The following 32 data points are sampled over a period of 0.0625 second.

y=[00 .9094 0.4251 −0.6030 −0.6567 0.2247 0.6840 0.1217 … −0.5462 −0.3626 0.3120 0.4655 −0.0575 −0.4373 −0.1537 … 0.3137 0.2822 −0.1446 −0.3164 −0.0204 0.2694 0.1439 −0.1702 … −0.2065 0.0536 0.2071 0.0496 −0.1594 −0.1182 0.0853 … 0.1441 −0.0078]

(a) Determine the DFT and estimate the frequency of the most signiﬁcant component present in the data. What is the frequency increment in the DFT? (b)To the end of the existing data, add an additional 480 zero values, thus increasing the number of data points to 512.Thisprocessiscalled“zeropadding”andisusedtoimprovethefrequency resolution in the DFT. Determine the DFT of the new data set and estimate the frequency of the most signiﬁcant component. What is the frequency increment in the DFT?

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