULATION

THE REALISTIC STOCHASTIC SIMULATION OF NOISE PROCESSES IS IMPORTANT IN A NUMBER OF AREAS INCLUDING (1) AIRCRAFT AND HELICOPTER NOISE, (2) ELECTRO-OPTICAL SENSOR (1/F) NOISE, (3) ATMOSPHERIC BACKGROUND NOISE FOR SCANNING SYSTEMS, (4) ATMOSPHERIC TURBULENCE FOR FLIGHT TRAINING SIMULATION, (5) OCEAN BACKGROUND NOISE FOR SONAR SYSTEMS, AND (6) SEISMIC NOISE FOR THE DETECTION OF UNDERGROUND EXPLOSIONS. UNFORTUNATELY, THE MOST RIGOROUS STOCHASTIC MODELS ARE OFTENCHARACTERIZED BY SPECTRA WITH CERTAIN IRRATIONAL PROPERTIES. PREVIOUSLY SUCH SPECTRA COULD ONLY BE APPROXIMATED IN THE STOCHASTIC GENERATION PROCESS. BY THE APPLICATION OF FRACTIONAL (NONINTEGER) DERIVATIVES IN THE TIME DOMAIN, IMPROVED DIFFERENCE EQUATIONS MAY BE OBTAINED WHICH WILL PERMIT NEW NOISE GENERATION TECHNIQUES WHICH ARE MORE EFFICIENT, MORE FLEXIBLE AND MORE RIGOROUS THAN THEIR PREDECESSORS. SUCH TECHNIQUES HAVE THE POTENTIAL FOR SIMULATING NOISE SERIES WITH TIME-VARYING SPECTRAL PROPERTIES.