We present extensive experimental data to objectively evaluate the benefits and limitations of common directional microphones in real-world sound fields. The microphones include a conventional directional microphone(DM), a balanced DM, etc., plus the Omni microphone (mic) as a benchmark. The evaluation focuses on noise outputs, signal-to-noise ratios(S/Ns) and distortions; the real-world sounds include male voices, female voices, babble noises, white noises and talking interferences. Each type of noises is at 4 or 5 levels, from 30 to 70 dB SPL, at 10 dB step, and each talking interference is at 3 levels: 50, 60 and 70 dB SPL. The research methods include analytically deriving sensitivity-gains, statistically calculating the three mics' outputs, experimentally viewing waveforms and spectra, and using large-sample wave files for a high confidence level. According to the experimental results, this paper concludes that 1) for a conversation in a quiet field, in soft or low noise field, the common DMs achieve comfortable S/Ns: 7 to 33 dB, similar to what the Omni mic does; 2) for a conversation in low, competing or strong talking interference fields, the common DMs achieve about 16 dB better S/N than the Omni mic does; 3) for a conversation in competing or strong surrounding noise field, the common DMs do not achieve beneficial S/N to understand speech; the common DMs' noises are close to the Omni mic noise; 4) in various experiments, the balanced DM preserve speech fidelity well as the Omni mic does, while the conventional DM does poorly. This paper further introduces the Simulink experimental manipulations, such as digital FIR filters' design, stereo channels' wave files creation, etc., in the Appendix.

The structures of common multichannel processing for hearing aids include equal bandwidth (BW) finite impulse response (FIR) filter bank, nonuniform BW FIR filter bank, and fast Fourier transform (FFT) plus inverse FFT (IFFT). This paper analyzes their operation principles, indicates the design methods by means of MATLAB R2018b resources, and describes the main characteristics: synthetical ripple, bank filters’ group delays, and individual filter sidelobe attenuation. Three schemes are proposed: equal BW sixteen-filter bank, logarithmic BW eight-filter bank, and 128-point FFT plus IFFT with overlap-add operation. To build the experimental modules, we introduce the settings of spectrum scopes, the acquirement of realistic speech and noises, and the gain enhancing/reducing needs of hearing aid features; the characteristics of synthetical outputs confirm precise control ability of the multichannel modules and differences between the three schemes. Subsequently, this paper illustrates two applications of the multichannel structures in hearing aids, the equal BW sixteen-filter bank with spectral subtraction (SS) for an artificial intelligence (AI) noise reduction (NR) and 128-point FFT plus IFFT spectral distortion removal for a directional microphone (DM). In Amy’s speech mixed with ringing, milk steamer, and strong wind noises separately, the SS processor improves signal-noise-ratio (SNR) by 6.5 to 15.9 dB. By measuring waveforms and spectra at the DM input and output, the DM system seamlessly removes the spectral distortion.

Some references discussed and evaluated performances of conventional directional microphones in hearing aids, from their conclusions, it is undoubted for the microphones to improve S/N, yet conditions of the advantage somewhat confused to hearing aid clinicians and professionals. To supplement the incompletion, we investigated behaviors of a directional microphone in extensive situations. We built an SimuLink laboratory, selected realistic talking voices and noises from wave files and made many experiments to find out illustrative evidences. Electroacoustic models are used for components of modelling a directional microphone; we operated the microphone with these sounds from real-world to calculate, view, measure and record behaviors of the directional microphone. We acquired  many waveforms, statistics and recordings of the experiments with woman’s and man’s talking voices, and environmental noises; we also listened to sounds at input and output of the directional microphone to perceive changes of the speech naturalness. Comparing to an omni microphone, the directional microphone does not enhances the speech signals on average; sensitivity-gain of the directional microphone is higher than that of the omni microphone when the tone frequency > 1.78 kHz; the directional microphone cancels the undesired speech well, as well as the babble noise and the environmental white noise from a beamed source at rear side; the directional microphone cannot improve the S/N of a speech within babble or white noise fields; in addition, we also observed and heard the speech spectrum distortion caused by the directional microphone

This paper describes new technologies of directional microphones for the practical hearing aids, referring to a front-delay direction microphone (DM), narrow beam DM, and minimum variance distortionless response (MVDR) beamformer. Each of the DM technologies was researched against weaknesses of those existing DMs, such as imperfection in low level noise, short suppression to adjacent interference, and failing to simultaneously perceive multiple target voices. In order to eliminate them, the conventional DM architectures have been innovated: the front-delay DM exchanged the elements' positions; the narrow beam DM employed binaural DMs to composite a relatively narrow lobe; the MVDR beamformer combined two types of processing in spatial and frequency domains; and the novel technologies are state-of-the-art beamformers for hearing aids. Based on some references related to the DM technologies and operation principles of the latest beamformers, we further researched the DM technologies, first proposed the implementing architectures, derived new gain equations of the relevant polar plots, accomplished the extensive experiments, and evaluated advantages and disadvantages of the DMs by the obtained evidences; then we confirmed that the new technologies could reach their expected goals. Meanwhile, we used the latest simulating software, Simulink of MatLab R2018b and audio edition software, SoundBooth, in our Lab computers.

Those theories of conventional filters for uniform-period signals do not apply to the analysis and design of the finite impulse response (FIR) filters for stagger-period signals. In this paper, we defined the fundamental concepts related to the stagger-period signals, derived the calculating equations, and described the time-variant property of the stagger-period filter; we proposed the Fourier transform pair between the frequency and impulse responses of this type filter, and proved the inverse of each other. Then, we discussed the design methods of stagger-period frequency-selective FIR filters, including lowpass, bandpass, and high-pass, presented the staggered windowing philosophies, illustrated different windows’ effectiveness, and described the principles and designs of optimized stagger-period high-pass filters with the match algorithm. As applications, we introduced three staggered optimization algorithms: eigenvalue, match, and linear prediction; and discussed performances of the filters designed for a moving target indication (MTI) radar. The stagger-period MTI filters not only extended the blind speed of flying targets, but also had an optimized improvement factor. Finally, we proposed a mathematical programming to search the best period code, which makes this type filter’s velocity response flattened. Meanwhile, we compared properties of the stagger-period to uniform-period filters, and provided with some examples to illustrate the theories and designs.