PhD thesis

Here you can download a pdf-file of my thesis:
Algorithms for the Constrained Design of Digital Filters with Arbitrary Magnitude and Phase Responses

All Matlab files used in the thesis can be downloaded here.

This thesis presents several new algorithms for designing digital
filters subject to specifications in the frequency domain. Finite impulse
response (FIR) as well as infinite impulse response (IIR) filter design
problems are considered.

Unlike many standard filter design algorithms, all methods proposed here
solve the problem of simultaneously approximating specified magnitude and
phase responses. Filters of this type can be used to optimally equalize
magnitude and phase distortions. Such problems occur e.g. in
data transmission systems or in oversampled analog-to-digital conversion.
Another application of the proposed algorithms is the design of filters
with low group delay in the passbands. In the FIR case, the exactly linear
phase property is given up in order to reduce the delay while maintaining
a good approximation to phase linearity in the passbands. IIR filters can
also be designed to have an approximately linear passband phase response.
Their passband group delay is usually considerably smaller than the delay
of linear phase FIR filters with equivalent magnitude responses.

An important feature of the algorithms presented in this thesis is
that they allow for design constraints which often arise in practical
filter design problems. Meeting a required minimum stopband attenuation or
a maximum deviation from the desired magnitude and phase responses in the
passbands are common design constraints that can be handled by the methods
proposed here. For the design of IIR filters, an important constraint is
the prescription of a maximum pole radius. This not only allows
to guarantee stability but also helps to avoid undesirable effects when
implementing the designed filter with fixed-point arithmetic. An
algorithm solving this constrained IIR design problem is presented.

During the development of the proposed design techniques special emphasis
has been placed on their computational efficiency. This and the fact
that this thesis includes Matlab programs implementing all proposed
algorithms makes all results of this dissertation directly
applicable to many practical design problems.

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