Optimum envelope-constrained filter design is concerned with time-domain
synthesis of a filter such that its response to a specific input signal
stays within prescribed upper and lower bounds, while minimizing the
impact of input noise on the filter output or the impact of the shaped
signal on other systems depending on the application. In many practical
applications, such as in TV channel equalization, digital transmission,
and pulse compression applied to radar, sonar and detection, the soft
least square approach, which attempts to match the output waveform with
a specific desired pulse, is not the most suitable one. Instead, it
becomes necessary to ensure that the response stays within the hard
envelope constraints defined by a set of continuous inequality
constraints. The main advantage of using the hard envelope-constrained
filter formulation is that it admits a whole set of allowable outputs.
From this set one can then choose the one which results in the
minimization of a cost function appropriate to the application at hand.
The signal shaping problems so formulated are semi-infinite optimization
problems.
This monograph presents in a unified manner results that have been
generated over the past several years and are scattered in the research
literature. The material covered in the monograph includes problem
formulation, numerical optimization algorithms, filter robustness issues
and practical examples of the application of envelope constrained filter
design.
Audience: Postgraduate students, researchers in optimization and
telecommunications engineering, and applied mathematicians
