A method of time‐domain approximation using tbt polynomials as the denominator of the transfer function
Genya Kishi, Takuro Kida, Yutaka Fukuda · Electronics and Communications in Japan (Part I Communications) · 1986
Abstract TBT polynomials are polynomials with roots which interpolate the poles of the transfer functions of the maximally flat amplitude filter and the maximally flat delay filter. This paper discusses a method in which a desired waveform is approximated by the impulse response of the transfer function using TBT polynomials as the denominator and gives a selection principle for two parameters for which the squared error in the time domain is minimized. Examples are given to show that the impulse response obtained by this method can approximate various practical desired waveforms very well. The above method based on the TBT polynomial is compared to the method involving the iterative process in which the least squares method is applied alternately to denominator and numerator of the transfer function to further decrease the squared error. It is shown that the approximation error for the above method is only about 1.5 times larger than that by the latter method. The properties of the approximated waveform are examined when not only the square norm but also the nth norm of error are used as error measures. Moreover, considering the band limiting in a real transmission line, we investigate a method of waveform approximation in the time domain in which the attenuation is prescribed and minimization is accomplished by the quadratic programming method. The method based on the TBT polynomials also performs well in this case.