#### 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.)

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