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 2nd order FIR fractional delay (FD) structure and the cutoff frequency, ƒc 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 ƒc 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 ƒc.

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