A new variable digital filter design based on fractional delay

This paper presents a new method for the design of finite impulse response (FIR) filter that provides variable frequency responses. The proposed idea is to replace each unit delay operator in a fixed-coefficient FIR filter with the 2^nd order FIR fractional delay (FD) structure and the cutoff frequency, f_c of the filter is changed by changing the FD value. The change in FD results in change in amplitude and length of an impulse response. This in turn changes f_c and transition bandwidth (TBW) of an FIR filter. The mathematical relation between cut-off frequency, TBW and FD value D is derived. The design example shows that the proposed method provides very fine control over f_c.