# Band Power calculation

The EmotivPRO Analyzer allows the following operations that involve the pre-processing and bandpower extraction.

* Basic EEG processing
* Basic EEG processing and Transformation
* Individual Band-Power Reports
* Band Power Report

**Limit slew rate :**

This limits the step change between 2 samples. Analyzer applies a slew rate limitation at 30 µV.

**High-pass filter :** 

The data is high-pass filtered before performing the fourier transform. We use the following coefficients ( 3dB at 0.5Hz filter):

```html
filter_coeffs": {
            "b": [0.96588528974407006000, -1.93177057948814010000, 0.96588528974407006000],
            "a": [1.00000000000000000000, -1.93060642721966810000, 0.93293473175661223000]}
```

**Re-referencing:**\
Analyzer supports three ways of re-referencing the EEG data. Interquartile mean (IQM), Median, and Mean.

**Hanning Window :**\
Users can choose a window size of N (e.g. 256) samples and this window by M (e.g. 16) samples to create the new window.

The exact implementation of the Hanning window we use: 

```html
hanning_window = [] 
for i in range(256): 
    hanning_window.append(0.5 * (1 - np.cos((2.0 * np.pi * (i + 1)) / (256 + 1))))
```

**Band Powers and Normalization :** 

Our normalization uses python and numpy. 

Multiplying the Hanning window by 2 (as the window reduces the amplitude of the Fourier transform by a factor of 2 and divide the output of the fft by the window length)

We also subtract the mean of the data for each epoch/window as the DC value is not usable and only distorts the Fourier transform of the lower frequencies.

```
    hanning_window = np.hanning(eeg.shape[0]) * 2
    eeg_norm = eeg - np.mean(eeg, axis=0)
    eeg_fft = (eeg_norm.T * hanning_window).T
    fourier_transform = fft(eeg_fft, axis=0)/eeg_fft.shape[0]
    fourier_transform_norm = (2 x fourier_transform) / hanning_window.shape[0]
    eeg_fft_square_3d = np.absolute(fourier_transform_norm)**2
    band = list(range(16, 25))
    band_power = np.sum(eeg_fft_square_3d[band, :, :], axis=0) / len(band)
    

//Finally EmotivPRO Analyzer will output band power in decibels (dB): 
    band_power_db = 10*np.log10(band_power))

```


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