Design of general-order shaping transfer functions for Bode-type variable-amplitude digital equalizers

In the design of Bode-type variable-amplitude digital equalizers, the constituent shaping transfer function is usually required to satisfy certain prescribed magnitude-frequency response characteristics. These characteristics include: a “passband” with a prespecified maximum gain, a “stopband” with unity, gain, and a single prespecified gain at the passband edge(s). This paper presents a novel approximation technique for the design of general-order shaping transfer functions with maximally flat or equiripple lowpass, highpass, or bandpass magnitude-frequency response characteristics. This is achieved by first deriving a corresponding normalized prototype lowpass shaping transfer function, and then by applying a lowpass-to-lowpass, lowpass-to-highpass, or lowpass-to-bandpass frequency transformation to obtain the desired (denormalized) shaping transfer function. These shaping transfer functions can be employed in the design of variable-amplitude digital equalizers having magnitude-frequency responses with sharp transition bands and reduced inter-band interference in the corresponding digital graphic equalizers