DESIGN AND ANALYSIS OF ANALOG FILTERS A Signal ...

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DESIGN AND ANALYSIS OF ANALOG FILTERS:
is the magnitude response, and (2) where the primary concern is constant time delay
/ linear phase.
General Filter Design
Papoulis introduced filters with a maximum magnitude slope at the passband
edge for a monotonic response falloff for a given order (1958). Halpern extended the
work of Papoulis for optimum monotonic transition band falloff, based on Jacobi
polynomials (1969). Ku and Drubin introduced filters based on Legendre and Hermite
polynomials (1962). Scanlan introduced filters with poles that fall on an ellipse with
equal frequency spacing, and noted the tradeoff between magnitude response
characteristics and time-domain response characteristics as the eccentricity of the
ellipse is varied (1965). Filter transfer functions based on ultraspherical polynomials,
where Chebyshev, Butterworth, and Legendre filters are shown to be special cases,
was introduced by Johnson and Johnson (1966). This was extended by ultraspherical
and modified ultraspherical polynomials where a single parameter determines many
transitional forms (Attikiouzel and Phuc, 1978). Extensions to Cauer filters have
recently been made in two ways: lowering the pole Qs by using quasi-elliptic
functions (Rabrenovic and Lutovac, 1992), and by significantly reducing the
complexity of designing elliptic filters without reference to elliptic functions (Lutovac
and Rabrenovic, 1992).
Constant Time-Delay Design
Whereas Bessel filters are designed for a maximally-flat time delay characteristic,
Macnee introduced filters that use a Chebyshev approximation to a constant time
delay (1963). By allowing small amounts of ripple in the group delay or phase
response (based on Chebyshev polynomials), similar to Macnee's objectives, Bunker
made ehancements in delay filters (1970). Ariga and Masamitsu developed a method
to extend the magnitude bandwidth of constant-delay filters (1970). By using
hyperbolic function approximation, Halpern improved on Bessel filters, at least for
low orders (1976). The so-called Hourglass filter design (Bennett, 1988) may be used
to obtain transfer functions that have simultaneously equiripple time-delay and
equiripple magnitude characteristics. Gaussian filters have magnitude and phase
characteristics very similar to Bessel filters, but with less delay for the same order
(Dishal, 1959; Young and van Vliet, 1995).
1.5 A NOTE ON MATLAB
Although a variety of programming languages and high-level software could
be used to design, analyze, and simulate analog filters, MATLAB has been selected
in this book because of its ease of use, wide-range availability, and because it
includes many high-level analog filter functions, and good graphics capabilities.
Chapter 1
Introduction