Properties:

• Side lobes 24 dB down
• Asymptotically optimal coding gain [144].
• Zero-phase-window transform (``truncated cosine window'') has smallest moment of inertia over all windows [186]:
     min

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 [196,45], and they became practical for audio coding with the advent of time-domain aliasing cancellation (TDAC) [198]. 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 [145]. The modulated lapped transform (MLT) is a variant of LOT used in conjunction with the modulated discrete cosine transform (MDCT) [145]. See also [264] and [267].

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written by Julius Orion Smith III
Julius Smith's background is in electrical engineering (BS Rice 1975, PhD Stanford 1983). He is presently Professor of Music and Associate Professor (by courtesy) of Electrical Engineering at Stanford's Center for Computer Research in Music and Acoustics (CCRMA), teaching courses and pursuing research related to signal processing applied to music and audio systems. See http://ccrma.stanford.edu/~jos/ for details.