Electroglottogram: Derivative...

Calculates the derivative of the Electroglottogram.

Settings

Low-pass frequency (Hz)
defines the highest frequency to keep in the derivative.
Smoothing (Hz)
defines the width of the transition area between fully passed and fully suppressed frequencies. Frequencies below lowpassFrequency will be fully passed, frequencies larger than lowpassFrequency+smoothing will be fully suppressed.
Scale absolute peak at 0.99
defines whether the derivative should be scaled or not.

Algorithm

The derivative of a wave form x(t) is most easily calculated in the spectral domain. According to Fourier theory, if x(t) = ∫X(f)exp(2πift) dt, then dx(t)/dt = ∫X(f)2πif exp(2πift)dt, where X(f) is the spectrum of the x(t).

Therefore, by taking the spectrum of the signal and from this spectrum calculate new real and imaginary components and then transform back to the time domain we get the derivative.

The multiplication of the spectral components with the factor 2πif will result in a new X′(f) whose components will be: Re(X′(f)) = -2πf Im (X(f)) and Im(X′(f)) =2πf Re(X(f)).

About dEGG

The derivative of the Electroglottogram is often indicated as dEGG or DEGG. Henrich et al. (2004) used the peaks in the derivative to find the glottal closure instants and sometimes also the glottal opening instants. However, in their paper and also in other papers like, for example, Herbst et al. (2014), the derivative they use is not the exact derivative as calculated in the way explained above. Instead they calculate an approximation of the derivative by taking either the first difference, (dx(t)/dt)[i] = (x[i] - x[i-1])/Δt, or by taking the first central difference, (dx(t)/dt)[i] = (x[i+1] - x[i-1])/(2Δt).

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© djmw, February 1, 2021