Differentiation

Differentiation is the operation that differentiates a signal according to time.

Note: As the primary application of this method is to convert displacement data into velocity, the method which is implemented contains several steps that are specifically designed to avoid or limit unwanted effects generated by the differentiation step itself.

The processing steps applied to the signal when using Differentiation are as follows:

  1. Up-sample 4x: the time signal is resampled to four times its original sampling frequency.

    Differentiation algorithms may create artifacts at high frequencies. By up-sampling the signal before differentiation, you ensure that the artifacts will be created outside the frequency band of interest.

  2. Differentiate: the time signal is then differentiated using the Central Difference Gradient method.

    This method appears to be the most appropriate when dealing with velocity and displacement time data.

  3. Down-sample x1/4: the current time signal is resampled to the sampling frequency of the original signal.

    To avoid aliasing, the resampling function applies a low-pass filter before the resampling itself. This ensures that the potential high-frequency artifacts are removed from the signal.

Note: Because of the different processing steps applied before and after the differentiation algorithm itself, using integration then differentiation on a signal will not revert to the exact original signal.