Fractional constraints based designing of 2-dimensional FIR filters

摘要

In this paper, the fractional derivative constraints are used for the designing of 2-dimensional (2-D) linear phase highpass (HP) and bandstop (BS) finite impulse response (FIR) filter. First, the quadrantally even symmetric impulse response filter is considered. Then, the fractional derivative constraints are imposed on integral square error at some frequency points such that the fractional derivative at these points is zero. In order to obtain optimal filter coefficients, conventional least square method and Lagrange multiplier are exploited to minimize the difference between the ideal frequency response and designed frequency response. The implementation of fractional derivative constraint provides large design flexibility and accuracy in the designing of the 2-D FIR filter. Finally, two design examples are illustrated to justify the effectiveness of the proposed design method.