ABSTRACT
Methods based on transformations can readily be used for the design of filters having piecewise-constant amplitude responses with quadrantal or half-plane symmetry. The design of analog filters is usually accomplished by applying analog-filter transformations to normalized continuous lowpass transfer functions like those obtained by using the Bessel, Butterworth, Chebyshev, and elliptic approximations. In applications where the passband or stopband of the required filter is a rectangular domain or a combination of rectangular domains, the design can be accomplished by using a method proposed by Hirano and Aggarwal. Transformations can also be used for the design of 2-D nonseparable filters having piece wise-constant amplitude responses with circular symmetry. Practical 2-D digital filters differ from their ideal counterparts in that their passband gain is only approximately equal to unity, their stopband gain is only approximately equal to zero, and transitions between passbands and stopbands are gradual.
