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- W2763569390 abstract "Basic operations in graph signal processing consist of processing signals indexed on graphs either by filtering them or by changing their domain of representation in order to better extract or analyze the important information they contain. The aim of this chapter is to review general concepts underlying such filters and representations of graph signals. We first recall the different Graph Fourier Transforms that have been developed in the literature, and show how to introduce a notion of frequency analysis for graph signals by looking at their variations. Then, we move to the introduction of graph filters that are defined like the classical equivalent for one-dimensional signals or two-dimensional images, as linear systems that operate on each frequency of a signal. Some examples of filters and their implementations are given. Finally, as alternate representations of graph signals, we focus on multiscale transforms that are defined from filters. Continuous multiscale transforms such as spectral wavelets on graphs are reviewed as well as the versatile approaches of filterbanks on graphs. Several variants of graph filterbanks are discussed for structured as well as arbitrary graphs with a focus on the central point of the choice of the decimation or aggregation operators." @default.
- W2763569390 created "2017-10-20" @default.
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- W2763569390 date "2018-01-01" @default.
- W2763569390 modified "2023-10-18" @default.
- W2763569390 title "Design of Graph Filters and Filterbanks" @default.
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- W2763569390 doi "https://doi.org/10.1016/b978-0-12-813677-5.00011-0" @default.
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