Create Signals

This section describes how to create new signals from various mathematical models.

Screenshot of the “Create” menu.

When the “Signal Panel” is selected, the menus and toolbars are updated to provide signal-related actions.

The “Create” menu allows you to create new signals from various models (see below).

New signal

Create a new signal from various models:

Icon	Model	Equation
	Zero	\(y[i] = 0\)
	Normal distribution	\(y[i]\) is normally distributed with configurable mean and standard deviation
	Poisson distribution	\(y[i]\) is Poisson distributed with configurable mean
	Uniform distribution	\(y[i]\) is uniformly distributed between two configurable bounds
	Gaussian	\(y = y_{0}+\dfrac{A}{\sqrt{2\pi} \cdot \sigma} \cdot \exp\left(-\dfrac{1}{2} \cdot \left(\dfrac{x-x_{0}}{\sigma}\right)^2\right)\)
	Lorentzian	\(y = y_{0}+\dfrac{A}{\sigma \cdot \pi} \cdot \dfrac{1}{1+\left(\dfrac{x-x_{0}}{\sigma}\right)^2}\)
	Voigt	\(y = y_{0}+A \cdot \dfrac{\Re\left(\exp\left(-z^2\right) \cdot \erfc(-j \cdot z)\right)}{\sqrt{2\pi} \cdot \sigma}\) with \(z = \dfrac{x-x_{0}-j \cdot \sigma}{\sqrt{2} \cdot \sigma}\)
	Blackbody (Planck’s law)	\(y = \dfrac{2 h c^2}{\lambda^5 \left(\exp\left(\dfrac{h c}{\lambda k T}\right)-1\right)}\)
	Sine	\(y = y_{0}+A\sin\left(2\pi \cdot f \cdot x+\phi\right)\)
	Cosine	\(y = y_{0}+A\cos\left(2\pi \cdot f \cdot x+\phi\right)\)
	Sawtooth	\(y = y_{0}+A \left( 2 \left( f x + \frac{\phi}{2\pi} - \left\lfloor f x + \frac{\phi}{2\pi} + \frac{1}{2} \right\rfloor \right) \right)\)
	Triangle	\(y = y_{0}+A \sawtooth\left(2 \pi f x + \phi, \text{width} = 0.5\right)\)
	Square	\(y = y_0 + A \sgn\left( \sin\left( 2\pi f x + \phi \right) \right)\)
	Cardinal sine	\(y = y_0 + A \sinc\left(2\pi f x + \phi\right)\)
	Linear chirp	\(y = y_{0} + A \sin\left(\phi_{0} + 2\pi \left(f_{0}\, x + \frac{1}{2} c\, x^{2}\right)\right)\)
	Step	\(y = y_{0}+A \left\{\begin{array}{ll}1 & \text{if } x > x_{0} \\ 0 & \text{otherwise}\end{array}\right.\)
	Exponential	\(y = y_{0}+A \exp\left(B \cdot x\right)\)
	Logistic	\(y = y_{0} + \dfrac{A}{1 + \exp\left(-k \left(x - x_{0}\right)\right)}\)
	Pulse	\(y = y_{0}+A \left\{\begin{array}{ll}1 & \text{if } x_{0} < x < x_{1} \\ 0 & \text{otherwise}\end{array}\right.\)
	Step Pulse	\(y = \left( \begin{cases} y_0 & \text{if } x < t_0 \\ y_0 + A \cdot \dfrac{x - t_0}{t_r} & \text{if } t_0 \leq x < t_0 + t_r \\ y_0 + A & \text{if } x \geq t_0 + t_r \end{cases} \right) + \mathcal{N}\left(0, \sigma_n\right)\) where: \(t_0\) is the pulse start time, \(t_r\) is the rise time, \(\sigma_n\) is the noise amplitude
	Square Pulse	\(y(x) = \left(\begin{cases} y_0 & \text{if } x < t_0 \\ y_0 + A \cdot \dfrac{x - t_0}{t_r} & \text{if } t_0 \leq x < t_0 + t_r \\ y_0 + A & \text{if } t_0 + t_r \leq x < t_1 \\ y_0 + A - A \cdot \dfrac{x - t_1}{t_f} & \text{if } t_1 \leq x < t_1 + t_f \\ y_0 & \text{if } x \geq t_1 + t_f \end{cases} \right) + \mathcal{N}(0, \sigma_n)\) where: \(t_0\) is the pulse start time, \(t_r\) is the rise time, \(t_f\) is the fall time, \(t_1 = t_0 + t_r + d\) is the time at which the decay starts, \(\sigma_n\) is the noise amplitude the duration of the plateau \(d\) is computed as \(d = t_{\mathrm{FWHM}} - \dfrac{t_r + t_f}{2}\) from the full width at half maximum \(t_{\mathrm{FWHM}}\) Warning The duration of the plateau \(d\) should not be negative.
	Polynomial	\(y = y_{0}+A_{0}+A_{1} \cdot x+A_{2} \cdot x^2+\ldots+A_{n} \cdot x^n\)
	Custom	Manual input of X and Y values