Harmonic tonal detectors based on the BOGA

Tonals generated by machineries with rotating elements typically have a harmonic structure with unknown fundamental frequencies, amplitude, harmonic order and phase. Detecting this type of signals is of great importance to numerous engineering applications. In the frequency domain, tonals are represented by a few harmonic frequencies, which appear in blocks, related to one or more fundamental frequencies. This block-sparsity property of the frequency content suggests alternative ways to recover and detect tonals by using sparse signal processing techniques. Motivated by the success of the block orthonormal greedy algorithm (BOGA), new detection architectures, which require no prior information about the number of the fundamental frequencies, are proposed for robust tonal detection in low signal to noise ratio (SNR) environments. The distributions of the test statistics of detection architectures are firstly analyzed theoretically and comprehensively based on the theory of order statistics. Detection performances are also analyzed and compared theoretically and experimentally. Significant improvements on detection performance in low SNR environments are shown over the conventional detectors that do not consider the harmonic structure and the sparsity of the tonals.