• Mechanical Systems and Signal Processing, v. , 2012

“The Hilbert Transform is a relative “newcomer” to the signal processing community, at least if compared to the traditional Fourier Transform methods. While its basic definitions and properties were known to mathematicians and physicists for almost 60 years, it was mainly Bendat, who brought it to the attention of the digital processing area by his tutorially oriented monograph [1].

Since then researches from many engineering disciplines have tried to apply it to many problems, often lured by the apparent simplicity of being able to compute Instantaneous Frequencies and envelopes. To mention just MSSP, approximately 100 submissions were received only in the last decade, attempting to apply the Hilbert Transform to vibrating systems, diagnostics of rotating machine elements and more.

Careful perusing of many such submissions showed strikingly how many of the difficulties, pitfalls or limitation involved with the application of Hilbert Transform were ignored or even unknown. It is this timely that an engineering oriented text on the application of HT was made available, and the book by Feldman seems exceptionally suitable in this respect, in spite of being partially geared to vibration problems.

The book is divided into 3 logically separated parts. The first one is mandatory to anyone attempting to understand or implement Hilbert Transform methods. It presents the theoretical background. The somewhat difficult concept of Instantaneous Frequency is especially illuminated, time and frequency domain analyzed, and even introduces some of the fundamental error mechanisms encountered with actual computations.

Part 2 is specifically geared to the vibration engineering community. Typical signals are first analyzed. The concept of envelopes, more complex than often realized by practitioners, is clearly expanded. Signals with Mono and Multi-components are also presented.

Finally, vibration decomposition methods, utilizing Hilbert Transform, are discussed. These methods, being signal adaptive (in contrast to the Fourier or wavelet decomposition) have attracted much interest in the last 2 decades, prompted by Huang’s seminal paper [2]. The Empirical Mode Decomposition, and Feldman’s recent method Hilbert Vibration Decomposition, are extensively exposed, enabling the reader to get a feeling on their suitability for various applications. For example, the topic of achievable frequency resolution is clearly presented, a topic sorely ignored by many users.

Part 3 is more specific, the choice of material obviously affected by Feldman’s own work, as well as his editorial activities for MSSP (where he serves on the editorial board). The detection and identification of nonlinearities in vibrating systems is introduced in details, using both simple and rigorous mathematical tools. These include the non-parametric identification of various damping mechanisms and stiffnesses. MDOF systems are analyzed and some industrial applications discussed, summarized. Many of the results presented were computed utilizing software tools developed by Feldman, and now available on the web.

The large amount of material covered necessitated a somewhat concise presentation. Hence some topics have to be read with careful attention. In spite of this, both the ideas and details are clearly presented. The reference list is extensive and up to date. This reviewer is obviously based, having known and cooperated with Feldman for a long period. It is, however, with professional sincerity that I can highly recommend this book to the general signal processing, and of course to the vibration engineering community. To attempt to understand or use Hilbert Transform methods, it should be a part of the chosen books on their bookshelves.”

[1] J.S.Bendat, The Hilbert Transform and Applications to Correlation Measurements, Bruel&Kjaer, Denmark,1985.
[2] N.E.Huang, Z.Shen, S.R.Long, M.C.Wu, H.H.Shih, Q.Zheng, N.C.Yen, C.C.Tung, H.H.Liu, The empirical mode decomposition and the Hilbert spectrum for nonlinear and non-stationary time series analysis, Proc. R.Soc. London Ser.A454 (1971) (1998) 903-995.

S. Braun
Technion-Israel Institute of Technology, Faculty of Mechanical Engineering, Technion City, Haifa32000, Israel
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  • The International Academy for Production Engineering (CIRP) NEWSLETTER Nº 42 – May 2011“This book, written by Dr Michael Feldman – a world expert, will appeal to both professionals and students working in mechanical, aerospace, and civil engineering, as well as naval architecture, biomechanics, robotics, and mechatronics.”
    Amazon customer review:
  • Worth it, March 10, 2012“Well written. Covers the basics of Hilbert transforms very well. As the title says, the emphasis is on mechanical engineering. I’m an electronic engineer with interests in communications and signal processing and it would be useful to have a book which covers these application areas of the Hilbert transform.”

    Michael Connelly “Mike”
    (Limerick, Ireland)

  • Excellent applications book, June 27, 2014
    “There are a lot of great applications of the Hilbert Transform contained therein. An EXCELLENT addition to Nonlinearity in Structural Dynamics by K. Worden and G.R. Timlinson. Can come across a bit as a cheer-leading session for the Hilbert Transform as an analytical tool, but is overall a good read.”

    Steven Whitican