A Computational Form of the Least Square Error Frequency Sampling Method for the Linear Phase FIR Filter Design

The frequency sampling method is very simple to design FIR filters with arbitrary frequency response. The generic problem of the FIR filter design via the frequency sampling method is to solve the normal equation accurately. A more explicit form to solve the coefficient matrix of the normal equation is derived in this paper. Both the mathematical derivation and the numerical verification are given in this paper. The numerical results compare the coefficient matrix of the proposed form and that of the direct multiplication of coefficient cosine matrix and its transpose. As the number of frequency points increases, the computational error increases accordingly. The proposed formulation can avoid this phenomenon and more robust algorithms can be developed via this approach.