Low Passband Sensitivity Research Articles

Low passband sensitivity digital filters: A generalized viewpoint and synthesis procedures

The concepts of losslessness and maximum available power are basic to the low-sensitivity properties of doubly terminated lossless networks of the continuous-time domain. Based on similar concepts, we develop a new theory for low-sensitivity discrete-time filter structures. The mathematical setup for the development is the bounded-real property of transfer functions and matrices. Starting from this property, we derive procedures for the synthesis of any stable digital filter transfer function by means of a low-sensitivity structure. Most of the structures generated by this approach are interconnections of a basic building block called digital "two-pair," and each two-pair is characterized by a lossless bounded-real (LBR) transfer matrix. The theory and synthesis procedures also cover special cases such as wave digital filters, which are derived from continuous-time networks, and digital lattice structures, which are closely related to unit elements of distributed network theory.

Sampling rate increase and decrease in wave digital filters

In addition to the regular input terminal at the input port and the regular output terminal at the output port, wave digital filters have available a second input terminal at the output port and a second output terminal at the input port. These additional terminals can be made use of for realizing efficient wave digital filters for sampling rate increase and decrease. An exact computation of the conversion (transfer) functions shows that their analytic expressions are strongly reminiscent of the conversion functions for analog conversion circuits. Among the advantages thus obtainable are improved loss performance for a given filter structure, increased dynamic range, and low passband sensitivity for the coefficients.