Design of FIR filter with small number of coefficients based on compactly supported fluency sampling function

FIR filter can perfectly realize linear phase, and it has an important role in some applications such as transmission, measurement and reproducing audio. However, FIR filter requires a large number of coefficients as compared with IIR filter in order to satisfy desired characteristics. In this paper, we propose a design method of FIR filter that maintain linear phase and can realize with small number of coefficients by an easy algorithm. In the proposed method, a basic low-pass filter is designed based on the compactly supported fluency sampling function that converges to 0 both left and right 2nd sampling points from the origin and is represented in the form of piecewise polynomials of degree 2. Also, this compactly supported fluency sampling function is an irregular function that has singular points at each 0.5 sampling interval from the origin. The values of sampling function at these singular points are then used in filter coefficients. Next, a basic high-pass filter and an upsampled filter based on the basic low-pass filter is defined. Then, a number of upsampled low-pass and high-pass filters are connected in series to satisfy the specifications. As such, since the proposed method uses a kind of filter, the procedure of designing filter is easy algorithm. In addition, the filter designed by the proposed method requires a small number of coefficients as compared with conventional methods such as the Remez exchange method.