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Analytical Design of Biquadratic Filter Sections for Parametric Filters
Quadratic and biquadratic filter sections are often used in audio applications since only moderate filter selectivities are usually required. When a number of filter sections are cascaded, it can be advantageous to use filters with a nominal stopband gain of unit. The passband of each filter can then be varied about the 0-dB level, thereby realizing a filtering system capable of boosting or attenuating an input signal within multiple frequency bands. New closed-form expressions for analog biquadratic bandpass filters meeting prescribed specifications are first derived. This is followed by a method for transforming conventional analog filters. These results are then extended to the discrete-time domain through the use of the bilinear transformation. A distinct advantage of the proposed method is that since closed-form methods are used, the coefficients of a parametric filter can be readily recomputed in real time in response to a user specifying any of a new center of frequency, bandwidth, or peak gain. Examples of digital filter designs are given in the context of audio-frequency filtering.
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