## Feature Extraction

Feature extraction is the process of deriving values from the set of measured values, such that the derived values provide valuable non – redundant information that facilitate further learning. Certain features are very much useful in the interpretation of EMG signals.

### Higuchi fractal dimensions

Fractal dimension is a measure of signal complexity. Higuchi Fractal Dimension (HFD) and Box Counting Method are the best algorithms available for calculating fractal dimension of time varying signals. The fractal dimension of the signal is calculated and used as a feature for training various learning algorithms.

Higuchi fractal dimension is calculated as shown. Consider that X(1), X(2),…,X(N) represents a finite time series. This is used to form a set of new time series given below.

Xkm : X(m), X(m+k), X(m+2k)……X(m+int((N-m)/k).k) where m=1,2,3….k where m denotes the starting time and k denotes denotes the interval time for the time series.

Length of each Xkm is calculated as shown:

The average value of the k time series sets defined in Equation is found to be exponentially related to the fractal dimension of the signal FD.

<L(k)> α k-FD

The solution to this equation is found out using linear regression.

Where xk = ln(1/k) and yk = ln(L(k)) k = k1,k2…..kmin and n denotes the total number of k values for which the linear regression has been calculated ie., (2≤ n ≤ kmax ).

### Shannon Entropy

It is a measure of randomness of the signal. The EMG signal becomes highly random when the muscle contracts and it exhibits a larger entropy value than when the muscle is relaxed, which is comparatively more regular. The Shannon entropy of a signal is calculated as shown:

Where P(x) is the probability of occurrence of event x.

### Zero Crossing Rate

Zero crossing rate (ZCR) is simply a measure of frequency of the signal. Zero crossing rate is the number of times the signal changes sign (positive to negative or negative to positive) in a given length of the signal, determined by the window size. It is calculated as shown :

Where T is the sampling rate and

In order to abstain from the background noise, the threshold condition is also taken into account. Then the ZCR is calculated using the Equation:

### Other feature extraction methods

Autoregressive coefficients.

Mean Absolute Value, Variance of EMG, Waveform length, Wilson amplitude etc.