A new type of perfect reconstruction filter bank is presented in this paper., This new class of filter bank has the following distinct features at the same time: linear-phase, distortion-free, IIR-FIR filter pair, closed form expression, orthogonal projection, and factorization-free. In contrast, the other existing filter banks do not possess all these properties simultaneously. For example, the classic Quadrature Mirror Filter (QMF) does not have the perfect reconstruction nature. Another example is the Conjugate Quadrature Filter (CQF), which lacks the linear- phase property. A qualitative comparison of different types of filter banks is also included. This newly developed perfect reconstruction IIR-FIR filter bank is then extended to the 2-D case. Both separable and non-separable filters are considered. In addition, both rectangular downsampling and non-rectangular downsampling schemes are discussed. Numerical optimization procedures are used to compute the optimal filter coefficients. The results are listed in tables for quick reference.