A new reconstruction formula and shift frame for WGFRFT

Abstract

The study of signals defined on irregular domains has garnered significant attention, and the field of graph signal processing has emerged as a way to model such signals using underlying graph structures. Vertex frequency analysis is a crucial tool for graph signal analysis and representation. Finding different kinds of frames via the windowed graph fractional Fourier transform (WGFRFT) is necessary to extract the characteristics of graph signals. To overcome this issue, we introduce the concept of the dual of WGFRFT frame and use it to develop a new reconstruction formula for graph signals. Additionally, we propose fractional shift frame. Finally, to highlight the utility of our proposed frames, we present some examples which use our fractional shift frame to extract the spectrum of graph signal.