2
\$\begingroup\$

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?

\$\endgroup\$
  • \$\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 '18 at 0:02
  • 1
    \$\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 '18 at 0:20
2
\$\begingroup\$

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.

| improve this answer | |
\$\endgroup\$
  • 1
    \$\begingroup\$ Exaclty :-) I would like to link an image that shows the rect in frequency domain. \$\endgroup\$ – Finkman Feb 6 '18 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 '18 at 17:07

Your Answer

By clicking “Post Your Answer”, you agree to our terms of service, privacy policy and cookie policy

Not the answer you're looking for? Browse other questions tagged or ask your own question.