Waveform

Radar waveform definitions and factory functions.

Provides the :class:WaveformSample dataclass and factory functions for four waveform types: uncoded (rectangular), Barker-coded, random phase-coded, and linear frequency modulated (LFM) chirp.

BARKER_DICT = {2: [1, -1], 3: [1, 1, -1], 4: [1, 1, -1, 1], 5: [1, 1, 1, -1, 1], 7: [1, 1, 1, -1, -1, 1, -1], 11: [1, 1, 1, -1, -1, -1, 1, -1, -1, 1, -1], 13: [1, 1, 1, 1, 1, -1, -1, 1, 1, -1, 1, -1, 1]} module-attribute

WaveformSample dataclass

Container for a radar waveform and its key parameters.

Created by the factory functions (:func:uncoded_waveform, :func:barker_coded_waveform, :func:random_coded_waveform, :func:lfm_waveform). Call :meth:set_sample before passing to :func:rad_lab.rdm.gen to generate the discrete pulse array at the radar's sample rate.

Attributes:

Name	Type	Description
type	WaveformType	Waveform type identifier.
bw	float	Waveform bandwidth [Hz].
time_bw_product	float	Time-bandwidth product [dimensionless]. Equal to 1 for uncoded pulses; greater than 1 for coded waveforms, indicating pulse-compression gain.
pulse_width	float	Pulse duration [s].
pulse_func	Callable	Callable that generates (time_array, pulse_array) when called with a sample rate [Hz].
pulse_sample	ndarray	Discrete complex pulse array at the radar sample rate. Populated by :meth:set_sample; not set at construction time.

Source code in src/rad_lab/waveform.py

@dataclass
class WaveformSample:
    """Container for a radar waveform and its key parameters.

    Created by the factory functions (:func:`uncoded_waveform`,
    :func:`barker_coded_waveform`, :func:`random_coded_waveform`,
    :func:`lfm_waveform`). Call :meth:`set_sample` before passing to
    :func:`rad_lab.rdm.gen` to generate the discrete pulse array at the
    radar's sample rate.

    Attributes:
        type: Waveform type identifier.
        bw: Waveform bandwidth [Hz].
        time_bw_product: Time-bandwidth product [dimensionless]. Equal to 1
            for uncoded pulses; greater than 1 for coded waveforms, indicating
            pulse-compression gain.
        pulse_width: Pulse duration [s].
        pulse_func: Callable that generates ``(time_array, pulse_array)`` when
            called with a sample rate [Hz].
        pulse_sample: Discrete complex pulse array at the radar sample rate.
            Populated by :meth:`set_sample`; not set at construction time.
    """

    type: WaveformType
    bw: float
    time_bw_product: float
    pulse_width: float
    pulse_func: Callable
    pulse_sample: np.ndarray = field(init=False)

    def set_sample(self, sample_rate: float) -> None:
        """Generate and store the discrete pulse array at the given sample rate.

        Args:
            sample_rate: ADC sampling rate [Hz].
        """
        _, self.pulse_sample = self.pulse_func(sample_rate)

bw instance-attribute

pulse_func instance-attribute

pulse_sample = field(init=False) class-attribute instance-attribute

pulse_width instance-attribute

time_bw_product instance-attribute

type instance-attribute

__init__(type, bw, time_bw_product, pulse_width, pulse_func)

set_sample(sample_rate)

Generate and store the discrete pulse array at the given sample rate.

Parameters:

Name	Type	Description	Default
sample_rate	float	ADC sampling rate [Hz].	required

Source code in src/rad_lab/waveform.py

def set_sample(self, sample_rate: float) -> None:
    """Generate and store the discrete pulse array at the given sample rate.

    Args:
        sample_rate: ADC sampling rate [Hz].
    """
    _, self.pulse_sample = self.pulse_func(sample_rate)

WaveformType

Bases: StrEnum

Enumeration of supported radar waveform types.

