A Time Domain Approximation Method and Its Application to Lumped Delay Lines

This paper presents a method of time domain approximation employing trigonometric polynomials. The result is in the form of a realizable rational function of the complex frequency variable. A simple procedure is given to establish the bounds of time domain error. The method is then applied to the problem of lumped parameter delay lines. The result of calculations made on an eighth-order network function obtained by the new method shows that if some ripple in the time response is tolerable, the delay rise-time ratio can be improved by more than 130 per cent from the maximally flat delay (Bessel) low-pass filter.