Closed-form design of FIR frequency selective filter using discrete sine transform

In this paper, the closed-form design of FIR frequency selective filter (FSF) using discrete sine transform (DST) is studied. First, the DST-based frequency selective method is used to obtain the filtered signal from the given digital signal. Then, the transfer function of FSF is derived from the filtered signal by using index mapping approach. Because the closed-form design is obtained, the filter coefficients are easily computed without performing any optimization. Finally, the long-length low-pass, band-pass and high-pass filter design examples are used to show the effectiveness of the proposed DST method.