This correspondence derives necessary and sufficient conditions for a
multirate linear phase FIR tilter bank, acting on a symmetrically exte
nded finite-length input signal, to produce either symmetric or antisy
mmetric downsampled subbands. Such techniques have gained popularity r
ecently for image coding applications, and we provide the solution to
a key technical problem in terms of the input and filter symmetries an
d the downsampling ratio.