. 2018 Aug 20;18(8):2739. doi: 10.3390/s18082739

Table 3.

The extracted time-frequency features obtained by extending five frequency-domain features to the joint time-frequency-domain.

Description of the Time-Frequency Features

Mathematical Formulation of the Extracted Time-Frequency Features

The flatness of the CWD (FLS)

F L S = M \times N \times \frac{\prod_{t = 1}^{M} \prod_{f = 1}^{N} (| ϱ_{a} (t, f) {|)}^{1 / M \times N}}{\sum_{t = 1}^{M} \sum_{f = 1}^{N} (| ϱ_{a} (t, f) |)}

(13)

The flux of the CWD (FLX)

F L X = \sum_{t = 1}^{M - l} \sum_{f = 1}^{N - k} (ϱ_{a} (t + l, f + k) - ϱ_{a} (t, f)), l = k = 1

(14)

The spectral roll-off of the CWD (SRO)

S R O = λ \sum_{t = 1}^{M} \sum_{f = 1}^{N} (ϱ_{a} (t, f)), λ = 0.85

(15)

The normalized Renyi entropy of the CWD (NRE)

N R E = \frac{1}{1 - ν} {log}_{2} \sum_{t = 1}^{M} \sum_{f = 1}^{N} {(\frac{ϱ_{a} (t, f)}{M \times N \times μ})}^{ν}, ν = 3

(16)

The energy concentration of the CWD (EC)

E C = {(\sum_{t = 1}^{M} \sum_{f = 1}^{N} \sqrt{| ϱ_{a} (t, f) |})}^{2}

(17)