Design of minimum-phase finite-impulse-response digital filters

A method is presented which can be used for the direct design of minimum-phase finite-impulse-response digital filters with arbitrary prescribed modulus-squared characteristics. This method uses the Fletcher-Powell optimisation technique to minimise an L2p norm to obtain a nonnegative polynomial fit to the desired characteristics in a transformed domain. The coefficients of the filter are then obtained from the zeros of this polynomial. Examples of lowpass and bandpass filter designs are given using an L20 norm. A comparison of the passband and stopband ripples and their ratio is made with linear-phase filter designs.