nth modified approximation coefficient at level
j
|
nth modified detail coefficient at level j
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λ
|
threshold of cj[n]
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MAD(cL − 1[n])
|
mean absolute deviation of cL − 1[n]
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modified approximation coefficients
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avg
|
arithmetic mean or average of
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std
|
standard derivation of
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max
|
maximal magnitude of
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min
|
minimal magnitude of
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ptp
|
peak‐to‐peak amplitude of
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kurt
|
kurtosis for measuring the peakedness of
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skew
|
skewness for measuring the asymmetry of
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RMS
|
root mean square value of
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CF
|
crest factor of
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T
|
duration of a continuous‐time signal
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t
|
specific time t of a continuous‐time signals
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cr
xy
|
correlation coefficient value of two signals: x(t) and y(t)
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CR
xy
|
cross‐correlation value of two signals: x(t) and y(t)
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γ
xy
|
covariance value of two signals: x(t) and y(t)
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m
|
displacement unit of a signal
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*
|
complex conjugate of a signal
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SF
CR(xy)
|
a feature set of CRxy
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FFT[n]
|
frequency amplitude at the nth Hz by FFT
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SF
FFT(q)
|
qth certain frequency band delimited by a lower frequency and an upper frequency
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Q
|
number of frequency band
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uf
q
|
qth upper frequency of the critical characteristics; and
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lf
q
|
qth lower frequency of the critical characteristics.
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SF
FFT(q)
|
qth FFT‐based SF
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u
|
uth wavelet packet at level L, u= 1, 2, …, L;
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v
|
subband length for each wavelet packet at level L, v = N/2L
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SF
WPT(u)
|
uth WPT‐based SF
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h
|
compressed code of the middle layer in AEN;
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output reconstructed from c in the middle layer of AEN;
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f
EN
|
encoder layer of AEN;
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f
DE
|
decoder layer of AEN;
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f
a
|
activation function of AEN;
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W
EN
|
network weight for node in the encoder;
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W
DE
|
network weight for node decoder;
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b
EN
|
bias for node in the encoder layer;
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b
DE
|
bias for node in the decoder layer
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SF
AEN
|
SFs extracted from AEN
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References
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nth modified approximation coefficient at level j
