On Parallelepiped-Shaped Passbands for Multidimensional Nonseparable ${\bf M}$th-Band Low-Pass Filters
Qutubuddin Saifee, P.G. Patwardhan, Vikram M. Gadre · IEEE Transactions on Circuits & Systems II Express Briefs · 2008
The ldquoshaperdquo of the desired frequency passband is an important consideration in the design of nonseparable multidimensional ( M-D) filters in M-D multirate systems. For M-D Mth-band filters, the passband shape should be chosen such that the Mth-band constraint is satisfied. The most commonly used shape of the passband for M-D Mth-band low-pass filters is the so-called symmetric parallelepiped (SPD) SPD(piM-T) . In this paper, we consider the more general parallelepiped passband SPD (piLT), and derive conditions on L such that the Mth-band constraint is satisfied. This result gives some flexibility in designing M-D Mth-band filters with parallelepiped shapes other than the commonly used case of L = M-1. We present design examples of 2-D Mth-band filters to illustrate this flexibility in the choice of L.