This paper proposes a general structure for FIR filters with adjustable magnitude and phase responses controlled by a few parameters. The Farrow structure which uses one parameter to control the fractional delay of an FIR filter can be viewed as special case. A filter bank structure consisting of different types of linear phase differentiators forms the basis of the structure. The filter bank outputs are combined with coefficients derived from a polynomial expansion of the desired frequency response. The magnitude and phase responses are controlled by synthesizing the polynomial coefficients from the small set of control parameters. A new optimal polynomial approximation strategy is also proposed to better approximate the family of target frequency responses.
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