openstb.simulator.system.signal

Classes:

Name	Description
HFMChirp	Hyperbolic frequency modulated chirp.
LFMChirp	Linear frequency modulated chirp.

HFMChirp

HFMChirp(f_start, f_stop, duration, rms_spl, rms_after_window=True, window=None)

Bases: Signal

Hyperbolic frequency modulated chirp.

For a start frequency \(f_a\), stop frequency \(f_b\) and chirp length \(\tau\), we can define a unitless parameter

\[ b = \frac{1/f_b - 1/f_a}{\tau}. \]

In the passband, the HFM chirp is then given by

\[ s(t) = \exp \left(j2\pi \frac{\ln(1 + b f_a t)}{b} \right) \qquad 0 \leq t \leq \tau, \]

which has a hyperbolic instantaneous frequency \(f(t) = f_a / (1 + b f_a t)\). The inverse of this is the instantaneous period

\[ \frac{1}{f(t)} = \frac{1}{f_a} + bt \]

which is linear, giving rise to the alternative name of linear period modulated (LPM) chirp.

Parameters:

Name	Type	Description	Default
f_start	float	The start frequency of the chirp.	required
f_stop	float	The stop frequency of the chirp.	required
duration	float	The duration of the chirp in seconds.	required
rms_spl	float	The RMS sound pressure level (decibels relative to 1 micropascal) of the signal.	required
rms_after_window	bool	If True, scale the signal to the desired RMS SPL after applying the window. If False, scale before applying the window, meaning the windowed signal will have a lower RMS SPL. If no window is applied, this will be set to False.	True
window	PluginOrSpec[SignalWindow] | None	Plugin specification for a signal window to apply to the samples of the signal.	None

Source code in openstb/simulator/system/signal.py

def __init__(
    self,
    f_start: float,
    f_stop: float,
    duration: float,
    rms_spl: float,
    rms_after_window: bool = True,
    window: PluginOrSpec[abc.SignalWindow] | None = None,
):
    """
    Parameters
    ----------
    f_start
        The start frequency of the chirp.
    f_stop
        The stop frequency of the chirp.
    duration
        The duration of the chirp in seconds.
    rms_spl
        The RMS sound pressure level (decibels relative to 1 micropascal) of the
        signal.
    rms_after_window
        If True, scale the signal to the desired RMS SPL after applying the window.
        If False, scale before applying the window, meaning the windowed signal will
        have a lower RMS SPL. If no window is applied, this will be set to False.
    window
        Plugin specification for a signal window to apply to the samples of the
        signal.

    """
    self.f_start = f_start
    self.f_stop = f_stop
    self._minimum_frequency = min(f_start, f_stop)
    self._maximum_frequency = max(f_start, f_stop)
    self._duration = duration
    self.rms_spl = rms_spl
    self.rms_after_window = rms_after_window and (window is not None)
    self.window = None if window is None else signal_window(window)

LFMChirp

LFMChirp(f_start, f_stop, duration, rms_spl, rms_after_window=True, window=None)

Bases: Signal

Linear frequency modulated chirp.

For a start frequency \(f_a\), stop frequency \(f_b\) and chirp length \(\tau\), we can calculate the chirp rate \(K = (f_b - f_a) / \tau\). In the passband, the LFM chirp is then

\[ s(t) = \exp (j\pi t (2f_a + Kt)) \qquad 0 \leq t \leq \tau, \]

which has a linear instantaneous frequency \(f(t) = f_a + Kt\).

Parameters:

Name	Type	Description	Default
f_start	float	The start frequency of the chirp.	required
f_stop	float	The stop frequency of the chirp.	required
duration	float	The duration of the chirp in seconds.	required
rms_spl	float	The RMS sound pressure level (decibels relative to 1 micropascal) of the signal.	required
rms_after_window	bool	If True, scale the signal to the desired RMS SPL after applying the window. If False, scale before applying the window, meaning the windowed signal will have a lower RMS SPL. If no window is applied, this parameter is ignored.	True
window	PluginOrSpec[SignalWindow] | None	Plugin specification for a signal window to apply to the samples of the signal.	None

Source code in openstb/simulator/system/signal.py

def __init__(
    self,
    f_start: float,
    f_stop: float,
    duration: float,
    rms_spl: float,
    rms_after_window: bool = True,
    window: PluginOrSpec[abc.SignalWindow] | None = None,
):
    """
    Parameters
    ----------
    f_start
        The start frequency of the chirp.
    f_stop
        The stop frequency of the chirp.
    duration
        The duration of the chirp in seconds.
    rms_spl
        The RMS sound pressure level (decibels relative to 1 micropascal) of the
        signal.
    rms_after_window
        If True, scale the signal to the desired RMS SPL after applying the window.
        If False, scale before applying the window, meaning the windowed signal will
        have a lower RMS SPL. If no window is applied, this parameter is ignored.
    window
        Plugin specification for a signal window to apply to the samples of the
        signal.

    """
    self.f_start = f_start
    self.f_stop = f_stop
    self._minimum_frequency = min(f_start, f_stop)
    self._maximum_frequency = max(f_start, f_stop)
    self._duration = duration
    self.rms_spl = rms_spl
    self.rms_after_window = rms_after_window and (window is not None)
    self.window = None if window is None else signal_window(window)