82
D. Rocchesso: Sound Processing
main-lobe width
side-lobe level
0
Y ( )
m
m
N-1
Y ( )
0
e
N-1
n
n
e
y(m)
j
j
1/ N w(0)
Figure 5: Reconstruction of a signal from a set of non-overlapping frequency
slices.
0
, . . . ,
N -1
are the central frequencies of the bands of the analysis
channels.
tentially inducing erroneous estimations of frequency components. In general,
there is a tradeoff between the main-lobe width and the side-lobe level that
can be exploited by choosing or designing an appropriate window. Table 4.1
describes concisely the form and features of the most-commonly used analysis
windows.
Window
Name
w(n)
in
R-1
2
n
R-1
2
Main-lobe
Width
(
R
)
Side-lobe Level
[dB]
Rectangular
1
4
-13.3
Hann
1
2
1 + cos
2n
R
8
-31.5
Hamming
0.54 + 0.46 cos
2n
R
8
-42.7
Blackman
0.42 + 0.5 cos
2n
R
+
0.08 cos
4n
R
12
-58.1
Table 4.1: Characteristics of popular windows.
Each window is characterized by the main-lobe width and the side-lobe level.
The larger the main-lobe width the smaller is the decimation that I can introduce
between the analysis and synthesis stages. This has a consequence in the choice
of the hop size. For instance, using Hann
1
or Hamming windows I have to use at
1
The Hann window is often called Hanning window, probably for the same reason that in
the US you may prefer saying "I xerox this document" rather than "I copy this document
using a Xerox copier".
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