Elementary NGD IIR/FIR Systems

This paper deals with the synthesis and design of impulse response digital systems exhibiting negative group delay (NGD). It is demonstrated that under certain condition, certain first order FIR and IIR systems can provide the NGD function. Synthesis methods of NGD FIR/IIR transfer functions are introduced. Then, the basic properties specific to the NGD digital functions are established. To validate the theory proposed, NGD FIR and IIR systems were synthesized and implemented with Matlab. As expected, group delay frequency responses with NGD in baseband frequency well-correlated to the theoretic hypothesis were found. Then, thanks to the NGD effect, arbitrary form discrete transient signals with limited bandwidth propagating in time advance were demonstrated in time-domain. It is proved that this counterintuitive function does not forbid the causality principle and the NGD numerical system respects the functioning condition of the classical digital system. The NGD principle presented is potentially useful for the group delay correction processes and the signal pure delay reduction.