### Zero Padding Applications

Zero padding in the time domain is used extensively in practice to
compute heavily *interpolated* spectra by taking the DFT of the
zero-padded signal. Such spectral interpolation is ideal when the
original signal is *time limited* (nonzero only over some finite
duration spanned by the orignal samples).

Note that the *time-limited* assumption directly contradicts our
usual assumption of *periodic extension*. As mentioned in
§6.7, the interpolation of a periodic signal's spectrum
from its harmonics is always zero; that is, there is no spectral
energy, in principle, between the harmonics of a periodic signal, and
a periodic signal cannot be time-limited unless it is the zero signal.
On the other hand, the interpolation of a time-limited signal's
spectrum is nonzero almost everywhere between the original spectral
samples. Thus, zero-padding is often used when analyzing data from a
non-periodic signal in blocks, and each block, or
*frame*, is treated as a finite-duration signal which can be
zero-padded on either side with any number of zeros. In summary, the
use of zero-padding corresponds to the *time-limited assumption*
for the data frame, and more zero-padding yields denser interpolation
of the frequency samples around the unit circle.

Sometimes people will say that zero-padding in the time domain yields
higher spectral *resolution* in the frequency domain. However,
signal processing practitioners should not say that, because
``resolution'' in signal processing refers to the ability to
``resolve'' closely spaced features in a spectrum analysis (see Book
IV [70] for details). The usual way to increase spectral
resolution is to take a longer DFT *without* zero padding--*i.e.*,
look at more data. In the field of *graphics*, the term
resolution refers to pixel density, so the common terminology
confusion is reasonable. However, remember that in signal processing,
zero-padding in one domain corresponds to a higher
interpolation-density in the other domain--not a higher resolution.

**Next Section:**

Ideal Spectral Interpolation

**Previous Section:**

Causal Zero Padding