Frequency Invariant Response Research Articles

Theoretical Lower Bounds on the Performance of the First-Order Differential Microphone Arrays With Sensor Imperfections

The first-order differential microphone arrays (DMAs) offer the appealing properties such as compact size, and frequency-invariant response, and thus have found a wide range of applications. However, they are known to be sensitive to sensor imperfections, i.e., microphone gain errors, phase errors and self-noise. In this paper, we study the analysis and design of the first-order DMAs in the presence of sensor imperfections. Particularly, the theoretical lower bounds on the performance of the first-order DMAs with sensor imperfections are derived in closed form by using the theory of interval analysis, including the lower bounds on directivity factor (DF) and front-to-back ratio (FBR), which are two essential performance measures in DMAs design. Unlike the existing related works, we have considered a more general and realistic scenario when all the above-mentioned three kinds of sensor imperfections coexist. Based on the derived performance lower bounds, a method is presented to design the first-order DMA with its performance exceeding the worst-case optimum performance. Moreover, an analysis is presented, which takes into account the sensor imperfections in the design of the first-order DMAs so the optimum worst-case performance is guaranteed. Extensive simulation results are also shown to demonstrate the effectiveness of our theoretical findings.

Circular Harmonics-Inspired Analytical Beampattern Synthesis with Beam-Steering Flexibility for Symmetric Uniform Circular Array Apertures

Beam-steering flexibility and frequency invariant response about symmetric uniform circular arrays (UCA) beampatterns synthesis are the critical issues addressed in this paper. The optimal approximation of beamformer’s beampattern is obtained with UCA via Jacobi-Anger expansion from the least-squares error perspective. We show how steering information can be initiated into the wanted beampattern. In addition, we propose a method for the modeling and synthesis of any wanted symmetric UCA beampattern, where the beampattern is flexible enough to be steered to any required direction. As such, we realized a beampattern synthesis with beam-steering flexibility and frequency-invariant response for symmetric UCA. With the method developed, clear-cut derivation of directivity pattern (DF) and white noise array gain (WNAG) are presented, and we clearly explained the amplification problem of white noise at low frequencies and how DF is degraded at high frequencies. To demonstrate the proposed method, we attempt to synthesize 16-element second-order dipole of 2 cm radius, operating at 2 GHz, in various signal directions, θs ∈[0°, 15°, 30°, 60°, 80°, 100°, 120°, 150°]. The numerical experiment and results obtained show the validity and effectiveness of the proposed method. Frequency invariant response is observed below 4 GHz. An increase in the number of elements constantly improves the gain. In addition, the proposed method is a generalization of UCA apertures.

On the Design of Frequency-Invariant Beampatterns With Uniform Circular Microphone Arrays

This paper deals with two critical issues about uniform circular arrays (UCAs): frequency-invariant response and steering flexibility. It focuses on some optimal design of frequency-invariant beampatterns in any desired direction along the sensor plane. The major contributions are as follows. 1) We explain how to include the steering information in the desired directivity pattern. 2) We show that the optimal approximation of the beamformer's beampattern with a UCA from a least-squares error perspective is the Jacobi–Anger expansion. 3) We develop an approach to the design of any desired symmetric directivity pattern, where the deduced beampattern is almost frequency invariant and its main beam can be pointed to any wanted direction in the sensor plane. 4) With the proposed approach, we derive an explicit form of the white noise gain (WNG) and the directivity factor (DF), and explain clearly the white noise amplification problem at low frequencies and the DF degradation at high frequencies. The analysis also indicates that increasing the number of microphones can always improve the WNG. We show that the proposed method is a generalization of circular differential microphone arrays. The relationship between the proposed method and the so-called circular harmonics beamformers is also discussed.

Design of Frequency Invariant Beamformer Without Temporal Filtering

A novel method for the design of frequency invariant beamformers for uniformly spaced three-dimensional (3-D) arrays is proposed. Unlike the traditional method, which is based on the use of temporal filtering, the proposed design can achieve a frequency invariant response without employing any temporal filtering process and the resultant beamformer does not suffer from the beam broadening effect at high off-boresight steering angles. A design example is provided to show the effectiveness of the proposed method.

The receiving of chirp signals with frequency invariant beam response

A frequency invariant response algorithm is proposed for getting over the signal distortion in high frequency when the beamformer receives the broadband signals. In this method, the weight vector of the reference beam pattern is designed firstly, then the weight vectors when the beam response in the frequency sub-bands approaching the reference response mostly are computed by optimized method or adaptive method. By this method, the beam pattern in each sub-band can be almost kept invariable. As a result, the receiving chirp signal can be improved. Owing to the adoption of the adaptive method to approach the optimized vectors, it has no restricting of the array format and the element directivity, and the method can be used widely.