In this paper, we present a numerical design method for two-dimensional (2-D) FIR linear-phase (LP) quincunx filter banks (QFB) with equiripple magnitude response and perfect reconstruction (PR). The necessary conditions for the filter length of analysis filters are derived. A dual affine scaling variant (DASV) of Karmarkar's algorithm is employed to minimize the peak ripples of analysis filters and an approximation scheme is introduced to satisfy the PR constraint for the 2-D filter banks (FB). The simulation examples are included to show the effectiveness of this proposed design technique.

The optimal design of complex infinite impulse response (IIR) two-channel quadrature mirror filter (QMF) banks with equiripple frequency response is considered. The design problem is appropriately formulated to result in a simple optimization problem. Therefore, based on a variant of Karmarkar's algorithm, we can efficiently solve the optimization problem through a frequency sampling and iterative approximation method to find the complex coefficients for the IIR QMFs. The effectiveness of the proposed technique is to form an appropriate Chebyshev approximation of a desired response and then find its solution from a linear subspace in several iterations. Finally, simulation results are presented for illustration and comparison.

This paper considers the problem of finding two-dimensional (2-D) direction of arrivals (DOAs) for coherent cyclostationary signals using a 2-D array with random position errors. To alleviate the performance degradation due to the coherence between the signals of interest (SOIs) and the random perturbation in 2-D array positions, a matrix reconstruction scheme in conjunction with an iterative algorithm is presented to reconstruct the correlation matrices related to the received array data so that the resulting correlation matrices possess the eigenstructures required for finding 2-D DOAs. Then, using the reconstructed matrices, we create a subspace orthogonal to the subspace spanned by the direction vectors of the SOIs. Therefore, the 2-D DOAs of the SOIs can be estimated based on a subspace-fitting concept and the created subspace. Finally, several simulation examples are presented for illustration and comparison.