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Doppler

Doppler shift module.

Attributes

SOUNDSPEED module-attribute 

SOUNDSPEED = 343.0

Speed of sound

Functions

velocity_from_doppler_shift 

velocity_from_doppler_shift(f1, f2, c=SOUNDSPEED) -> float

Calculate velocity based on measured frequency shifts due to Doppler shift.

\[ v = c \cdot \left( \frac{f_2 - f_1}{f_2 + f_1} \right) \]

The assumption is made that the velocity is constant between the observation times.

PARAMETER DESCRIPTION
f1

Lower frequency \(f_1\).
f2

Upper frequency \(f_2\).
c

Speed of sound \(c\).

DEFAULT: SOUNDSPEED

RETURNS DESCRIPTION
float

Calculated velocity.
Source code in acoustic_toolbox/doppler.py 
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def velocity_from_doppler_shift(f1, f2, c=SOUNDSPEED) -> float:
    r"""Calculate velocity based on measured frequency shifts due to Doppler shift.

    $$
    v = c \cdot \left( \frac{f_2 - f_1}{f_2 + f_1} \right)
    $$

    The assumption is made that the velocity is constant between the observation times.

    Args:
      f1: Lower frequency $f_1$.
      f2: Upper frequency $f_2$.
      c: Speed of sound $c$.

    Returns:
        Calculated velocity.
    """
    return c * (f2 - f1) / (f2 + f1)

frequency_shift 

frequency_shift(
    frequency,
    velocity_source,
    velocity_receiver,
    soundspeed=SOUNDSPEED,
) -> float

Frequency shift due to Doppler effect.

PARAMETER DESCRIPTION
frequency

Emitted frequency \(f\).
velocity_source

Velocity of source \(v_s\). Positive if the source is moving away from the receiver (and negative in the other direction).
velocity_receiver

Velocity of receiver \(v_r\). Positive if the receiver is moving towards the source (and negative in the other direction);
soundspeed

Speed of sound \(c\). $$ f = \frac{c + v_r}{c + v_s} f_0 $$

DEFAULT: SOUNDSPEED

RETURNS DESCRIPTION
float

Frequency after shift.
Source code in acoustic_toolbox/doppler.py 
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def frequency_shift(
    frequency, velocity_source, velocity_receiver, soundspeed=SOUNDSPEED
) -> float:
    r"""Frequency shift due to Doppler effect.

    Args:
      frequency: Emitted frequency $f$.
      velocity_source: Velocity of source $v_s$.
        Positive if the source is moving away from the receiver (and negative in the other direction).
      velocity_receiver: Velocity of receiver $v_r$.
        Positive if the receiver is moving towards the source (and negative in the other direction);
      soundspeed: Speed of sound $c$.
        $$
        f = \frac{c + v_r}{c + v_s} f_0
        $$

    Returns:
        Frequency after shift.
    """
    return (soundspeed + velocity_receiver) / (soundspeed + velocity_source) * frequency

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