Complex hilbert transform filter

Juuso T. Olkkonen, Hannu Olkkonen

Research output: Contribution to journalArticleScientificpeer-review

Abstract

Hilbert transform is a basic tool in constructing analytical signals for a various applications such as amplitude modulation, envelope and instantaneous frequency analysis, quadrature decoding, shift-invariant multi-rate signal processing and Hilbert-Huang decomposition. This work introduces a complex Hilbert transform (CHT) filter, where the real and imaginary parts are a Hilbert transform pair. The CHT filtered signal is analytic, i.e. its Fourier transform is zero in negative frequency range. The CHT filter is constructed by half-sample delay operators based on the B-spline transform interpolation and decimation procedure. The CHT filter has an ideal phase response and the magnitude response is maximally flat in the frequency range 0 ≤ ω ≤ π. The CHT filter has integer coefficients and the implementation in VLSI requires only summations and register shifts. We demonstrate the feasibility of the CHT filter in reconstruction of the sign modulated CMOS logic pulses in a fibre optic link.
Original languageEnglish
Pages (from-to)112-116
JournalJournal of Signal and Information Processing
Volume2
Issue number2
DOIs
Publication statusPublished - 2011
MoE publication typeA1 Journal article-refereed

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Shift registers
Amplitude modulation
Splines
Fiber optics
Decoding
Mathematical operators
Interpolation
Fourier transforms
Signal processing
Decomposition

Keywords

  • Hilbert Transform
  • Analytic Signal
  • Fractional Delay Filters

Cite this

Olkkonen, Juuso T. ; Olkkonen, Hannu. / Complex hilbert transform filter. In: Journal of Signal and Information Processing. 2011 ; Vol. 2, No. 2. pp. 112-116.
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Complex hilbert transform filter. / Olkkonen, Juuso T.; Olkkonen, Hannu.

In: Journal of Signal and Information Processing, Vol. 2, No. 2, 2011, p. 112-116.

Research output: Contribution to journalArticleScientificpeer-review

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