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This letter proposes a new method for designing finite-impulse response (FIR) filters with variable characteristics. The impulse response of the variable digital filter (VDF) is parameterized as a linear combination of functions in the spectral or tuning parameters. Using the least square objective function, the optimal solution is obtained by solving a system of linear equations. Design results show that this method is simple and effective in designing FIR VDF with good frequency characteristics. Furthermore, by using a piecewise polynomial, instead of an ordinary polynomial, more complicated frequency characteristics, or a larger tuning range can be approximated.