Minimum phase transfer functions providing a compromise between phase and amplitude approximation

Transfer functions of low-pass filters with no finite transmission zeros are introduced satisfying a number of phase flatness conditions at the origin and providing more stopband rejection than the corresponding Butterworth filters. If only one of the available degrees of freedom is used to shape the passband magnitude response, while all remaining are assigned to phase linearity, the largest fractional banwidth of phase linearity is obtained but the maximum passband loss cannot be specified beforehand and increases with increasing the order of the network. It is shown, however, that assigning two parameters to magnitude requirements in the resulting transfer function almost any prescribed maximum passband loss can be met while still retaining excellent phase linearity over a large part of the passband. In addition, a class of transitional filter functions is obtained the frequency and time domain characteristics of which can be adjusted over a wide range of filter specifications by varying one parameter only. It is shown that the time domain characteristics of these filters compare favorably with those for the well-known transitional Butterworth-Thomson filters.