Frequency Selective Filtering of Graph Signal in Directed Graph Fourier Transform Domain

In this paper, a frequency selective filtering of real-valued graph signal in the directed graph Fourier transform (DGFT) domain is presented. First, the spectral properties of the GDFT are investigated. Then, the eigenvalues of directed Laplacian are divided into real and complex valued sets to constrain the ideal spectral response of graph filter such that real-valued filtered signal can be preserved. Next, lowpass, bandpass and highpass filtering methods of graph signals are studied. Finally, the proposed filtering method is used to reduce the unwanted noise superimposed on temperature data for demonstrating the effectiveness of the proposed method.