Optimal FIR filters with almost linear phase

FIR filters are known to be stable and have a linear phase when symmetry properties, e.g., h[n]=h[M-n], are kept. A common FIR filter design method is the Parks-McClellan algorithm. In this algorithm, linear phase FIR filters, which are optimal in the minimax sense, are designed. These filters have the form of H(ω)=A(ω)e^j(β-ωα), where A(ω) is real, α is an integer or an integer plus 1/2 and β is 0 or π/2. These FIR filters are always symmetric or antisymmetric. We introduce a simple procedure for designing almost linear phase FIR filters, having a similar form to H(ω), but an arbitrary α, that are optimal in a similar sense.