Carbon nanotubes (CNTs) is widely used as electromagnetic materials. Study on the calculation of complex permittivity of carbon nanotubes not only can make us understand the characteristics of the dielectric properties of CNTs materials, but also has an important significance for material design. Based on the equivalent transmission line model of CNTs, the connection model of the wall capacitance and quantum capacitance of multi-walled carbon nanotubes (MWCNTs) in the microwave field was established, and the impedance expression of MWCNTs equivalent transmission line was derived. Based on the complex conductivity and the resistance capacitance network model of composite materials, the analytical expression of complex permittivity of MWCNTs composites was established. The complex permittivity of CNTs composites with the tube length of 20μm, the pipe outer diameter of 25nm, 40nm and 70nm respectively ,and the microwave reflection loss of CNTs coating with the pipe outer diameter of 20nm, the tube length of  60μm, 100μm respectively,  and the thickness of 4mm were calculated with this analytical expression at the frequency of 2~18GHz. The calculated results are well agreed with the experimental results in reference. The calculation results also show that the imaginary part of the complex permittivity increases with the increase of the diameter and the length of the CNTs, and the effect of the tube length on the complex permittivity is greater than that of the tube diameter.

In one of our recent work, a signal panning method called “local Ambisonics” for creating vertical virtual source was proposed. It was proved that the local Ambisonics panning can create desired dynamic cue for vertical localization for a subject at the sweet point, and thus local Ambisonics panning is better than the traditional pair wise panning method. In actual listening, however, the translation of subjects head may change the binaural sound pressures and the corresponding localization cues, consequently influence the accuracy and stability of the synthesized virtual sources. In this paper, the influence of subjects head translation on the summing localization cues in local Ambisonics panning was analyzed, and a psychoacoustic experiment on the stability of virtual source localization was conducted. The results indicate that, for the target sound source within the loudspeakers arrangement and an appropriate content of head translation less than 0.20m, the local Ambisonics panning is still able to create appropriate localization cues, and the subjects still can perceive virtual sources in reasonable locations with mean error mostly less than 5°. Hence, local Ambisonics panning exhibits better stability against subjects head translation.

The spatial distribution of the localization spectral characteristics at various distances was studied by using the spectral deviation algorithm and the correlation algorithm. The best-match angles at different distances were obtained, and a subjective localization experiment was further carried out to validate the audio effects. Calculation results show that, the spatial distortion of the localization spectral characteristics occurs at different distances, in which the distortion degree increases for decreasing distance and large deviation angle relative to the lateral direction.The further localization experiment shows that the calculated spatial distortions of the localization spectral characteristics lead to audible distortion of sound images, especially at the front and back directions. Meanwhile, compared to the correlation algorithm, the spectral deviation algorithm is more suitable in selecting the best-match angles for different distances in view of localization confusion rate as well as localization accuracy.