Title :
Two-dimensional perfect reconstruction FIR filter banks with triangular supports
Author :
Yan, Hua ; Ikehara, Masaaki
Author_Institution :
Dept. of Electr. Eng., Keio Univ., Yokohama, Japan
fDate :
4/1/1999 12:00:00 AM
Abstract :
We present a theory and design of two-dimensional (2-D) perfect reconstruction (PR) filter banks (FBs) (PRFBs) in which the supports of the analysis and synthesis filters consist of two triangulars. The two-triangular FB can be realized by designing an appropriate 2-D complex prototype whose passband support is a triangle that is a half of a parallelepiped-shaped passband support defined by the sampling matrix. Then a complex prototype filter is modulated by the DFT, and each analysis filter is derived by taking the real part of the modulated output. We show that the two-triangular FB satisfies the condition of permissibility. A necessary and sufficient condition for 2-D PRFBs is 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 confirm the validity of the proposed method
Keywords :
FIR filters; channel bank filters; discrete Fourier transforms; matrix algebra; modulation; network synthesis; signal reconstruction; signal sampling; two-dimensional digital filters; 2D complex prototype; 2D perfect reconstruction FIR filter banks; DFT; analysis filters; cost function minimisation; filter design; frequency constraint; modulated complex prototype filter; necessary condition; parallelepiped-shaped passband support; passband support; permissibility; sampling matrix; sufficient condition; synthesis filters; triangular supports; Cost function; Design methodology; Filter bank; Filtering theory; Finite impulse response filter; Passband; Prototypes; Sampling methods; Sufficient conditions; Two dimensional displays;
Journal_Title :
Signal Processing, IEEE Transactions on
