Modified DFT filter banks with perfect reconstruction

Design of a new DFT filter bank with modified sampling kernels and its application to arbitrary image scaling

“…For the down/up sampling by L (L > 1) in the M-band FB, the scaling factor a in (1)-(2) can be replaced by L. Also, the upper/lower limits in the integral of (1) and (2) (3) and (4). Furthermore, a CSSF of degree 2, ψ 3 [s],0 (t), with a finite support of [−2 ∼ 2] [5], is employed, instead of the sinc function [7], as a sampling kernel, since the sinc function has some problems in practical implementation (e.g., truncation effects) [3,8].…”

“…Also, the upper/lower limits of the integral in (2) are set to [−π/a ∼ π/a] to eliminate unwanted images due to up-sampling. By utilizing (1)- (2) further for the M-band low-pass prototype pre/post filters as in [4], the following down/up samplers with a factor L (L < M: i.e., non-critically sampled case) can be newly derived as…”

“…The conventional MDFT FB [4] is designed by modifying the DFT FB structure to cancel all odd-alias components causing quality degradation in the image reconstruction by the DFT FB. Also, it is known that the MDFT FB requires lower computational burden than the DFT FB [9].…”

“…However, the OAI technique requires high computational burden [5,6]. In this paper, a new modified DFT (MDFT) FB is proposed for arbitrary image scaling, whereby analysis and synthesis parts of the conventional MDFT [4] are revised in an efficient manner. More specifically, down/up sampling kernels are newly introduced along with a compactly supported sampling function (CSSF) of degree 2.…”

“…To solve those problems, an arbitrary image scaling method, utilizing a DFT FB with closed-form sampling kernels, was recently reported [3]. While the DFT FB has some advantages such as high-speed implementation, it is not suitable for subband coding, since it is not easy to eliminate aliasing effects due to subsampling [4]. Also, another DFT filter bank designed by employing an optimized adaptive interpolation (OAI) [3,5] was proposed to compensate for such quality degradation in the image reconstruction.…”