Hilbert Transform, Analytic Signal, and Modulation Analysis for Graph Signal Processing

Understand

We propose Hilbert transform (HT) and analytic signal (AS) construction for signals over graphs.

• This is motivated by the popularity of HT, AS, and modulation analysis in conventional signal processing, and the observation that complementary insight is often obtained by viewing conventional signals in the graph setting.
• Our definitions of HT and AS use a conjugate-symmetry-like property exhibited by the graph Fourier transform (GFT).
• We show that a real graph signal (GS) can be represented using smaller number of GFT coefficients than the signal length.