3. ( The Effects of Zero-padding) We had said in lecture that if we pad zeros to the end of a length-N signal rin] to create a length-L signal ?
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The effect of zero padding in signal processing

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3. ( The Effects of Zero-padding) We had said in lecture that if we pad zeros to the end of a
length-N signal rin] to create a length-L signal ? with & > N, then we can use the DFT
of this zero-padded signal to sample the DTFT of an] on a finer frequency grid defined
with sample spacing w = J. We also commented that this zero-padding procedure does
not add any new information, and can be viewed as a simple frequency-domain interpolation
procedure.
(a) In this problem, we will formalize the relationship between XT] = EL
End in] We". Start by observing that
Emailnjwe and
N-I
(1)
and that
1
N 2
(2)
Insert the expression for an from Eq. (2) into Eq. (1), and simplify as much as you can
to obtain an expression for X [&] in terms of the X[q] values.
(b) Zero-padding in the time-domain is often described as "periodic sinc interpolation" in
the frequency domain. Do you think this terminology is justified based on your answer
to (a)?

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