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Speech enhancement is one of the most important fields in audio and speech signal processing. The speech enhancement methods are divided into the single and multi-channel algorithms. The multi-channel methods increase the speech enhancement performance by providing more information with the use of more microphones. In addition, spatial aliasing is one of the destructive factors in speech enhancement strategies. In this article, we first propose a uniform circular nested microphone array (CNMA) for data recording. The microphone array increases the accuracy of the speech processing methods by increasing the information. Moreover, the proposed nested structure eliminates the spatial aliasing between microphone signals. The circular shape in the proposed nested microphone array implements the speech enhancement algorithm with the same probability for the speakers in all directions. In addition, the speech signal information is different in frequency bands, where the sub-band processing is proposed by the use of the analysis filter bank. The frequency resolution is increased in low frequency components by implementing the proposed filter bank. Then, the affine projection algorithm (APA) is implemented as an adaptive filter on sub-bands that were obtained by the proposed nested microphone array and analysis filter bank. This algorithm adaptively enhances the noisy speech signal. Next, the synthesis filters are implemented for reconstructing the enhanced speech signal. The proposed circular nested microphone array in combination with the sub-band affine projection algorithm (CNMA-SBAPA) is compared with the least mean square (LMS), recursive least square (RLS), traditional APA, distributed multichannel Wiener filter (DB-MWF), and multichannel nonnegative matrix factorization-minimum variance distortionless response (MNMF-MVDR) in terms of the segmental signal-to-noise ratio (SegSNR), perceptual evaluation of speech quality (PESQ), mean opinion score (MOS), short-time objective intelligibility (STOI), and speed of convergence on real and simulated data for white and colored noises. In all scenarios, the proposed method has high accuracy at different levels and noise types by Appl. Sci. 2020, 10, 3955; doi:10.3390/app10113955 www.mdpi.com/journal/applsci Appl. Sci. 2020, 10, 3955 2 of 29 the lower distortion in comparison with other works and, furthermore, the speed of convergence is higher than the compared researches.

Multiresolution Speech Enhancement Based on Proposed Circular Nested Microphone Array in Combination with Sub-Band Affine Projection Algorithm