Digital signal processing requires digital filters with variable frequency characteristics. A variable digital filter (VDF) is a filter whose frequency characteristics can be easily and instantaneously changed. In this paper, we present a design method for variable linear-phase finite impulse response (FIR) filters with multiple variable factors and a reduction method for the number of polynomial coefficients. The obtained filter has a high piecewise attenuation in the stopband. The stopband edge and the position and magnitude of the high piecewise stopband attenuation can be varied by changing some parameters. Variable parameters are normalized in this paper. An optimization methodology known as semidefinite programming (SDP) is used to design the filter. In addition, we present that the proposed VDF can be implemented using the Farrow structure, which suitable for real time signal processing. The usefulness of the proposed filter is demonstrated through examples.

A high-frequency approximate method for calculating the diffraction by a smooth convex surface is presented. The advantage of this method is the validity of it in the caustic region of the creeping rays where the Geometrical Theory of Diffraction (GTD) becomes invalid. The concept used in this method is based on the Method of Equivalent Edge Currents (EEC), and the equivalent line currents for creeping rays which are derived from the diffraction coefficients of the GTD are used. By evaluating the radiation integral of these equivalent line currents, the creeping ray contribution which is valid within the caustic region is obtained. In order to check the accuracy and the validity of the method, the diffraction problem by a perfectly conducting sphere of radius a is solved by applying the method, and the obtained results are compared with the exact and the GTD solutions. It is confirmed from the comparison that the failure of the GTD near the caustic is removed in this method and accurate solution is obtained in this area for high-frequency (ka8). Furthermore, it is also found that this method is valid in the backward region (0θ90, θ is an observation angle mesuered from an incident direction), whereas not in the forward region (90θ180).

A novel approximate equivalent edge currents (EECs) are proposed for use in the modified edge representation (MER) for flat plates. It was reported that PO-EECs with classical PO diffraction coefficients, as applied to MER, perfectly recover PO surface integration. The inclusion of classical FW-EECs as it is, however, would not enhance the accuracy since the reality of the fringe wave is lost in the edge modification. This paper presents simple approximation for inclusion of FW-EECs in MER; FW-EECs are weighted by the function of the angle between the modified edge and the real edge. The key feature of this approach is that uniform fields are predicted everywhere though only classical diffraction coefficients are used. MER also simplifies the ray-tracing in the secondary diffraction analysis. Numerical results for diffraction from flat plates demonstrate the potential of these EECs.