Source code in src/rad_lab/waveform.py

class WaveformType(StrEnum):
    """Enumeration of supported radar waveform types."""

    UNCODED = "uncoded"
    BARKER = "barker"
    RANDOM = "random"
    LFM = "lfm"

BARKER = 'barker' class-attribute instance-attribute

LFM = 'lfm' class-attribute instance-attribute

RANDOM = 'random' class-attribute instance-attribute

UNCODED = 'uncoded' class-attribute instance-attribute

barker_coded_pulse(sample_rate, bw, nchips, normalize=True)

Generates a baseband, Barker-coded pulse.

Barker codes are specific binary phase codes known for their low autocorrelation sidelobes.

Parameters:

Name	Type	Description	Default
sample_rate	float	The sampling rate in Hz.	required
bw	float	The chip bandwidth in Hz. The chip duration is 1/bw.	required
nchips	int	The number of chips in the Barker code. Must be a valid Barker code length (2, 3, 4, 5, 7, 11, or 13).	required
normalize	bool	If True, the pulse is normalized to have unit energy. Defaults to True.	True

Returns:

Type	Description
tuple[ndarray, ndarray]	tuple[np.ndarray, np.ndarray]: A tuple containing: - t (np.ndarray): Time vector for the pulse in seconds. - mag (np.ndarray): The real-valued, Barker-coded magnitude of the pulse.

Raises:

Type	Description
AssertionError	If nChips is not a valid Barker code length.

Source code in src/rad_lab/waveform.py

def barker_coded_pulse(
    sample_rate: float, bw: float, nchips: int, normalize: bool = True
) -> tuple[np.ndarray, np.ndarray]:
    """Generates a baseband, Barker-coded pulse.

    Barker codes are specific binary phase codes known for their low
    autocorrelation sidelobes.

    Args:
        sample_rate (float): The sampling rate in Hz.
        bw (float): The chip bandwidth in Hz. The chip duration is 1/bw.
        nchips (int): The number of chips in the Barker code. Must be a valid
            Barker code length (2, 3, 4, 5, 7, 11, or 13).
        normalize (bool, optional): If True, the pulse is normalized to have
            unit energy. Defaults to True.

    Returns:
        tuple[np.ndarray, np.ndarray]: A tuple containing:
            - t (np.ndarray): Time vector for the pulse in seconds.
            - mag (np.ndarray): The real-valued, Barker-coded magnitude of the pulse.

    Raises:
        AssertionError: If nChips is not a valid Barker code length.
    """
    assert nchips in BARKER_DICT, f"{nchips=} is not a valid Barker code length."
    return coded_pulse(
        sample_rate,
        bw,
        BARKER_DICT[nchips],
        normalize=normalize,
    )

barker_coded_waveform(bw, nchips)

Returns a WaveformSample for a Barker-coded pulse.

Parameters:

Name	Type	Description	Default
bw	float	Chip bandwidth in Hz. Chip duration is 1/bw.	required
nchips	int	Number of chips. Must be a valid Barker length (2,3,4,5,7,11,13).	required

Returns:

Type	Description
WaveformSample	WaveformSample for use with rdm.gen.

Source code in src/rad_lab/waveform.py

def barker_coded_waveform(bw: float, nchips: int) -> WaveformSample:
    """Returns a WaveformSample for a Barker-coded pulse.

    Args:
        bw: Chip bandwidth in Hz. Chip duration is 1/bw.
        nchips: Number of chips. Must be a valid Barker length (2,3,4,5,7,11,13).

    Returns:
        WaveformSample for use with rdm.gen.
    """
    assert nchips in BARKER_DICT, f"nchips={nchips} is not a valid Barker code length."
    return WaveformSample(
        type=WaveformType.BARKER,
        bw=bw,
        time_bw_product=nchips,
        pulse_width=nchips / bw,
        pulse_func=partial(barker_coded_pulse, bw=bw, nchips=nchips),
    )

coded_pulse(sample_rate, bw, code, normalize=True)

Generates a baseband, phase-coded pulse.

