When the nonlinear, complicated behavior of natural phenomena and man-made artifacts cannot be modeled perfectly by one-dimensional modeling, multidimensional modeling can be an effective alternative. It is an emerging technique in digital signal processing, with its special complexities.

The main theme of the paper is a comparative, technical discussion of two multidimensional (M-D) filtering methods to mitigate the aliasing in multilinear time-series signals. Based on sound engineering, “there are cases when the M-D filter can be applied more efficiently than a resampling filter.” The authors model the input-output, including stopband, passband, and transition regions, “to demonstrate the advantages of using the proposed M-D filter.” Next, they define a nonlinear optimization problem for finding filter coefficients.

The paper reports that the complexity of the solution increases as the dimension of the filter grows. Its presented contribution uses symmetries to reduce complexity and computational cost, that is, time-reversal symmetry “for a filter with linear phase and zero delay” and permutation symmetry. Experimental results for a generic baseband receiver front-end and its low-noise amplifier (LNA) are detailed.

Although the proposed techniques are not a general solution, the work is a significant attempt to solve a complicated issue.