Closed-Form FIR Filter Design Based on Convolution Window Spectrum Interpolation

This paper proposes a closed-form linear phase FIR filter design concurrently possessing high efficiency and excellent transfer characteristic. This design is derived from conventional frequency sampling method through replacing its frequency-domain interpolation function with the Fourier spectrum of a convolution window. Meanwhile, this derivation inherently contains a mechanism of synthesizing all possible sub filters into one better FIR filter, which also plays the role of optimizing the transfer characteristic in nature. The above synthesizing process is equivalent to three simple steps, from which a closed-form formula of tap coefficients can be summarized. We further prove the proposed filter's five properties, from which a modified closed-form design without any redundant parameters is also derived. Numerical results show that, the transfer performance of the proposed design is comparable to the mainstream designs (such as WLS method, Parks- McClellan method). Meanwhile, the proposed design can achieve an extremely high efficiency when designing high-order FIR filters.