The memristor, a novel device, has been widely utilized due to its small size, low power consumption, and memory characteristics. In this paper, we propose a new three-dimensional discrete memristor map based on coupling a one-dimensional chaotic map amplifier with a memristor. Firstly, we analyzed the memristor model to understand its characteristics. Then, a Simulink model for this three-dimensional discrete memristor map was developed. Lastly, the complex dynamical characteristics of the system were analyzed via equilibrium points, bifurcation diagrams, Lyapunov exponent spectra, complexity, and multistability. This study revealed the phenomena of coexisting attractors and hyperchaotic attractors. Simulink modeling confirmed that the discrete memristors effectively enhanced the chaos complexity in the three-dimensional discrete memristor map. This approach addresses the shortcomings of randomness, the lack of ergodicity, and the small key space in a one-dimensional chaotic map, thereby enriching the theoretical analysis and circuit implementation of chaos.

Differential beamforming has attracted much research since it can utilize an array with a small aperture size to form frequency-invariant beampatterns and achieve high directional gains. It has recently been applied to the loudspeaker line array to produce a broadside frequency-invariant radiation pattern. However, designing steerable frequency-invariant beampatterns for the loudspeaker line array has yet to be explored. This paper proposes a method to design a steerable differential beamformer with a loudspeaker line array. We first determine the target differential beampatterns according to the desired direction, the main lobe width, and the beampattern order. Then, we transform the target beampattern into the modal domain for representation. The Jacobi-Anger expansion is subsequently used to design the beamformer so that the resulting beampattern matches the target differential beampattern. Furthermore, based on the criterion of minimizing the mean square error between the synthesized beampattern and the ideal one, a multi-constraint optimization problem, which compromises between the robustness and the mean square error, is formulated to calculate the optimal desired weighting vector. Simulations and experimental results show that the proposed method can achieve steerable frequency-invariant beamforming from 300 Hz–4 kHz.

The significance of the coherent-to-diffuse-power ratio (CDR) has grown in the fields of speech dereverberation and noise reduction. However, existing CDR estimators are typically limited to applications with only two microphones. In this paper, we investigate CDR estimation in multichannel acoustic systems with more than two microphones. We propose two estimation methods. The first approach involves decomposing the microphone array into several groups of subarrays, where each subarray consists of only two sensors. We estimate the CDR for each group and then fuse these group CDR estimates through weighted averaging to form the multichannel CDR estimate. This weighted average CDR estimation can be seen as an extension of traditional two-channel CDR estimation methods to the multichannel scenario. The second method is based on array manifold estimation using a joint matrix diagonalization technique, eliminating the need for subarray decomposition. By integrating the CDR estimates with a parametric Wiener-type post-filter, we demonstrate, via simulations, the superior performance of the proposed techniques in terms of CDR estimation accuracy, signal-to-noise ratio (SNR) gain, log-spectral distortion (LSD), and direct-to-reverberant-energy ratio (DRR).