Discrete Signal Processing on Graphs: Frequency Analysis

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

A Discrete Fractional Gabor Expansion for Time–Frequency Signal Analysis

In this work, we present a discrete fractional Gabor representation on a general, non-rectangular timefrequency lattice. The traditional Gabor expansion represents a signal in terms of time and frequency shifted basis functions, called Gabor logons. This constant-bandwidth analysis uses a fixed, and rectangular time-frequency plane tiling. Many of the practical signals require a more flexible, ...

Discrete Frequency Warped Wavelets: Theory and Applications - Signal Processing, IEEE Transactions on

In this paper, we extend the definition of dyadic wavelets to include frequency warped wavelets. The new wavelets are generated and the transform computed in discrete-time by alternating the Laguerre transform with perfect reconstruction filterbanks. This scheme provides the unique implementation of orthogonal or biorthogonal warped wavelets by means of rational transfer functions. We show that...