Then, the subblocks are oversampled and transformed to time domain by LN-point IFFT (inverse fast Fourier transform) and using an optimization algorithm or conventional searching method, each subblock is multiplied by a

phase factor as follows:

The attenuation factor and the

phase factor are related to the dielectric properties of medium as follows [14]:

In [6, 7], all-phase fast Fourier transform (apFFT) spectral analysis was proposed to obtain the

phase factor between subbands.

Allen and his collaborators proved that the complex amplitude of an optical vortex possessing an azimuthal

phase factor exp (im[theta]) carries an orbital angular momentum of mh, where m is the topological charge and d is the azimuthal angle [4].

If the potential [[alpha].sub.0]A(x) associated with it is present, then the wave function undergoes a change of the

phase factor by the AB effect.

As a matter of fact, the EM fields radiated by finite size sources enclosed in a convex domain D, bounded by a surface [SIGMA] with rotational symmetry and observed on a regular surface M external to D and having the same symmetry, can be always represented by a finite number of NF data also for an unbounded observation domain, provided that a proper

phase factor is extracted from the field expression and proper parameterizations are adopted to describe M.

The first method employs CSS with varied delays and fixed phase rotation vector defined by the scaling factor while the second method employs fixed delay and calculates the optimum

phase factor such that candidate with minimum PAPR is produced.

The unified theory [10] also allows the determination of the parameter [xi] and

phase factor [gamma] to get a nonredundant representation along the spiral.

(6-9), must be generated by the presence of the different side-bands n, which come with

phase factor exp (-in[omega]t).

The scattering of x-rays on a crystal structure with spatially distributed heterogeneities depends on the

phase factor of the lattice [phi](x, z) = exp (ihu(x, z)), where u(x,z) is the vector of atomic displacement, h is the vector of the reciprocal lattice.

While [[phi].sub.PC] contributes an overall

phase factor dependent on [f.sub.PC], [[phi].sub.PV] produces a rotation of the neutron spin vector about the momentum axis.

Choosing master/slave boundary pairs prompts the user for the

phase factor between the boundaries.