Digital Signal Processing Reference
In-Depth Information
A bird sound
1
0
−1
−2
0
0.2
0.4
0.6
0.8
1
Time, sec
0.015
0.01
0.005
0
0
0.1
0.2
0.3
0.4
0.5
Normalized frequency
60
40
20
0
0
0.1
0.2
0.3
0.4
0.5
normalized frequency
Fig. 3.44
A bird sound signal (Top) with its FT (Middle) and TFD (Bottom)
q
ð
t
;
f
Þ¼
FT
s
!
f
f
p
ð
t
;
s
Þg
where: p
ð
t
;
s
Þ¼
G
ð
t
;
s
Þ
ð
t
Þ
K
z
ð
t
;
s
Þ;
K
z
ð
t
;
s
Þ¼
z
ð
t
þ
s
=
2
Þ
z
ð
t
s
=
2
Þ
is the instanta-
neous autocorrelation, z(t) is the analytic signal associated with the original signal
s(t), and G(t, s) is known as the kernel of the TFR. The kernel completely char-
acterizes the particular TFR and is in general a symmetric 2D low-pass shaped
function in the time-lag (t, s) domain. Further details on Cohen's Class and TFRs
in general can be found in the topic [
8
].
3.7.3 The Discrete Cosine Transform
In multimedia communications it is often necessary to transmit a large amount of
data in a short period of time. This is one of the challenges for 4G mobile
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