Two-dimensional perfect reconstruction FIR filter banks with triangular supports

In this paper, we present a theory and design of two-dimensional (2-D) perf ect reconstruction (PR) filter banks (FB's) (PRFB's) in which the supports of the analysis and synthesis filters consist of two triangulars, The two-t riangular FB can be realized by designing an appropriate 2-D complex protot ype whose passband support is a triangle that is a half of parallelepiped-s haped passband support defined by sampling matrix. Then a complex prototype filter is modulated by DFT, and each analysis filter is derived by taking the real part of the modulated output. We show that the two-triangular FB s atisfies the condition of permissibility, A necessary and sufficient condit ion for 2-D PRFB's will be derived. Moreover, we present a design method of the 2-D PRFB that minimizes the cost function consisting of the frequency constraint and PR condition, Finally, a design example is presented to conf irm the validity of the proposed method.