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The discrete Hilbert transform and its application to the analysis of reverberant decay of modal vibrations in enclosures

The Hilbert transform is an important tool for a signal analysis, and it has been widely used in many areas of science and technology. An application of this method to an analysis of reverberant decay of modal vibrations in enclosures enables a detection of a pressure envelope resulting in a more accurate prediction of a reverberation time. It is shown that the discrete Hilbert transform is not accurate in an envelope detection even for the moderately damped harmonic signals, and a generated error strongly depends on the ratio of a modal damping coefficient to a mode frequency. This inexactness is due to the fact that for exponentially decaying harmonic signals the Bedrosian identity is not satisfied. In order to increase the accuracy of the envelope prediction, appropriate modifications of discrete signals corresponding to different kinds of modes are proposed. This method is successfully tested in the multi-mode case using discrete signals simulating a reverberant response of two coupled rooms.