Gibbs phenomenon for fractional Fourier series ABSTRACT:It is well known that the partial sums of a Fourier series of a non-periodic analytic function on a finite interval exhibit spurious oscillations near the interval boundaries. This phenomenon is known as the Gibbs effect. The authors show that a similar phenomenon is observed for the fractional Fourier series (FrFS) of a function with jump discontinuities. The convergence of FrFS is discussed and proved in a theorem. Specifically, the present work proves the uniform convergence of the FrFS for a non-periodic analytic function in the smooth region. The maximum amplitude of the oscillations for the FrFS remains constant (the Gibbs constant), similar to that for a classical Fourier series expansion. Finally, three numerical examples are investigated to demonstrate that the Gibbs constant for an FrFS is the same as for a Fourier series. Did you like this research project? To get this research project Guidelines, Training and Code... Click Here facebook twitter google+ linkedin stumble pinterest Adaptive generalised selection-combining receiver over time-varying mobile communication channel H∞ filtering for systems with time-varying delay satisfying a certain stochastic characteristic