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. 2022 Oct 28;22(21):8251. doi: 10.3390/s22218251
Abbreviations
AWGN Additive white Gaussian noise
TFD Time-frequency distribution
DFT Discrete Fourier transform
TF Time-frequency
LRE Local Rényi entropy
SNR Signal-to-noise ratio
Nomenclature
Al instantaneous amplitude of the l-th component
C set of observations derived from a TFD
Ct set of observations derived from one TFD building block
CI subset of TFD’s observations derived from useful information
Ck k-th set of partitioned TFD’s observations
Ck,t k-th set of partitioned observations from one TFD building block
dk closeness value between LRE estimates Hk and Hk+1
dk closeness value between block-wise LRE estimates Hk,t and Hk+1,t
f continuous frequency
fl(t) instantaneous frequency of the l-th component
fs sampling frequency
G time-lag kernel
Hk Rényi entropy of the k-th TFD class
Hk,t Rényi entropy of the k-th class, and t-th building block
i smallest index of useful classes ρk
it smallest index of building-block useful classes ρk,t
L number of signal components
K number of TFD classes
l discrete lag
m discrete frequency
M number of frequency bins
n discrete time
n0 parameter defining the amplitude modulation time-shift
N number of time samples
p specific time instant
t continuous time
T parameter defining the signal component amplitude modulation variance
UI extracted TFD useful information
UIt         useful information extracted per one TFD building-block
w non-constant positive noise amplitude modulation
xl l-th signal component
x noise-free signal
y noisy signal
α Rényi entropy order
β parameter defining the amplitude noise modulation variance
Δm frequency resolution
Δn duration of LRE estimation interval
Δt duration of one TFD building block
ν additive white noise
ρ quadratic TFD
ρI TFD of extracted useful information
ρk k-th TFD class
ρk,t k-th class of TFD building block
ρt TFD building block
ρy TFD of a noisy signal
τ continuous lag
Φl instantaneous phase of the l-th component