On Pascal Matrix for Transforming Lowpass Analog Filter to Bandpass Digital Filter

Recently, a method has been proposed in the literature for transforming lowpass analog filter to bandpass digital filter. In the method, the transformation matrix consists of Pascal matrix and some additional columns that were empirically obtained. In this letter, it is shown that such additional columns are not required if the coefficient vectors are slightly modified. In addition, the transformation was expressed in a biquadratic form. Then a simple procedure is presented which enables one to successively compute biquadratic transformation matrices of various order.