  This paper extends the existing theory of perfect reconstruction two-channel
filter banks from bipartite graphs to non-bipartite graphs. By generalizing the
concept of downsampling/upsampling we establish the frame of two-channel filter
bank on arbitrary connected, undirected and weighted graphs. Then the equations
for perfect reconstruction of the filter banks are presented and solved under
proper conditions. Algorithms for designing orthogonal and biorthogonal banks
are given and two typical orthogonal two-channel filter banks are calculated.
The locality and approximation properties of such filter banks are discussed
theoretically and experimentally.
