Department Publications

The number of coefficients of multi-dimensional (M-D) finite-extent impulse response (FIR) filters increases exponentially with the number of dimensions leading to significantly high computational complexities. In this brief, we propose a minimax design method for M-D FIR filters having sparse coefficients, therefore, having low computational complexities. We consider the design of M-D FIR filters with arbitrary frequency responses and low group delays of which the coefficients are complex valued. We formulate the minimax design as a second-order cone programming problem. Design examples confirm that M-D sparse FIR filters designed using the proposed method provide more than 60% reduction in the computational complexity for a similar error in the frequency response approximation compared to M-D FIR nonsparse filters designed using previously proposed minimax methods.

Transformers combined with convolutional encoders have been recently used for hand gesture recognition (HGR) using micro-Doppler signatures. In this letter, we propose a vision-transformer-based architecture for HGR with multiantenna continuous-wave Doppler radar receivers. The proposed architecture consists of three modules: 1) a convolutional encoder–decoder, 2) an attention module with three transformer layers, and 3) a multilayer perceptron. The novel convolutional decoder helps to feed patches with larger sizes to the attention module for improved feature extraction. Experimental results obtained with a dataset corresponding to a two-antenna continuous-wave Doppler radar receiver operating at 24 GHz (published by Skaria et al.) confirm that the proposed architecture achieves an accuracy of 98.3% which substantially surpasses the state-of-the-art on the used dataset.

We propose a minimax design method for finite impulse response (FIR) graph filters in this brief. We first convert the graph filter design problem into a numerically stable equivalent problem using a shifted monomial basis. Then, we convert the minimax graph filter design problem into a semidefinite programming problem. Furthermore, we propose a computationally-efficient structure to implement the FIR graph filters designed using the proposed method. Design examples confirm that the proposed method can be used to design FIR graph filters having reasonably high orders, and the proposed implementation structure substantially saves additions required to process a graph signal compared to graph filters designed using a previously proposed Chebyshev polynomial approximation method.

We propose a novel multi-dimensional zero-phase infinite impulse response (IIR) notch filter having multiple independently-tunable notches. The proposed notch filter employs a cascade structure with M N-dimensional ( N -D) zero-phase IIR filters to realize an N -D notch filter with M notches. In the proposed filter, the frequency and the bandwidth of each notch can be independently tuned. Furthermore, the proposed filter can have odd number of notches, which may be required for complex-valued signals. Experimental results confirm that the proposed filter significantly attenuates multiple narrowband interference and provides significant improvement in the signal-to-interference ratio compared to a previously proposed three-dimensional IIR filter.

We propose a weighted least-square (WLS) method to design autoregressive moving average (ARMA) graph filters. We first express the WLS design problem as a numerically-stable optimization problem using Chebyshev polynomial bases. We then formulate the optimization problem with a non-convex objective function and linear constraints for stability. We employ a relaxation technique and convert the non-convex optimization problem into an iterative second-order cone programming problem. Experimental results confirm that ARMA graph filters designed using the proposed WLS method have significantly improved frequency responses compared to those designed using previously proposed WLS design methods.

Two-dimensional (2-D) infinite-extent impulse response (IIR) filter design is a challenging problem due to the difficulty in verifying stability. optimization methods proposed so far predominantly consider the design of 2-D IIR filters having quadrantally-symmetric frequency responses, where the transfer functions have separable denominators. In this paper, we propose a weighted least-squares (WLS) design method for 2-D IIR filters having arbitrary frequency response and stable in the practical bounded-input bounded-output (P-BIBO) sense. Our design considers transfer functions with nonseparable numerators and denominators having complex-and real-valued coefficients, respectively. We formulate the WLS design as an iterative second-order cone programming problem, which includes constraints to guarantee the P-BIBO stability. Design examples confirm that the proposed WLS method leads to P-BIBO stable …