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I won’t show ALL the calculations, but I’ll describe the problem fairly enough to understand.

We’ve been taught that upsampling on one domain leads to padding zeroes or added time period which is zero on the second domain.

That means, that if I add zeroes as samples in between the values of a frequency domain (of some periodic signal) then I’ll get padding zeroes in between the periods.

But, in one class we’ve seen also that adding zero samples in between the values of frequency domain of a continuous time Fourier transform, we can also get the following from calculations:

enter image description here

enter image description here

Which basically means, that if we add zeroes as samples in between the existing samples at the discrete frequency of a periodic signal, then we can both reverse transform it to a scaled version in time domain and/or padded with zeroes version in the time domain. Is that true?

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