Last Modified: March 15, 2017

Computes the real Laplace transform of a sequence.

The array describing the evenly sampled time signal.

The first element of this array belongs to *t* = 0, the last to * t* = **end**.

The instant in time of the last sample.

The entire sample interval is between 0 and **end**.

Error conditions that occur before this node runs.

The node responds to this input according to standard error behavior.

Standard Error Behavior

Many nodes provide an **error in** input and an **error out** output so that the node can respond to and communicate errors that occur while code is running. The value of **error in** specifies whether an error occurred before the node runs. Most nodes respond to values of **error in** in a standard, predictable way.

**Default: **No error

The result of the Laplace transform as an array.

Error information.

The node produces this output according to standard error behavior.

Standard Error Behavior

**error in** input and an **error out** output so that the node can respond to and communicate errors that occur while code is running. The value of **error in** specifies whether an error occurred before the node runs. Most nodes respond to values of **error in** in a standard, predictable way.

The real Laplace transform of a real signal *x*(*s*) is defined by the following equation:

$\mathrm{Laplace}\left\{X\right\}\left(s\right)={\int}_{0}^{\infty}x\left(t\right)\mathrm{exp}(-st)dt$

for real $s\ge 0$.

The discrete version of the Laplace transform of a discretely and evenly-sampled signal is a generation of the above continuous version.

The definition of the Laplace transform is not of much use if the time signal increases rapidly with the time. The discrete version of the Laplace transform cannot fully detect the convergence behavior of the original definition.

The discrete version of the Laplace transform is computationally expensive. An efficient strategy for the discrete Laplace transform is based on the fast fractional Fourier transform (FFFT). The definition of the FFFT is as follows:

$\mathrm{FFFT}\left\{X\right\}\left(t\right)={\int}_{0}^{\infty}x\left(s\right)\mathrm{exp}(-iast)ds$

with an arbitrarily chosen complex alpha.

The following image shows the real Laplace transform of the function $f\left(t\right)=\mathrm{sin}\left(t\right)$ in the interval (0, 6).

**Where This Node Can Run: **

Desktop OS: Windows

FPGA: This product does not support FPGA devices