Linear-phase FIR filter design based on the weighted L2 norm

Concentrating on the problem of approximating the desired magnitude response of a filter by designing a linear-phase FIR filter, this paper derives the formulas to obtain the filter coefficients of type I, II, III and IV linear-phase filters based on the weighted L2 norm. Through several numerical examples of low pass filter, band pass filter, high pass filter and band stop filter, it shows that the filters designed with method in this paper are of less weighted L₂ errors than other filters designed by using Kaiser Window, equiripple approximation theory and so on.