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My lecture notes say it's done by interpolation. enter image description here

I do see that they have interpolated several sinc function peaks What I don't get is how the sinc function comes into the equation? why is sinc used?

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    \$\begingroup\$ The sinc function in the time domain is a rectangle in the frequency domain. The frequency of your sinc function determines the edges of the rectangle in the frequency domain. \$\endgroup\$
    – Samuel
    Feb 6, 2018 at 0:02
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    \$\begingroup\$ In real-world use a low pass filter (LPF) is used to emulate interpolation based on a useful time-constant, which is based on the sample rate vs. the actual signal rate. \$\endgroup\$
    – user105652
    Feb 6, 2018 at 0:20

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To elaborate on Samuel's comment. When you sample a signal the spectrum of that signal will become periodic in the Nyquist frequency. To reconstruct the actual signal, you need to remove all of the frequencies that appear as artifacts of the sampling process. Ideally, this would require a brick-wall low pass filter. In the time domain, this corresponds to the procedure your lecturer mentioned with sinc functions, as sinc is the inverse fourier transform of the rect function.

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    \$\begingroup\$ Exaclty :-) I would like to link an image that shows the rect in frequency domain. \$\endgroup\$
    – Finkman
    Feb 6, 2018 at 8:54
  • \$\begingroup\$ If you google it there's an image of it. The derivation of this probably has something to the with Fourier transforms? YouTube has some help on that. \$\endgroup\$
    – bleepblop
    Feb 6, 2018 at 17:07

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