A new envelope algorithm of Hilbert–Huang Transform

• Published in: Mechanical systems and signal processing Vol. 20; no. 8; pp. 1941 - 1952
• Main Authors: Qin, S.R., Zhong, Y.M.
• Format: Journal Article
• Language: English
• Published: London Elsevier Ltd 01.11.2006; Elsevier
• Subjects: Acoustic signal processing; Acoustics; Algorithm; Envelope-line; Exact sciences and technology; Fundamental areas of phenomenology (including applications); Hilbert–Huang Transform; Measurement and testing methods; Physics; Segment power function method; Signal analysis; Solid mechanics; Structural and continuum mechanics; Hilbert–Huang Transform; Envelope-line; Segment power function method; Signal analysis; Algorithm; Signal processing; Hilbert-Huang Transform; Modeling; Algorithm analysis; Hilbert transformation; Spline approximation; Cubic spline
• ISSN: 0888-3270; 1096-1216
• DOI: 10.1016/j.ymssp.2005.07.002

The algorithm to compute the envelope-line in Hilbert–Huang Transform (HHT) has major drawbacks. This paper first introduces the problem of an envelope-line algorithm in HHT, analyses the shortcomings of two classic algorithms, cubic spline interpolation algorithm and the Akima interpolation algorithm, and then proposes an important theory called the Segment Slide Theory in light of the principle of parabola parameter spline interpolation method and proves it. Based on the theory we proposed and with intuitive geometric meaning, a new envelope algorithm, the segment power function method, is put forward. The new algorithm is superior to existing algorithms because in most situations it is more flexible than the cubic spline interpolation algorithm and smoother than the Akima interpolation algorithm as shown in the experimental examples, and it is less likely to introduce a false frequency when applied to HHT.