ExpSine

Exponentially damped sine wave with configurable amplitude, frequency, and damping.

Generates a sinusoidal signal that exponentially decays over time based on the damping coefficient. The signal remains at the offset value until the start time is reached, after which it follows the equation:

$$y(t)=\text{offset}+\text{amplitude}\cdot e^{-\text{damping}\cdot (t-t_{\text{start}})}\cdot \sin (2\pi \cdot \text{frequency}\cdot (t-t_{\text{start}})+\text{phase})$$

Signal

Usage

ExpSine(start_time=0.0, offset=0.0, amplitude, damping, frequency, phase)

Parameters:

Name	Description	Units	Default value
start_time	Time at which the signal starts changing from its offset value	s	0
offset	Constant value added to the signal output	–	0
amplitude	Maximum amplitude of the sine wave	–
damping	Coefficient controlling how quickly the sine wave decays	s-1
frequency	Frequency of the sine wave oscillation	Hz
phase	Phase angle offset of the sine wave in radians	rad

Connectors

• y - This connector represents a real signal as an output from a component (RealOutput)

Behavior

$$\begin{array}{rl}y\left(t\right)& =ifelse(\mathtt{start}\mathtt{\_}\mathtt{time}<t,\mathtt{offset}+\mathtt{amplitude}{e}^{-\mathtt{damping}(-\mathtt{start}\mathtt{\_}\mathtt{time}+t)}\sin (\mathtt{phase}+6.2832\mathtt{frequency}(-\mathtt{start}\mathtt{\_}\mathtt{time}+t)),\mathtt{offset})\end{array}$$

Source

# Exponentially damped sine wave with configurable amplitude, frequency, and damping.
#
# Generates a sinusoidal signal that exponentially decays over time based on the damping coefficient.
# The signal remains at the offset value until the start time is reached, after which it follows the
# equation:
#
# ```math
# y(t) = \text{offset} + \text{amplitude} \cdot e^{-\text{damping}\cdot(t-t_{\text{start}})} \cdot \sin(2\pi \cdot \text{frequency} \cdot (t-t_{\text{start}}) + \text{phase})
# ```
component ExpSine
  extends Signal
  # Maximum amplitude of the sine wave
  parameter amplitude::Real
  # Coefficient controlling how quickly the sine wave decays
  parameter damping::DampingCoefficient
  # Frequency of the sine wave oscillation
  parameter frequency::Frequency
  # Phase angle offset of the sine wave in radians
  parameter phase::Angle
relations
  y = if start_time<time then offset+amplitude*exp(-damping*(time-start_time))*sin(2*π*frequency*(time-start_time)+phase) else offset
metadata {"Dyad": {"icons": {"default": "dyad://BlockComponents/ExpSine.svg"}}}
end

Flattened Source

# Exponentially damped sine wave with configurable amplitude, frequency, and damping.
#
# Generates a sinusoidal signal that exponentially decays over time based on the damping coefficient.
# The signal remains at the offset value until the start time is reached, after which it follows the
# equation:
#
# ```math
# y(t) = \text{offset} + \text{amplitude} \cdot e^{-\text{damping}\cdot(t-t_{\text{start}})} \cdot \sin(2\pi \cdot \text{frequency} \cdot (t-t_{\text{start}}) + \text{phase})
# ```
component ExpSine
  # Real-valued output connector for the component
  y = RealOutput() [{"Dyad": {"placement": {"icon": {"x1": 950, "y1": 450, "x2": 1050, "y2": 550}}}}]
  # Time at which the signal starts changing from its offset value
  parameter start_time::Time = 0.0
  # Constant value added to the signal output
  parameter offset::Real = 0.0
  # Maximum amplitude of the sine wave
  parameter amplitude::Real
  # Coefficient controlling how quickly the sine wave decays
  parameter damping::DampingCoefficient
  # Frequency of the sine wave oscillation
  parameter frequency::Frequency
  # Phase angle offset of the sine wave in radians
  parameter phase::Angle
relations
  y = if start_time<time then offset+amplitude*exp(-damping*(time-start_time))*sin(2*π*frequency*(time-start_time)+phase) else offset
metadata {"Dyad": {"icons": {"default": "dyad://BlockComponents/ExpSine.svg"}}}
end

Test Cases

No test cases defined.

Related

• Examples

• Experiments

• Analyses

• Tests

  • ExpSineTest