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,X₁andX₂, 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 therth iteration step, the maximum frequency response error, which appeared at the(r - 1)th step, is minimized, andX₂(r- 1)becomesX₂⁽ʳ⁾)· X₁⁽ʳ⁾is obtained from linear equations includingX₂⁽ʳ⁾as a constant. The frequency response at the rth step is evaluated using the above obtainedX₁⁽ʳ⁾andX₂⁽ʳ⁾. 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.