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Time Series Processing and Time Series Features

Transform your signals into stationary time series, and from the time series, extract specialized features. Time series features provide unique insights into the data.

Obtain Stationary Time Series from Signal Data

A stationary time series has no trends or periodic fluctuations, and constant variance and autocorrelation over time. Second-order stationary signals, which are usually sufficient for engineering applications, have zero mean and constant variance. The app provides a set of processing transformations that you can use to eliminate nonstationary components and reduce time-dependent variance. These transformations include:

  • Difference — Remove nonstationary level (first order) or slope (second order).

  • Seasonal — Remove periodic components such as seasonal variations. Specify the seasonal period in number of samples in one period.

  • Detrend — Remove deterministic polynomial trend. Specify the polynomial type as constant, linear, cubic, or quadratic.

  • Natural Logarithm — Stabilize variance over time.

  • Box-Cox Transform — Stabilize variance over time, using a power level that you specify. Using a power level of 0 is equivalent to taking the logarithm. The data is normalized and shifted to have a minimum of 1 so that negative powers and logarithms are always meaningful.

To specify an operation, select a transformation and click Add Selected. You can select a single transformation or stack multiple transformations in the order that you choose. You can experiment with different transformation selections and different orders. Then visually assess the results so that you can assess how well the processing performs. For example, you can visually assess the general flatness of the signal for the absence of obvious trends.

To access this processing in the app, select the source signal, and then, in the Feature Designer tab, in the Data Processing section, select Residue Generation > Time-Series Processing.

Extract Features from Stationary Time Series

Time series features in the app include distribution features, autocorrelation features, and partial autocorrelation features.

  • The Distribution Features section contains standard statistical features that characterize the overall dispersion of the data. These features include the overall minimum, median, maximum, quartile statistics, and custom quantiles.

  • The Autocorrelation Features section contains features that describe the linear dependence of a variable with itself at two points in time. For stationary processes, the autocorrelation between any two points depends only on the time lag between them. The autocorrelation function (ACF) is the sequence containing the autocorrelation values that correspond to each possible lag value. The sum of squares for a specified value of n is the sum of the squares of the first n autocorrelations.

  • The Partial Autocorrelation Features section contains features that are similar to autocorrelation features, but account for the effects of mutual linear dependence on other variables in the sequence. The partial autocorrelation function (PACF) is the sequence containing the partial autocorrelations for each lag value. The sum of squares for a specified value of n is the sum of the squares of the first n partial autocorrelations.

To access these features in the app, select the source signal, and then, in the Feature Designer tab, in the Feature Generation section, select Time-Domain Features > Time-Series Features.