Appendix 2.B ‐ List of Symbols in Equations
F s | sampling rate for acquiring a signal | ||||||||||
F B | highest frequency component contained in a signal | ||||||||||
M | number of precision items | ||||||||||
N | data length of discrete signals | ||||||||||
s[i] | ith data point of a discrete signal | ||||||||||
p | pth precision item |
|
raw sensor data of pth precision item |
|
cleaned sensor data of pth precision item | ||||||
g[k] | DWT low‐pass filters | ||||||||||
h[k] | DWT high‐pass filters | ||||||||||
L | number of decomposition levels; | ||||||||||
j | scale parameters | ||||||||||
n | translation parameter | ||||||||||
cj[n] |
nth discrete wavelet coefficient of |
|
nth approximation coefficient at level j |
|
nth detail coefficient at level j |
|
nth modified wavelet coefficients at level j |
|
nth modified approximation coefficient at level j |
|
nth modified detail coefficient at level j |
λ | threshold of cj[n] | ||||||||||
MAD(cL − 1[n]) | mean absolute deviation of cL − 1[n] |
|
modified approximation coefficients | ||||||||
avg |
arithmetic mean or average of |
||||||||||
std |
standard derivation of |
||||||||||
max |
maximal magnitude of |
||||||||||
min |
minimal magnitude of |
||||||||||
ptp |
peak‐to‐peak amplitude of |
||||||||||
kurt |
kurtosis for measuring the peakedness of |
||||||||||
skew |
skewness for measuring the asymmetry of |
||||||||||
RMS |
root mean square value of |
||||||||||
CF |
crest factor of |
||||||||||
T | duration of a continuous‐time signal | ||||||||||
t | specific time t of a continuous‐time signals | ||||||||||
cr xy | correlation coefficient value of two signals: x(t) and y(t) | ||||||||||
CR
xy
|