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However, the vast majority of this study is original, and new algorithms and scenarios are introduced firstly in the paper. In this paper, a frequency estimation method named exponential sampling is amended to calculate the initial sampling frequency in the inner-layered process of the DFT iteration. Performance of new algorithm were studied and analyzed in some non-steady states of different scenarios (e.g., sudden and random frequency change, signal modulated by a cosine signal).","order":1,"name":"Ethics","group":{"name":"EthicsHeading","label":"Competing interests"}},{"value":"Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.","order":2,"name":"Ethics","group":{"name":"EthicsHeading","label":"Publisher\u2019s Note"}}],"article-number":"28"}}