1. Naval Research Academy, PLA (NVRA), Beijing 100073, China
2. Key Laboratory of Underwater Acoustic Signal Processing of Ministry of Education, Southeast University, Nanjing 210096, China
Corresponding author (firstname.lastname@example.org)
There exists a distinct envelope modulation of the radiated noise of underwater acoustic target because of the propeller beat. These parameters related with envelop modulation imply a wealth of physical information such as the speed of the propeller. Therefore, the detection of envelope modulation on noise (DEMON) characteristics is critical for classifying and recognizing the underwater acoustic target. In this study, a novel high-resolution reconstruction approach of DEMON is proposed by exploiting its group sparsity across subbands compared with the drawback in Fourier transform (FT)-based DEMON. On the one hand, the estimation of sparse DEMON is converted into solving underdetermined equation in the inverse Fourier basis by exploiting the sparsity of DEMON; on the other hand, the reconstruction method can be improved and developed using the exploitation of the group sparsity across subbands. Unlike the non-sparse FT-based DEMON, which requires a further detection of line spectrum for classification or recognition, our proposed DEMON is sparse and directly provides the line spectrum. It effectively avoids the threshold choice in the detection and artificial interference in the feature extraction. Furthermore, the proposed method is developed in the non-parametrical sparse Bayesian learning framework, so it has the capability of learning the sparsity of DEMON automatically.
Flow chart of demodulation
Flow chart of demodulation in multiple subbands.
(Color online) Group sparsity in multiple bands
(Color online) Spectrum of radiated noise of underwater target. (a) Stationary continuous spectrum; protectłinebreak (b) demodulation spectrum
(Color online) DEMON of radiated noise signal. (a) Weights in shaft frequency and the blade-passing frequency; (b) non-coherent DEMON in multiple bands; (c) sub-band DEMONs
(Color online) Estimation of sparse sub-band DEMON. Sparse DEMON in the band of (a) [50,~100], (b) [100,~500], (c) [500,~1000], and (d) [1000,~2000] Hz
(Color online) Reconstruction results of sparse DEMON. (a) Non-coherent sparse DEMON; (b) the enlarged images in [0,~20] Hz with non-coherent result; (c) reconstructed sparse DEMON with group sparsity; and (d) the enlarged images in [0,~20] Hz with group-sparsity result
(Color online) Precision and F-measure performance versus modulation depth. (a) Precisionand recallvs. modulation depth; (b) F-measure vs. modulation depth
(Color online) Waveform and spectrum of real data. (a) Time-domain waveform of real data; (b) spectrum of real data
(Color online) Estimated sparse DEMON. (a) Sub-band sparse DEMONs; (b) non-coherent sparse DEMON in multiple subbands; (c) estimated sparse DEMON with group sparsity
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