A simultaneous frequency and time-domain approximation method for discrete-time filters

A simultaneous frequency- and time-domain approximation method for discrete-time filters is proposed in this paper. In the proposed method, transfer function coefficients are divided into two subsets, and , which are employed for optimizing a time response and a frequency response, respectively. Frequency and time responses are optimized through the iterative Chebyshev approximation method and a method of solving linear equations, respectively. At the th iteration step, the maximum frequency response error, which appeared at the th step, is minimized, and becomes is obtained from linear equations including as a constant. The frequency response at the rth step is evaluated using the above obtained and . This means the optimum time response is always guaranteed in the frequency-response approximation procedure. A design example of a symmetrical impulse response shows the new approach is more efficient than conventional methods from the filter order reduction viewpoint.