On Parallelepiped-Shaped Passbands for Multidimensional Nonseparable bf Mth-Band Low-Pass Filters

The “shape” of the desired frequency passband is an important consideration in the design of nonseparable multidimensional ( -D) filters in -D multirate systems. For -D th-band filters, the passband shape should be chosen such that the th-band constraint is satisfied. The most commonly used shape of the passband for -D th-band low-pass filters is the so-called symmetric parallelepiped (SPD) . In this paper, we consider the more general parallelepiped passband , and derive conditions on such that the th-band constraint is satisfied. This result gives some flexibility in designing -D th-band filters with parallelepiped shapes other than the commonly used case of . We present design examples of 2-D th-band filters to illustrate this flexibility in the choice of .