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I have one confused question. one continuous exponential decay function f=exp(-lamda*t) start from t=0 to infinity. I sample 1024 data points from the decay function. time variable (t) ranges from 0 to 1 second. the tail data of this exponential function is zero. I apply discret FFT on this sampled data. Am I supposed to get frequency spectrum with ring side lobe? When we apply FFT on this sampled data, does FFT assume my sampled data repeat themselves from negative infinity to positive infinity? If so, in this repeated data, a discontinuity point in exponential function exists. We are supposed to see oscillating side lobe because abrupt amplitude change between the tail data and the first point of my sampled data. Am My understanding correct? thanks in advance.

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