A New Approach for Designing Orthogonal Wavelets for Multicarrier Applications

yesThe Daubechies, coiflet and symlet wavelets, with properties of orthogonal wavelets are suitable for multicarrier transmission over band-limited channels. It has been shown that similar wavelets can be constructed by Lagrange approximation interpolation. In this work and using established wavelet design algorithms, it is shown that ideal filters can be approximated to construct new orthogonal wavelets. These new wavelets, in terms of BER behave slightly better than the wavelets mentioned above, and much better than biorthogonal wavelets, in multipath channels with additive white Gaussian noise (AWGN). It is shown that the construction, which uses a simple simultaneous solution to obtain the wavelet filters from the ideal filters based on established wavelet design algorithms, is simple and can easily be reproduced

Enno Littmann's letter to Ignaz Goldziher

A numerical method is presented for sizing of highly conductive penetrable and perfectly electrically conducting (PEC) submicron wires on substrates. For efficiency, the Method of Auxiliary Sources is used in the forward model of the inverse Kirsch-Kress Method. The radius of the circular cross section of PEC and silver wires positioned on a semi-infinite silicon substrate is estimated based on numerically simulated scattered far field. The illumination is monochromatic, transverse electric (TE) polarised, and with fixed angle of incidence. Average relative errors smaller than 1% and 5% are achieved for PEC and penetrable wires, respectively, in the dynamic ranges 0.2–1.3 and 0.8–1.3 times the operating free-space wavelength, respectively. In all cases, the inversion time is less than 1 sec

Near-and far-field simulations of 2D particles with photonic structure

We present a numerical computation scheme for calculation of the reflected and transmitted near- and farfields arising from the interaction of 2D cylindrical shaped particles with photonic structures. The photonic structures are illuminated with either planar or Gaussian incident fields. The interaction between the cylindrical particle and the photonic structure is generally too complex to be handled analytically, so we will use the semianalytical Fourier Modal Method (FMM) to calculate the near- and far-fields. The Gaussian field is written as a sum of plane waves with varying amplitudes. We present a very general method for obtaining the plane wave amplitudes by combining the angular spectrum theory, Parseval's theorem and Shannon's sampling theorem. We demonstrate the use of this method in our rigorous calculation of reflected and transmitted near- and far-fields of single cylindrical particle located in the vicinity of a periodic photonic structure or a planar silicon surface. The examples demonstrate that the method may be applied to particle counting