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N. E. Huang, Z. Shen, and S. R. Long, M. C. Wu, E. H. Shih, Q. Zheng, C. C. Tung, and H. H. Liu, “The Empirical Mode Decomposition and the Hilbert Spectrum for Nonlinear and Nonstationary Time Series Analysis,” Proceedings of the Royal Society of London A, Vol. 454, pp. 903-995, 1998.

has been cited by the following article:

• TITLE: Computation of Hilbert Transform via Discrete Cosine Transform

  AUTHORS: Hannu Olkkonen, Peitsa Pesola, Juuso T. Olkkonen

  KEYWORDS: Hilbert Transform, Analytic Signal, Envelope Analysis, FFT

  JOURNAL NAME: Journal of Signal and Information Processing, Vol.1 No.1, December 1, 2010

  ABSTRACT: Hilbert transform (HT) is an important tool in constructing analytic signals for various purposes, such as envelope and instantaneous frequency analysis, amplitude modulation, shift invariant wavelet analysis and Hilbert-Huang decomposition. In this work we introduce a method for computation of HT based on the discrete cosine transform (DCT). We show that the Hilbert transformed signal can be obtained by replacing the cosine kernel in inverse DCT by the sine kernel. We describe a FFT-based method for the computation of HT and the analytic signal. We show the usefulness of the proposed method in mechanical vibration and ultrasonic echo and transmission measurements.