### The MLT Sine Window

The *modulated lapped transform* (MLT) [160] uses the
*sine window*, defined by

(4.24) |

The sine window is used in MPEG-1, Layer 3 (MP3 format), MPEG-2 AAC, and MPEG-4 [200].

**Properties:**

- Side lobes 24 dB down
- Asymptotically optimal coding gain [159]
- Zero-phase-window transform (``truncated cosine window'')
has smallest
*moment of inertia*over all windows [202]:min (4.25)

Note that in perceptual audio coding systems, there is both an
*analysis window* and a *synthesis window*. That is, the
sine window is deployed *twice*, first when encoding the signal,
and second when decoding. As a result, the sine window is
*squared* in practical usage, rendering it equivalent to a Hann
window (
) in the final output signal (when there are no
spectral modifications).

It is of great practical value that the second window application
occurs *after* spectral modifications (such as spectral
quantization); any distortions due to spectral modifications are
tapered gracefully to zero by the synthesis window. Synthesis windows
were introduced at least as early as 1980
[213,49], and they became practical for
audio coding with the advent of time-domain aliasing cancellation
(TDAC) [214]. The TDAC technique made it possible
to use windows with 50% overlap without suffering a doubling of the
number of samples in the short-time Fourier transform. TDAC was
generalized to ``lapped orthogonal transforms'' (LOT) by Malvar
[160]. The modulated lapped transform (MLT) is a variant
of LOT used in conjunction with the modulated discrete cosine
transform (MDCT) [160]. See also [287] and
[291].

**Next Section:**

Blackman Window Family

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Summary of Generalized Hamming Windows