All Phase Digital Filtering And Image Interpolation Based On IDCT/DCT

IDCT/DCT and All Phase philosophy are integrated in research on digital filtering and image interpolation.Firstly, the design formula of all phase digital filter (APDF) based on DFT, WHT, IDCT and DCT are unified in one frame, and based on the existed theory of All Phase digital filtering, the formula of inverse transition matrix G^-1 is derived. Then through the transition matrix G and the inverse transition matrix G^-1, the design method of APDF based on DFT, WHT, IDCT and DCT is unified, also the design method of APDF and windowed APDF is unified.Secondly, to find the suited application, the characteristics of APDF based on IDCT/DCT are discussed. Zero-phase and sub-band filtering with complementary are two characters of APDF.Thirdly, to put the APDF based on IDCT/DCT into practice, three fast realizations are put forward. The amplitude frequency response characteristics of the filter all can be tuned in real time, and are especially suited in adaptive filtering where the response of filter is changing in real time. The recursive formula of the DCT/IDCT of all phase input data space is given in direct sequency field realization, and transition matrix is also given in time and sequency field equivalence realization. Direct sequency field recursive realization is especially suited in continuous data processing, and sequency field equivalence realization is especially suited in narrow band filtering. In most condition, the calculation complication of time field equivalence realization is the least.Fourthly, to improve the amplitude frequency response characteristics of APDF based on IDCT/DCT, the design formula of windowed APDF based on IDCT/DCT is derived. Experiments show that when using the window of Kaiser better amplitude frequency response characteristics of APDF are achieved. On the condition of using the same number of frequency samples, the amplitude frequency response characteristics of Kaiser windowed APDF based on IDCT/DCT is better than of FIR digital filter designed by frequency sampling method.Fifthly, the interpolation characters of diamond half band filter which designed based on IDCT applied in sampling structure conversion are discussed. Fourier analysis method is extended to 2-D. It shows that higher order can achieve better interpolation results, and the interpolator keeps the edges well but keeps the texture worse.