Example: Effect of Sampling on the Fourier Transform of a Bandlimited Signal

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Step by step example of how sampling in time impacts the Fourier transform: 1) Copying the spectrum in frequency, 2) multiplying the frequency axis by the sampling period, and 3) rescaling the amplitude by 1/sampling period.
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But why do we do it like this, i mean why do we process cont in dis any specific reason?

muhammadmuneeb