ABSTRACT

The first part of the paper discusses designing of the lowpass filter that gives both a constant group delay over the passband and a sharp cut-off slope, which is one of the most difficult challenges in continuous-time signal processing. Furthermore, equalisation of the group delay distortion of the Chebyshev filter has been performed through a cascade connection of the allpass filters. The Newton–Raphson method is applied for solving the system of nonlinear equations that calculate the allpass filter parameters for equalising the constant group delay in an equiripple sense. This procedure gives nearly symmetric impulse response of the resulting filtering system, as well as a longer duration. In the second part of the paper, two solutions for synthesising polynomial filter transfer functions are discussed: filter with monotonic amplitude characteristic (LSM) and filter using Chebyshev polynomial. For the purpose of comparison, the passband ripple factor of the Chebyshev filter is necessary to be adjusted so that both filters have the same stopband insertion loss, group delay and transient response. It is shown that Chebyshev filter is preferable since the passband magnitude distortions and sensitivity to the element deviation tolerance are significantly superior.

摘要

本文的第一部分讨论了低通滤波器的设计，该滤波器在通带上提供恒定的群延迟和尖锐的截止斜率，这是连续时间信号处理中最困难的挑战之一。此外，通过全通滤波器的级联实现了切比雪夫滤波器的群延迟失真的均衡。牛顿-拉夫森方法用于求解非线性方程组，计算全通滤波器参数，以均衡等波纹意义上的恒定群延迟。该过程给出了所得滤波系统的几乎对称的脉冲响应，以及更长的持续时间。在本文的第二部分中，讨论了合成多项式滤波器传递函数的两种解决方案：具有单调幅度特性 (LSM) 的滤波器和使用切比雪夫多项式的滤波器。为了进行比较，需要调整切比雪夫滤波器的通带纹波系数，以使两个滤波器具有相同的阻带插入损耗、群延迟和瞬态响应。结果表明，切比雪夫滤波器是更可取的，因为通带幅度失真和对元件偏差容限的灵敏度明显优越。