The study has involved fractional calculus applied to active broad-band noise control. Noise processes with regular or rational spectra can be adequately modeled by common distributions and linear filters. Noise processes, however, are often characterized by irregular or non-rational spectra. The large number of coefficients associated with the filter transfer functions for these processes results from the use of rational approximation techniques. By fractional calculus techniques such noise processes can be described with significantly fewer coefficients. In the adaptive filter design, with fewer coefficients to handle, the search algorithm can be accelerated. An adaptive filter design based on fractional calculus was developed for active noise control. A numerical procedure based on the Grunwald relation was developed for solving the governing fractional differential equation for generating the antinoise of a class of noise processes with only one spectral peak. The residual noise was minimized by the method of steepest descent. Based on such procedures the ANFRAC program was developed. The study demonstrates that an adaptive filter based on fractional calculus for active broad-band noise control is clearly feasible.

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