Properly Anti-Aliasing Window Transforms
For simplicity, define window-transform bandlimits at first
zero-crossings about the main lobe. Given the first zero of
at
, we obtain
![]() |
(10.27) |
The following table gives maximum hop sizes for various window types in the Blackman-Harris family, where


L | Window Type (Length ![]() |
![]() |
![]() |
1 | Rectangular | M/2 | M |
2 | Generalized Hamming | M/4 | M/2 |
3 | Blackman Family | M/6 | M/3 |
L | ![]() |
M/2L | M/L |

It is interesting to note that the maximum COLA hop size is
double the maximum downsampling factor which avoids aliasing of the
main lobe of the window transform in FFT-bin signals
. Since the COLA constraint is a sufficient condition
for perfect reconstruction, this aliasing is quite heavy (see
Fig.9.21), yet it is all canceled in the
reconstruction. The general theory of aliasing cancellation in perfect
reconstruction filter banks will be taken up in Chapter 11.
It is important to realize that aliasing cancellation is
disturbed by FBS spectral modifications.10.4For robustness in the presence of spectral modifications, it is
advisable to keep
. For compression, it
is common to use
together with a ``synthesis window'' in a weighted overlap-add (WOLA)
scheme (§8.6).
Next Section:
Hop Sizes for WOLA
Previous Section:
Filter Bank Reconstruction