# Graph Fourier Decomposition This function performs the graph Fourier decomposition. ```r gfdecomp(graph, K) ``` ## Arguments - `graph`: an `igraph` graph object with vertex attributes of coordinates `x`, `y`, a signal `z`, and edge attribute of `weight`. - `K`: specifies the number of frequency components. ## Details This function performs the graph Fourier decomposition. ## Returns - **fc**: list of frequency components according to the frequencies with `fc[[1]]` the lowest-frequency component. - **residue**: residue signal after extracting frequency components. ## References Ortega, A., Frossard, P., Kovačević, J., Moura, J. M. F., and Vandergheynst, P. (2018). Graph signal processing: overview, challenges, and applications. **Proceedings of the IEEE 106**, 808--828. tools:::Rd_expr_doi("https://doi.org/10.1109/JPROC.2018.2820126") Shuman, D. I., Narang, S. K., Frossard, P., Ortega, A., and Vandergheynst, P. (2013). The emerging field of signal processing on graphs: Extending high-dimensional data analysis to networks and other irregular domains. **IEEE Signal Processing Magazine**, 30(3) , 83--98. tools:::Rd_expr_doi("https://doi.org/10.1109/MSP.2012.2235192") ## See Also `sgemd`. ## Examples ```r #### example : composite of two components having different frequencies ## define vertex coordinate x <- y <- seq(0, 1, length=30) xy <- expand.grid(x=x, y=y) ## weighted adjacency matrix by Gaussian kernel ## for connecting vertices within distance 0.04 A <- adjmatrix(xy, method = "dist", 0.04) ## signal # high-frequency component signal1 <- rep(sin(12.5*pi*x - 1.25*pi), 30) # low-frequency component signal2 <- rep(sin(5*pi*x - 0.5*pi), 30) # composite signal signal0 <- signal1 + signal2 # noisy signal with SNR(signal-to-noise ratio)=5 signal <- signal0 + rnorm(900, 0, sqrt(var(signal0) / 5)) # graph with signal gsig <- gsignal(vertex = cbind(xy, signal), edge = A, edgetype = "matrix") # display of absolute values of the graph Fourier coefficients vs the eigenvalues gftplot(gsig) gftplot(gsig, K=5, size=3) outgft <- gftplot(gsig, K=5, plot=FALSE) outgft$eigenvalues # graph Fourier decomposition out <- gfdecomp(gsig, K=4) names(out) # display of a signal, the extracted low- and high-frequency components by GFD gplot(gsig, size=3) gplot(gsig, out$fc[[1]]+out$fc[[2]], size=3) gplot(gsig, out$fc[[3]]+out$fc[[4]], size=3) ```

gfdecomp function