Sound: To Sound (derivative)...

Calculates the derivative of a Sound.

## Settings

Low-pass frequency (Hz)
  defines the highest frequency to keep in the derivative. Because taking a derivative is comparable to multiplying the strength of each frequency component by its frequency value it has the effect of high-pass filtering. E.g. a 10000 Hz component is amplified 100 times stronger than a 100 Hz component. Low-pass filtering then becomes essential for removing high-frequency noise.
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.
New absolute peak
  the new absolute peak of the derivative. By specifying a value smaller than 1.0 the derivative can be made audible without distortion. If you want to listen to the derivative without distortion, it is absolutely necessary to scale the peak to a value somewhat smaller than 1.0, like 0.99. For example, for a pure sine tone with a frequency of 300 Hz and an amplitude of 1.0 whose formula is s(t) = sin(2π300t) the derivative with respect to time t is 2π300 cos(2π300t) .The result is a cosine of 300 Hz with a huge amplitude of 2π300. You can prevent any scaling by supplying a value of 0.0.

## 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)).

### Links to this page

- Electroglottogram: Derivative...