This paper deals with the similitude between the behaviours of linear filter gain and negative group delay (NGD) function. The transposition method of low‐pass/high‐pass, low‐pass/band‐pass and low‐pass/band‐stop NGD circuits is established. To the best of the author knowledge, it acts as the first paper devoted on the NGD function generalized theory. The introduced transform relationships simplify the synthesis of any NGD circuits from simple elementary low‐pass NGD topologies. Families of innovative NGD topologies are identified. To verify the relevance of the concept proposed, frequency‐ and time‐domain analysis results from realistic proofs of concept demonstrating the feasibility of developed NGD transforms were performed. Thanks to the NGD phenomenon, the possibility of the ultra‐wideband pulse signals propagating in time‐advance is verified. Finally, potential applications of NGD circuits are discussed. Copyright © 2013 John Wiley & Sons, Ltd.