This paper deals with an orthogonal functional expansion of a non-linear stochastic functional of a stationary binary sequence taking 1 with equal probability. Several mathematical formulas, such as multi-variate orthogonal polynomials, recurrence formula and generating function, are given in explicit form. A simple example of orthogonal functional expansion and stationary random seqence generated by the stationary binary sequence are discussed.

A periodic approach introduced previously is applied to the TM wave scattering from a finite periodic surface. A mathematical relation is proposed to estimate the scattering amplitude from the diffraction amplitude for the periodic surface, where the periodic surface is defined as a superposition of surface profiles generated by displacing the finite periodic surface by every integer multiple of the period . From numerical examples, it is concluded that the scattering cross section for the finite periodic surface can be well estimated from the diffraction amplitude for a sufficiently large .

This paper presents a low-power video A/D conversion technique using features of moving pictures. Neighboring frames in typical video sequences and neighboring pixels in each video frame are highly correlated. This property is effectively used for the video A/D conversion to reduce the number of comparators and the resulting power consumption. A set of reference voltages is given to a comparator array so that the iterative A/D conversion converges in the logarithmic order of the prediction error. Simulation results using standard moving pictures showed that the average number of iterations for the A/D conversion is less than 3 for all the moving pictures tested. In the proposed 12 b A/D converter, the number of comparators can be reduced to about 1/5 compared with that of the two-step flash A/D converters, which are commonly used for video applications. The A/D converter is particularly useful for the integration to CMOS image sensors.

10G-EPON systems have attracted a great deal of attention as a way of exceeding to realize over 10 Gb/s for optical subscriber networking. Rapid burst-mode transmitting/receiving techniques are the key technologies enabling the burst-mode upstream transmission of 10G-EPON systems. In this paper, we have developed a OLT burst-mode 3R receiver incorporating a burst-mode AGC optical receiver and an 82.5 GS/s over-sampling burst-mode CDR and a ONU burst-mode transmitter with high launch power DFB-LD of 1.27 µm wavelength to fully compliant with IEEE802.3av 10G-EPON PR30 standards. The transmitting characteristics of a fast LD turn-on/off time of less than 6ns and a high launch power of more than +8.0 dBm, and the receiving characteristics of receiver sensitivity of -30.1 dBm and the upstream power budget of 38.1 dB are successfully achieved.

We present an 82.5GS/s over-sampling based burst-mode clock and data recovery (BM-CDR) IC chip-set comprising an 82.5GS/s over-sampling IC using 8×10.3GHz multi-phase clocks and a dual-rate data selector logic IC to realize the 10.3Gb/s and 1.25Gb/s dual-rate burst-mode fast-lock operation required for 10-Gigabit based fiber-to-the-x (FTTx) services supported by 10-Gigabit Ethernet passive optical network (10G-EPON) systems. As the key issue for designing the proposed 82.5GS/s BM-CDR, a fresh study of the optimum number of multi-phase clocks, which is equivalent to the sampling resolution, is undertaken, and details of the 10.3Gb/s cum 1.25/Gb/s dual-rate optimum phase data selection logic based on a blind phase decision algorithm, which can realize a full single-platform dual-rate BM-CDR, ate also presented. By using the power of the proposed 82.5GS/s over-sampling BM-CDR in cooperation with our dual-rate burst-mode optical receiver, we further demonstrated that a short dual-rate and burst-mode preamble of 256ns supporting receiver settling and CDR recovery times was successfully achieved, while obtaining high receiver sensitivities of -31.6dBm at 10.3Gb/s and -34.6dBm at 1.25Gb/s and a high pulse-width distortion tolerance of +/-0.53UI, which are superior to the 10G-EPON standard.

This paper deals with the singular behavior of the diffraction of transverse magnetic (TM) waves by a perfectly conductive triangular periodic surface at a low grazing limit of incidence. The wave field above the highest excursion of the surface is represented as a sum of Floquet modes with modified diffraction amplitudes, whereas the wave field inside a triangular groove is written as a sum of guided modes with unknown mode amplitudes. Then, two sets of equations are derived for such amplitudes. From the equation sets, all the amplitudes are analytically shown to vanish at a low grazing limit of incidence. From this fact, it is concluded analytically that no diffraction takes place and only reflection occurs at a low grazing limit of incidence for any period length and any triangle height. This theoretical result is verified by a numerical example.

As a method of analyzing the wave scattering from a finite periodic surface, this paper introduces a periodic approach. The approach first considers the wave diffraction by a periodic surface that is a superposition of surface profiles generated by displacing the finite periodic surface by every integer multiple of the period . It is pointed out that the Floquet solution for such a periodic case becomes an integral representation of the scattered field from the finite periodic surface when the period goes to infinity. A mathematical relation estimating the scattering amplitude for the finite periodic surface from the diffraction amplitude for the periodic surface is proposed. From some numerical examples, it is concluded that the scattering cross section for the finite periodic surface can be well estimated from the diffraction amplitude for a sufficiently large .

This paper deals with the scattering of a cylindrical wave by a perfectly conductive periodic surface. This problem is equivalent to finding the Green's function G(x,z|xs,zs), where (x,z) and (xs,zs) are the observation and radiation source positions above the periodic surface, respectively. It is widely known that the Green's function satisfies the reciprocity: G(x,z|xs,zs)=G(xs,zs|x,z), where G(xs,zs|x,z) is named the reversal Green's function in this paper. So far, there is no numerical method to synthesize the Green's function with the reciprocal property in the grating theory. By combining the shadow theory, the reciprocity theorem for scattering factors and the average filter introduced previously, this paper gives a new numerical method to synthesize the Green's function with reciprocal property. The reciprocity means that any properties of the Green's function can be obtained from the reversal Green's function. Taking this fact, this paper obtains several new formulae on the radiation and scattering from the reversal Green's function, such as a spectral representation of the Green's function, an asymptotic expression of the Green's function in the far region, the angular distribution of radiation power, the total power of radiation and the relative error of power balance. These formulae are simple and easy to use. Numerical examples are given for a very rough periodic surface. Several properties of the radiation and scattering are calculated for a transverse magnetic (TM) case and illustrated in figures.