Hilbert Spectrum in Time-Frequency Representation of Audio Signals Considering Disjoint Orthogonality

The performance of Hilbert spectrum (HS) in time-frequency representation (TFR) of audio signals is investigated in this paper. HS offers a fine-resolution TFR of time domain signals. It is derived by applying empirical mode decomposition (EMD), a newly developed data adaptive method for nonlinear and non-stationary signal analysis together with Hilbert transform. EMD represents any time domain signal as a sum of a finite number of bases called intrinsic mode functions (IMFs). The instantaneous frequency responses of the IMFs derived through Hilbert transform are arranged to obtain the TFR of the analyzing signal yielding the HS. The disjoint orthogonal property of audio signals is used as the decisive factor to measure the efficiency in TFR. Several audio signals are considered as disjoint orthogonal if not more than one source is active at any time-frequency cell. The performance of HS is compared with well known and widely used short-time Fourier transform technique for TFR. The experimental results show that HS based method performs better in time-frequency representation of the audio signals with the consideration of disjoint orthogonality.

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