Discrete Signal Processing on Graphs

Expository Notes on Signal Processing on Graphs

Graph theory has developed into a useful tool in applied mathematics as many modern data sets are or can be represented as a graph. In these data sets, vertices correspond to different sensors, observations, or data points and edges represent connections, similarities, or correlations among those points. Some immediate applied examples include social network data, electricity networks, and imag...

Discrete Time Signal Processing

Discrete Signal Processing Notes

The Undersampled Discrete Gabor Transform - Signal Processing, IEEE Transactions on

Conventional studies on discrete Gabor transforms have generally been confined to the cases of critical sampling and oversampling in which the Gabor families span the whole signal space. In this paper, we investigate undersampled discrete Gabor transforms. For an undersampled Gabor triple (g; a; b), i.e., a b>N, we show that the associated generalized dual Gabor window (GDGW) function is the sa...

Discrete uncertainty principles and sparse signal processing

We develop new discrete uncertainty principles in terms of numerical sparsity, which is a continuous proxy for the 0-norm. Unlike traditional sparsity, the continuity of numerical sparsity naturally accommodates functions which are nearly sparse. After studying these principles and the functions that achieve exact or near equality in them, we identify certain consequences in a number of sparse ...