DER – Derivation, filtering and prediction from the last n+1 samples

Block SymbolLicensing group: STANDARD

Function Description
The DER block interpolates the last $n + 1$ samples ( $n \leq N - 1$ , $N$ is implementation dependent) of the input signal u by a line $y = a t + b$ using the least squares method . The starting point of the time axis is set to the current sampling instant.

In case of $RUN = on$ the outputs y and z are computed from the obtained parameters $a$ and $b$ of the linear interpolation as follows:

\begin{matrix} Derivation: & y & = & a \\ Filtering: & z & = & b, for t_{p} = 0 \\ Prediction: & z & = & a t_{p} + b, for t_{p} > 0 \\ Retrodiction: & z & = & a t_{p} + b, for t_{p} < 0 \end{matrix}

In case of $RUN = off$ or $n + 1$ samples of the input signal are not yet available ( $RDY = off$ ), the outputs are set to $y = 0$ , $z = u$ .

Inputs

u	Analog output of the block	Double (F64)
RUN	Enable execution	Bool
	off .. tracking ( $z = u$ ) on ... filtering (y – estimate of the derivative, z – estimate of u at time $t_{p}$ )
tp	Time instant for prediction/filtering ( $tp = 0$ corresponds with the current sampling instant)	Double (F64)

Outputs

y	Estimate of input signal derivative	Double (F64)
z	Predicted/filtered input signal	Double (F64)
RDY	Ready flag (all $n + 1$ samples are available)	Bool

Parameters

n	Number of samples for interpolation ( $n + 1$ samples are used); $1 \leq n \leq n m a x$ $↓$ 1 $↑$ 10000000 $⊙$ 10	Long (I32)
nmax	Limit for parameter n (used for internal memory allocation) $↓$ 1 $↑$ 10000000 $⊙$ 10	Long (I32)

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