Symmetric Half-plane Research Articles

Analytical Solution of Ground Stress Induced by Shallow Tunneling with Arbitrary Distributed Loads on Ground Surface

The impact of shallow tunnel construction on the surrounding environment is often considered as a symmetric half-plane problem with circular holes. In this research, the analytical solutions of the ground stresses and displacements of a shallow circular tunnel in an elastic half-plane under arbitrary distributed loads on ground surface were derived, based on the complex variable method. Then, an application was implemented to analyze the potential plastic zone induced by shallow tunneling adjacent to the ground surface structures. The verification of the results obtained from the proposed analytical prediction model was carried out using the numerical simulations. Additionally, the influences of different boundary condition (different magnitudes and ranges of arbitrary distributed loads and different symmetric boundary conditions of the tunnel perimeter) on the distribution characteristics of the potential plastic zones were analyzed. In general, the results showed that the larger the pile loads and the closer the relative position between the tunnel and distributed loads, the more distinct the coalesced trends of the potential plastic zones around the tunnel and the potential plastic zones around the distributed loads.

Design of 2-D interpolation/decimation filters using a general 2-D digital allpass filter

Two-dimensional (2-D) interpolation/decimation digital filters are widely used for sampling rate conversion. A general structure consisting of a 2-D recursive digital allpass filter (DAF) and a 2-D pure delay block is presented for designing 2-D recursive interpolation/decimation filters. We utilize a 2-D DAF with symmetric half-plane (SHP) support for its filter coefficients to comply with the symmetry possessed by 2-D interpolation/decimation filters. The structure also possesses a preferable doubly complementary half-band (DC-HB) property that reduces the number of required independent coefficients for designing 2-D interpolation/decimation filters. We appropriately formulate the design problem to obtain a simple linear optimization problem that minimizes the phase error of the 2-D recursive SHP DAF in the pth norm (Lp) sense. Simulation results are provided for illustration and comparison.

Two‐dimensional recursive digital filters with nearly circular‐symmetric magnitude response and approximately linear phase

AbstractThis paper presents a general structure using 1‐D and two‐dimensional (2‐D) recursive digital all‐pass filters (DAFs) for the design of 2‐D recursive circularly symmetric digital low‐pass filters (CS‐DLFs). The general structure is a cascade of two stages composed of all‐pass building blocks. The first stage is a parallel connection of a 2‐D recursive DAF with a symmetric half‐plane (SHP) support for its filter coefficients and a 2‐D pure delay block. The second stage composed of a parallel connection of a 1‐D recursive DAF and a 1‐D pure delay block is used for eliminating the unwanted pass‐band induced by the first stage. As a result, the design of a 2‐D CS‐DLF in either the least‐squares or the minimax sense can be formulated in a simple linear optimization problem in terms of the weighted‐phase response error for each DAF. Design results with nearly circularly symmetric magnitude response and approximately linear phase are also provided for illustration and comparison. Copyright © 2010 John Wiley & Sons, Ltd.

Two-Channel Quincunx QMF Banks Using Two-Dimensional Digital Allpass Filters

This paper presents a novel structure for the analysis and synthesis filters of two-channel quincunx quadrature mirror filter (QQMF) banks. This structure uses an appropriate combination of 2-D recursive digital allpass filters (DAFs) with symmetric half-plane (SHP) support regions. The proposed analysis/synthesis filters possess a 2-D doubly complementary half-band (DC-HB) property that facilitates the design and implementation of the proposed two-channel QQMF banks. Moreover, the proposed structure provides approximately linear-phase response without magnitude distortion. The design problem of the proposed QQMF banks is appropriately formulated to result in a linear optimization problem that only minimizes the linear-phase error associated with the 2-D SHP DAFs in the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">p</i> th-norm ( <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Lp</i> ) sense. Efficient design techniques are developed to solve the <i xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Lp</i> optimization problem for finding the coefficients of the 2-D recursive SHP DAFs. Finally, we provide simulation results for illustration and comparison.

Two-dimensional block implementation of symmetric half-plane recursive digital filters

Two-dimensional (2-D) block implementation of 2-D symmetric half-plane (SHP) recursive filters is considered. A 2-D block-recursive equation is first derived. It is found that all the coefficient matrices associated with the input and previous output blocks are Toeplitz in their submatrices. Therefore, high-speed convolution algorithms can be utilized to perform the associated submatrix-vector multiplications. The block implementation using the fast Fourier transform is compared to the direct implementation as regards computational requirements.< <ETX xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">&gt;</ETX>

Sectioned implementation of two-dimensional symmetric half-plane recursive filters

This paper concerns sectioning approaches for the implementation of two-dimensional recursive filters with symmetric half-plane support. Two new algorithms are presented and compared to the direct implementation as regards computational requirements. Procedures for choosing optimal sectioning parameters for both infinite and finite size rows are provided. This method has been implemented on a scientific minicomputer (Prime 750) and examples are given to illustrate the computational requirements. The method is also suitable for microprocessor implementation with an associated signal processing chip to perform the section FFT's.

Direct convolution and the initial conditions of two-dimensional infinite impulse response digital filters

An expression for the direct convolution of two-dimensional infinite impulse response digital filters, which corresponds to that presented by Gold and Jordan for one-dimensional filters, is derived. Specifically, the output of the filter is given in terms of the input and output values and a set of initial conditions. The analysis is based on the two-dimensional block realization model. The cases of the quarter plane, non-symmetric half-plane and symmetric half-plane, primarily with respect to the required initial conditions, which are given explicitly, are considered.

A design method for two-dimensional recursive digital filters

A method for designing two-dimensional, symmetric half-plane recursive digital filters is presented: a filter is first designed as a parametrized family of one-dimensional filters; a simple approximation is then used to find a rational, stable, two-dimensional filter. Some advantages and disadvantages of the method are discussed, and several examples are given.

2-D recursive phase filters for the solution of two-dimensional wave equations

This paper deals with two-dimensional wave equation migration in seismic Signal processing according to a frequency domain model. The required ideal phase specifications are approximated by a 2-D all-pass digital filter with symmetric half-plane hyperbolic impulse response. Examples are included to compare this recursive filtering approach with existing processing techniques.