?url_ver=Z39.88-2004&rft_id=UET-AVITECH-2019001&rft_val_fmt=info%3Aofi%2Ffmt%3Akev%3Amtx%3Adc&rft.relation=https%3A%2F%2Feprints.uet.vnu.edu.vn%2Feprints%2Fid%2Feprint%2F3443%2F&rft.title=A+new+windowed+digraph+Fourier+transform&rft.creator=Le%2C+Trung+Thanh&rft.creator=Nguyen%2C+Linh+Trung&rft.creator=Nguyen%2C+Viet+Dung&rft.creator=Abed-Meraim%2C+Karim&rft.subject=Electronics+and+Communications&rft.subject=Information+Technology+(IT)&rft.description=Signal+processing+on+graphs+is+an+emerging+topic+of+signal+processing%2C+considering+graphs+as+signals.+Hence%2C+similar+concepts+and+tools+in+signal+processing+can+be+extended%2C+for+understanding+graph+signals%2C+such+as+graph+frequency%2C+graph+operators%2C+graph+Fourier+transform.+In+this+report%2C+we+focus+on+the+joint+relationship+of+vertex-frequency+representation+of+graphs.+Motivated+by+the+existing+relationship+between+the+incidence+matrix+and+the+Laplacian+matrix+for+undirected+graphs%2C+we+define+a+generalized+Laplacian+matrix+for+directed+graphs.+This+allows+us+to+propose+a+unified+framework+for+the+graph+Fourier+transform%2C+graph+modulation+and+graph+translation.+Then%2C+built+upon+the+graph+modulation+and+translation+operators%2C+we+propose+a+new+windowed+graph+Fourier+transform+which+a+tight+vertex-frequency+frame.+The+experimental+results+indicate+that+our+proposed+methods+are+better+than+state-of-the-art+methods+and+beneficial+for+analyzing+various+different+types+of+graphs%2C+including+directed%2C+undirected%2C+weighted%2C+unweighted+and+connected+graphs.&rft.publisher=University+of+Engineering+and+Technology%2C+Vietnam+National+University&rft.date=2019-04-18&rft.type=Technical+Report&rft.type=NonPeerReviewed&rft.format=application%2Fpdf&rft.language=en&rft.identifier=https%3A%2F%2Feprints.uet.vnu.edu.vn%2Feprints%2Fid%2Feprint%2F3443%2F1%2FGSP_Technical_Report_Final.pdf&rft.identifier=++Le%2C+Trung+Thanh+and+Nguyen%2C+Linh+Trung+and+Nguyen%2C+Viet+Dung+and+Abed-Meraim%2C+Karim++(2019)+A+new+windowed+digraph+Fourier+transform.++Technical+Report.+University+of+Engineering+and+Technology%2C+Vietnam+National+University%2C+Hanoi%2C+Vietnam.+++++&rft.relation=UET-AVITECH-2019001