Zero-Padding for Interpolating Spectral Displays
Suppose we perform spectrum analysis on some sinusoid using a length
window. Without zero padding, the DFT length is
. We may
regard the DFT as a critically sampled DTFT (sampled in
frequency). Since the bin separation in a length-
DFT is
,
and the zero-crossing interval for Blackman-Harris side lobes is
, we see that there is one bin per side lobe in the
sampled window transform. These spectral samples are illustrated for
a Hamming window transform in Fig.2.3b. Since
in
Table 5.2, the main lobe is 4 samples wide when critically
sampled. The side lobes are one sample wide, and the samples happen
to hit near some of the side-lobe zero-crossings, which could be
misleading to the untrained eye if only the samples were shown. (Note
that the plot is clipped at -60 dB.)
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If we now zero pad the Hamming-window by a factor of 2
(append 21 zeros to the length
window and take an
point
DFT), we obtain the result shown in Fig.2.4. In this case,
the main lobe is 8 samples wide, and there are two samples per side
lobe. This is significantly better for display even though there is
no new information in the spectrum relative to Fig.2.3.3.10
Incidentally, the solid lines in Fig.2.3b and
2.4b indicating the ``true'' DTFT were computed
using a zero-padding factor of
, and they were virtually
indistinguishable visually from
. (
is not enough.)
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Zero-Padding for Interpolating Spectral Peaks
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Zero-Padding to the Next Higher Power of 2