Digital Signal Processing Reference
In-Depth Information
•
Shannon entropy calculation of signal
•
Magnitude and power estimation of signal
•
Calculation of discrimination measure for PSD analysis
•
Exon and intron boundaries' estimation
As an elaboration, the DNA sequence is passed through a filter that transforms it into a digi‐
tal pattern. This phase is accomplished employing an indicator sequence with the following
weights for nucleotides,
Adenine
(
A
)
=X
(
A
)
=0.260
Thymine
(
T
)
=X
(
T
)
=0.375
Guanine
(
G
)
=X
(
G
)
=0.125
Cytosine
(
C
)
=X
(
C
)
=0.370
The corresponding transform becomes
N
å
-
j kn N
2 /
p
X
[ ]
k
=
x
[ ]
n e
IndSeq
IndSeq
(1)
n
=
1
k
=
1, 2,...,
N
Indicator sequence
The signal is decomposed employing the wavelet transforms of order three at level three
y t A t D t
cA k
( )
=
( )
+
( )
1
1
å
å
å
=
( )
f
( )
t
+
cD k w
( )
( )
t
+
cD k w
( )
( )
t
2
j k
-
2,
2
j k
-
2,
1
j k
-
1,
k
k
k
=
A t D t D t
A t D t D t D t
cA k
( )
+
( )
+
( )
(2)
2
2
1
=
( )
+
( )
+
( )
+
( )
3
3
2
1
å
å
å
å
=
( )
f
( )
t
+
cD k w
( )
( )
t
+
cD k w
( )
( )
t
+
cD k w
( )
( )
t
3
j k
-
3,
3
j k
-
3,
2
j k
-
2,
1
j k
-
1,
k
k
k
k
3
rd
order wavelet decomposition
The wavelet decomposition passes the signal into a series of low and high pass filters that
decompose and synthesize the signal for reducing flicker noise (pink noise).
The signal is then convoluted with a window function (Kaiser Window) defined below,
ì
æ
(
)
2 2
ö
(
)
ï ç
÷
I
b
1 (
-
n
-
a a
)/
/ ( ) 0
I
b
£ £
n M
-
1
ï
0
ç
÷
0
w n
( )
=
í
(3)
è
ø
î
0
otherwise
Kaiser window of length 351 bp
