Efficient frequency-sampling design of one-and two-dimensional FIR filters using structural subband decomposition

A new method is presented for the fast and efficient design of one-dimensional (1D) and two-dimensional (2D) linear phase FIR filters. In this approach, the concept of structural subband decomposition of 1D and 2D sequences is applied to an improved method for frequency-sampling FIR filter design. Using this decomposition the filter is implemented as a parallel connection (bank) of sparse subfilters cascaded with interpolators. An algebraic relationship is then developed to determine the frequency samples of the subband filters from the original specified frequency samples. Filter designs based on various types of interpolators derived from transform matrices such as the Hadamard, binomial, and DCT are investigated. Significant computational savings arise from discarding subbands that contribute little to the overall frequency response and selectively quantizing the wordsize of the coefficients of the remaining subfilters. In addition to implementation advantages over traditional techniques, the proposed method enables a more accurate specification of filter design parameters, near optimal responses, and a design time considerably faster than that of the Parks-McClellan algorithm