Limit-cycle free complex biquad recursive digital filters

A novel type of complex biquad recursive digital structure, based on the concept of a generalized immittance converter, is discussed. Orthogonal filters which are widely used in time-division multiplexing-frequency-division multiplexing (TDM-FDM) transmultiplexers can be obtained as a special class of these complex biquads. It is shown that the proposed structure is completely free from zero-input limit cycles under linear conditions, and further, that the stability under finite arithmetic conditions can be achieved using the technique of magnitude truncation. It is also shown that for this structure, the stability of the forced response can be ensured for certain types of overflow nonlinearities