Digital filters are presented which are designed to equalize frequency-domain characteristics such as, for example, the magnitude and phase responses of analog systems which are parts of combined analog and digital audio signal processing. A unified frequency-domain equalization approach is introduced. Basic filter design principles such as minimax and least-squares filters, tolerance schemes, as well as simultaneous equalization of magnitude and phase responses by recursive and nonrecursive digital filters are studied. Several design methods and available software in the areas of identification, approximation, and optimization methods and available software in the areas of identification, approximation, and optimization are presented. Short commends on the relations between complex approximation and simultaneous approximation of magnitude and phase responses as well as a comparison of phase approximation by recursive and nonrecursive filters are offered. A second part will contain examples and illuminate some important aspects of practical equalization.
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