When is a discrete sequence periodic

Because the DFT operates on discrete sequences and produces a discrete sequence as a result, the DFT can be used to process signals on a digital computer. If a continuous signal is sampled at twice its highest frequency or higher, then the DFT of the sampled signal is a sampled version of the Fourier transform of the original continuous signal.

Further, all of the information in the continuous signal is present in the sampled signal. This is the power of the DFT. In principle, we can take a continuous signal, sample it, process the samples on a computer and then convert the processed samples back into a continuous signal. The result will be identical to processing the continuous signal with an equivalent analog system. Active 4 years ago. Viewed 8k times. Plotting the function in mathematic shows that the period is around 7.

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