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Based on the Type\u2010I bilinear double\u2010order filter circuit, our theory has been verified by strong agreements between the formulae and their proof\u2010of\u2010concept (POC) circuit\u2010based simulation results. Both formula\u2010based and POC circuit\u2010based simulations give the minimum group delay of \u22125\u00a0ms yet the cut\u2010off frequency of 10 and 9\u00a0rad\/s, respectively. Such slight deviation is caused by the approximation error of the bilinear double\u2010order impedance. By employing two orders, the bilinear double\u2010order transfer function has been found to be the basis transfer function for the NGD filtering function with the highest degree of freedom. Based on our design equation for the NGD filtering function, it can be seen that the distances between zero and pole and the characteristic frequency of the bilinear double\u2010order transfer function are governed by such characteristic frequency itself, the cut\u2010off frequency of the NGD filtering function, and the fractional order of the Laplacian operator. In addition, the effects of the fractional order of the Laplacian operator, the fractional order of the transfer function, and the ratio of the abovementioned distances to the characteristics of the newly found double\u2010order NGD filtering function have been studied in detail.<\/jats:p>","DOI":"10.1002\/cta.4213","type":"journal-article","created":{"date-parts":[[2024,8,7]],"date-time":"2024-08-07T23:30:02Z","timestamp":1723073402000},"page":"3157-3169","update-policy":"https:\/\/linproxy.fan.workers.dev:443\/https\/doi.org\/10.1002\/crossmark_policy","source":"Crossref","is-referenced-by-count":0,"title":["Double\u2010order negative group delay filtering function: A brilliant capability of the bilinear double\u2010order transfer function"],"prefix":"10.1002","volume":"53","author":[{"ORCID":"https:\/\/linproxy.fan.workers.dev:443\/https\/orcid.org\/0000-0003-4392-8493","authenticated-orcid":false,"given":"Rawid","family":"Banchuin","sequence":"first","affiliation":[{"name":"Faculty 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