1. Statistics

1.1. Purpose

Compute basic statistical quantities for a set of input signals.

1.2. Description

For a signal \(x=x(k)\), where \(k=1,2,…,N\), the statistical quantities are computed as follows:

  • Maximum value: \(x_\mathrm{max} =\max_{k} x(k)\)

  • Maximum absolute value: \(x_\mathrm{absmax} = \max_k |x(k)|\)

  • Minimum value: \(x_\mathrm{min} = \min_k x(k)\)

  • Mean value: \(\bar{x} = \frac{1}{N}\sum_{k=1}^N x(k)\)

  • Standard deviation: \(\sigma = \sqrt{\frac{1}{N}\sum_{k=1}^N(x_k-\bar{x})^2}\)

  • Skewness: \(\gamma_1 = \frac{m_3}{\sigma^3} \)

  • Kurtosis: \(\gamma_2 = \frac{m_4}{\sigma^4}\)

where \(m_n = \frac{1}{N}\sum_{k=1}^N(x_k-\bar{x})^n\) is the \(n\)-th central moment of \(x\).

1.3. Input

Any equidistant or non-equidistant signal (see Signal Types ). The maximum amount of input signals is 1000.

1.4. Output

One output slot for each of the computed statistical quantities. A table with the results are shown if the user double-clicks the statistics box. This table is also available in the ReportTask.