## 1 Introduction
This method used the same interpolation factor for all frequencies; thus, its performance for enhancing a stereophonic image might have been limited when the direction of the input stereo signals was dependent on the frequency [14]. In another study, a delay-and-sum (DS) beamformer was utilized to convert AB stereo signals into XY stereo signals [13]. However, in real reverberant recording environments, the DS beamformer changed the direction of stereophonic images due to the reverberant effects [15]. This was because the reverberation time changed according to the frequency, and the DS beamforming weights could not be adapted to this reverberation time change [14]. These results suggest that frequency-dependent amplitude panning for stereophonic image enhancement is necessary for real reverberant environments. Accordingly, we propose frequency-dependent amplitude panning for stereophonic image enhancement when two omni-directional microphones are closely spaced, as deployed in portable devices. In [16,17], frequency-dependent amplitude panning was also used to enhance the stereophonic image for portable devices equipped with closely spaced stereo microphones, where the ratio of spectral magnitudes between the left- and right-channel signal was used for the panning. On the other hand, the proposed method first introduces azimuth-frequency (A-F) analysis [18] to estimate the direction of the input audio according to frequency. In other words, we first apply short-time Fourier transform (STFT) to the input stereo audio signal, and then project the spectral component of each frequency bin on an azimuth plane that is generated by converting the time difference between two microphones into their level difference. Next, the direction at each frequency bin is assigned as the azimuth at which the projected magnitude is minimized. Finally, a frequency-dependent amplitude panning technique is proposed to enhance the stereophonic image by modifying the stereophonic law of sines [19]. To evaluate the performance of the proposed method, three different recording environments are considered: anechoic, convolutive, and real reverberant. First, the directivity pattern of the proposed method is compared with that of a conventional method based on the DS beamformer [13] in the three recording environments. Second, the directional accuracy of the stereo audio processed by the proposed method is compared to that of the audio processed by the conventional method by measuring the subjective directions of listeners depending on the horizontal direction of the sources. Finally, a degraded mean opinion score (DMOS) assessment [20] is carried out to evaluate the quality as an aspect of the audio distortion after the proposed method has been applied. The remainder of this paper is organized as follows: a conventional method based on the DS beamformer [13] is described in Section 2. Section 3 describes the proposed stereophonic image enhancement method based on A-F analysis and a frequency-dependent amplitude panning technique. Section 4 then evaluates the performance of the proposed method applied to audio signals recorded in anechoic, convolutive, and real reverberant environments. Finally, Section 5 concludes this paper.