Dr Michail Arvanitidis

Surface EMG swings above and below zero, because the electrode sees the electrical activity of many muscle fibres as positive and negative phases. So the average of the raw signal is close to zero, however hard the muscle works.

Two standard fixes: rectify the signal (take absolute values) and average it, or take the RMS (root mean square). Computed over a short sliding window, either gives an envelope that follows how much the muscle is working.

The same steps in R (it runs right here, on the signal above) and in MATLAB (copy it, and download the 5 s recording to run it yourself). The three values match the ones on this page.

% Demo recording: 5 s of surface EMG at 1000 Hz (µV), downloaded from this page
emg = readmatrix('emg_demo.csv');

win = 100;                    % window length (ms = samples at 1000 Hz)

rect = abs(emg);                % 1) full-wave rectification
env  = sqrt(movmean(rect.^2, win));   % 2) moving RMS

m_raw  = mean(emg)              % positive and negative phases cancel
m_rect = mean(rect)             % mean rectified value
peak   = max(env)               % peak of the envelope

Change win to 20 or 300 and compare peak: it changes with the window here too.

Hold a muscle at a fixed force and the force still wobbles. How much it wobbles is the force steadiness, and it is a sensitive marker of how well the nervous system controls the muscle; it worsens with fatigue, ageing and pain.

It is usually reported as the coefficient of variation (CoV): the standard deviation relative to the mean, CoV = SD / mean × 100. Dividing by the mean makes holds at different force levels comparable.

Run it in R right here, or copy the MATLAB and download the force trace on the screen (6 s at 50 Hz): the values match the ones on this page.

% Force (% of maximum), 6 s at 50 Hz, downloaded from this page
force = readmatrix('force_demo.csv');

m  = mean(force)                % mean force
s  = std(force)                 % standard deviation
cv = s / m * 100                % coefficient of variation (%)

Move the sliders, download again and see how the three values change.

High-density EMG records from a grid of electrodes, so the RMS amplitude at each electrode forms a map of activity across the muscle. Where that activity sits, and how it moves, changes with fatigue, pain and training.

Two simple summaries: the peak electrode, and the centroid, the amplitude-weighted mean position, x̄ = Σ(amplitude × column) / Σ amplitude. The centroid is less sensitive to one noisy electrode and moves smoothly.

The map as a 4 × 8 matrix (RMS in µV, one value per electrode). The centroid is a weighted mean of the column and row numbers.

M = readmatrix('hdemg_map.csv');       % 4 rows x 8 columns, RMS (µV)
[col_no, row_no] = meshgrid(1:size(M, 2), 1:size(M, 1));

cx = sum(M(:) .* col_no(:)) / sum(M(:))     % centroid: amplitude-weighted mean column
cy = sum(M(:) .* row_no(:)) / sum(M(:))     % ... and mean row
[~, k] = max(M(:));
[peak_row, peak_col] = ind2sub(size(M), k) % the electrode with the highest RMS
mean_amp = mean(M(:))

Move the hotspot to column 7, download again and compare cx with peak_col: close, but not the same.