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,
X_{1}
and
X_{2}
, 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
r
th iteration step, the maximum frequency response error, which appeared at the
(r - 1)
th step, is minimized, and
X_{2}^{(r- 1)}
becomes
X_{2}^{(r)})\cdot X_{1}^{(r)}
is obtained from linear equations including
X_{2}^{(r)}
as a constant. The frequency response at the rth step is evaluated using the above obtained
X_{1}^{(r)}
and
X_{2}^{(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.