Abstract:
All-pass networks with prescribed group delay
are used for analogue signal processing and equalisation
of transmission channels. The state-of-the-art methods for
synthesising quasi-arbitrary group delay functions using
all-pass elements lack a theoretical synthesis procedure
that guarantees minimum-order networks. We present an
analytically-based solution to this problem that produces
an all-pass network with a response approximating the
required group delay to within an arbitrary minimax error.
For the first time, this method is shown to work for any
physical realisation of second-order all-pass elements, is
guaranteed to converge to a global optimum solution
without any choice of seed values as an input, and allows
synthesis of pre-defined networks described both
analytically and numerically. The proposed method is also
demonstrated by reducing the delay variation of a practical
system by any desired amount, and compared to state-ofthe-
art methods in comparison examples.
