  The classical support uncertainty principle states that the signal and its
discrete Fourier transform (DFT) cannot be localized simultaneously in an
arbitrary small area in the time and the frequency domain. The product of the
number of nonzero samples in the time domain and the frequency domain is
greater or equal to the total number of signal samples. The support uncertainty
principle has been extended to the arbitrary orthogonal pairs of signal basis
and the graph signals, stating that the product of supports in the vertex
domain and the spectral domain is greater than the reciprocal squared maximum
absolute value of the basis functions. This form is then used in compressive
sensing and sparse signal processing to define the reconstruction conditions.
In this paper, we will revisit the graph signal uncertainty principle using the
graph Rihaczek distribution as an analysis tool and derive an improved bound
for the support uncertainty principle of graph signals.
