  This paper proposes a class of $M$-channel spectral graph filter banks with a
symmetric structure, that is, the transform has sampling operations and
spectral graph filters on both the analysis and synthesis sides. The filter
banks achieve maximum decimation, perfect recovery, and orthogonality.
Conventional spectral graph transforms with decimation have significant
limitations with regard to the number of channels, the structures of the
underlying graph, and their filter design. The proposed transform uses sampling
in the graph frequency domain. This enables us to use any variation operators
and apply the transforms to arbitrary graphs even when the filter banks have
symmetric structures. We clarify the perfect reconstruction conditions and show
design examples. An experiment on graph signal denoising conducted to examine
the performance of the proposed filter bank is described.
