Measured directivity pattern for 2 Audix-TM1 microphones placed d = 5 cm apart. 

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... ratio can be determined given the ATF estimate A l and the beamforming filter W l at each time frame l . The PSD matrix Γ N N is a constant. The directional and diffuse component of the sound field, Z ˆ ′ and Z ˆ ′′ , are estimated online using Eqn. ( 3). Their respective PSDs are found by recursive averaging, e.g. Φ Z ˆ ′ Z ˆ ′ ,l = Φ Z ˆ ′ Z ˆ ′ ,l − 1 α + (1 − α ) Z ˆ ′ Z ˆ ′ H . The DD-SNR ξ ( j Ω) is obtained by using Eqn. (6). We used the well-known Optimally-Modified Log-Spectral Amplitude Es- timator (OM-LSA) algorithm [13] to calculate the real-valued gain G ( j Ω) . Finally, an estimate of the clean speech signal is obtained by X ( j Ω) = Y ( j Ω) G ( j Ω) . Our first experiment aims at presenting the enhanced directivity of a two microphone beamforming array with an aperture of d = 5 cm. Since the postfilter depends on the beamformer’s state by using the ATF estimate A ˆ ( j Ω) and the beamforming filter W ( j Ω) , we can easily incorporate the postfilter into the overall Directivity Pattern . We used the procedure described in [14] to simulate the directivity pattern of the GSC with our postfilter. The beamformer is fixed to look towards 0 ◦ . To measure the real directivity pattern for comparison, we used a physical array consisting of two microphones. For this experiment we used the room from Figure 1, a turntable and an exponential chirp for measuring the frequency response. Figure 4 shows that the measured beampattern is a bit sharper than the theoretical result. A cause for this effect could be minor gain differences in the microphones being used. However, the most relevant property is the high spatial selectivity for low frequencies. It can be seen that signals impinging from outside ± 20 ◦ are completely suppressed, even with two microphones. Increasing the number of microphones up to four does not change the directivity pattern significantly. In order to test the speech quality of our MCSE system against a significant amount of speech data, the TIMIT [15], KCORS [16], and (KCOSS) [17] speech corpora have been used. All three databases use f s = 16 kHz and data from both male and female speakers. The speech signals have been replayed with the loudspeaker located at the 0.5m position (see Figure 1). For the noise data, recordings from various sources, e.g. traf- fic noise, industry parks, subway stations and the NOIZEUS database have been replayed with the loudspeaker located at the 5m position. In total, about 60 minutes of test material has been generated. For comparison, we also implemented two other postfilter approaches – the MC-SPP approach and the TBRR. We use the PEASS Toolkit [9, 10] to evaluate the performance of the algorithms in terms of speech quality. It explicitly aims at the psycho-acoustically motivated quality assessment of audio source separation algorithms. In a wider sense, a beamformer can also be thought of as a source separation task, i.e. the enhanced speech signal is an estimate of the speech source at the reference microphone. PEASS delivers four scores: The Target Perceptual Score (TPS) measures the perceptual quality of the desired speech signal con- tained in the postfilter output. The Interference Perceptual Score (IPS) measures the influence of the residual noise components in the beamformer output. The Artifact Perceptual Score (APS) measures the influence of artifacts like musical noise generated by the algorithm. And the Overall Perceptual Score (OPS) provides a global measure of the perceptual quality of the enhanced output. Each score ranges from 0 to 100 and large values indicate better performance. Each algorithm is tested with a signal-to-interference ratio (SIR) ranging from -20dB to +20dB in 5dB steps. Figure 5 shows the comparison of the postfilters in terms of the PEASS measures. The OPS score of the TBRR and the MC-SPP postfilters are more or less equal. However, the TBRR performs better than the MC-SPP for the IPS and TPS score, and the APS score indicates that the TBRR introduces the most artifacts. The MC-SPP algorithm has the lowest IPS score, as it relies on the inversion of the spatial noise PSD matrix which is numerically unstable at low frequencies due to high signal correlation. The TBRR algorithm has the lowest APS score, as it relies on classical noise floor estimation techniques such as IMCRA or MS, which introduce musical artifacts depends on the instationarity of the noise. The speech quality of our DD-PF does not depend on spatial noise PSD estimation or a speech presence probability, but solely on the estimate of the directional and the diffuse sound components Φ Z ˆ ′ Z ˆ ′ and Φ Z ˆ ′′ Z ˆ ′′ . Their accuracy is determined by the shape of the noise sound field and the target leakage in the blocking matrix (e.g. speech leaking through the blocking matrix due to reflections). We found the target leakage to be quite low in our experiments, and the diffuse noise sound field was almost ideal diffuse. Therefore, we achieved both a good speech quality and a good noise sup- pression at the same time, even for low frequencies. This can be seen by the OPS and TPS score. In this paper, we introduced the Directional-to-Diffuse Postfilter (DD-PF), which splits the sound field at the microphones into its directional and diffuse components, and calculates a Directional-to-Diffuse SNR from the PSDs of these components, from which a noise reduction Wiener filter is derived. Its performance depends only on target leakage in the beamformer and the diffuse sound field assumption. In our experiments, we have shown that these conditions are met in a typical setup using four microphones and a variety of speech and noise tracks. The achieved directivity pattern is selective even at low frequencies and the speech quality is significantly higher compared to the TBRR and MC-SPP ...