This paper investigates the properties of the extended finite Fourier transform of the firmly fixed of two vector-valued continuously time series. In their own terms, both time series can be conceived of as continuous. Both of the different time series have the property of having a continuous advance throughout their entire. The two relevant time series both have the attribute of a continuous progression throughout their data. This is one of the characteristics that allow them to be flexible. The extended finite Fourier transform provides the basis for the investigations while these characteristics is studied using the framework that it provides. Following that, a data analysis is carried out, during which time both regular and irregular repeating patterns are searched for and examined. This happens while the analysis is being carried out. This process immediately follows the phase in which the data was obtained. This is done simultaneously with data analysis, so the two operations are parallel.