The pulse is constructed by concatenating rectangular "chips", where each chip has a phase determined by the input code (1 for 0 phase, -1 for pi phase).

Parameters:

Name	Type	Description	Default
sample_rate	float	The sampling rate in Hz.	required
bw	float	The chip bandwidth in Hz. The chip duration is 1/bw.	required
code	list[int]	A list of code values, which must be either 1 or -1. The length of the list determines the number of chips.	required
normalize	bool	If True, the pulse is normalized to have unit energy. Defaults to True.	True

Returns:

Type	Description
tuple[ndarray, ndarray]	tuple[np.ndarray, np.ndarray]: A tuple containing: - t (np.ndarray): Time vector for the pulse in seconds. - mag (np.ndarray): The real-valued, coded magnitude of the pulse.

Raises:

Type	Description
AssertionError	If any value in the code is not 1 or -1.

Source code in src/rad_lab/waveform.py

def coded_pulse(
    sample_rate: float, bw: float, code: list[int], normalize: bool = True
) -> tuple[np.ndarray, np.ndarray]:
    """Generates a baseband, phase-coded pulse.

    The pulse is constructed by concatenating rectangular "chips", where each
    chip has a phase determined by the input code (1 for 0 phase, -1 for pi
    phase).

    Args:
        sample_rate (float): The sampling rate in Hz.
        bw (float): The chip bandwidth in Hz. The chip duration is 1/bw.
        code (list[int]): A list of code values, which must be either 1 or -1.
            The length of the list determines the number of chips.
        normalize (bool, optional): If True, the pulse is normalized to have
            unit energy. Defaults to True.

    Returns:
        tuple[np.ndarray, np.ndarray]: A tuple containing:
            - t (np.ndarray): Time vector for the pulse in seconds.
            - mag (np.ndarray): The real-valued, coded magnitude of the pulse.

    Raises:
        AssertionError: If any value in the code is not 1 or -1.
    """
    Tc = 1 / bw
    dt = 1 / sample_rate
    samples_per_chip = round(Tc * sample_rate)

    code_array = np.asarray(code)
    assert np.all(np.abs(code_array) == 1), "Code values must be either 1 or -1."
    mag = np.repeat(code_array, samples_per_chip).astype(float)
    t = np.arange(mag.size) * dt

    if normalize:
        mag = mag / norm(mag)

    return t, mag

complex_tone_pulse(sample_rate, bw, fc, normalize=True)

Generates a complex-valued pulse with a constant frequency offset.

This function creates a rectangular pulse and modulates it with a complex exponential at a given carrier frequency.

Parameters:

Name	Type	Description	Default
sample_rate	float	The sampling rate in Hz.	required
bw	float	The pulse bandwidth in Hz. The pulse duration is 1/bw.	required
fc	float	The carrier frequency offset in Hz.	required
normalize	bool	If True, the pulse is normalized to have unit energy. Defaults to True.	True

Returns:

Type	Description
tuple[ndarray, ndarray]	tuple[np.ndarray, np.ndarray]: A tuple containing: - t (np.ndarray): Time vector for the pulse in seconds. - mag_c (np.ndarray): The complex-valued samples of the pulse.

Raises:

Type	Description
AssertionError	If the sample rate is below the Nyquist rate (2 * bw).

Source code in src/rad_lab/waveform.py

def complex_tone_pulse(
    sample_rate: float, bw: float, fc: float, normalize: bool = True
) -> tuple[np.ndarray, np.ndarray]:
    """Generates a complex-valued pulse with a constant frequency offset.

    This function creates a rectangular pulse and modulates it with a complex
    exponential at a given carrier frequency.

    Args:
        sample_rate (float): The sampling rate in Hz.
        bw (float): The pulse bandwidth in Hz. The pulse duration is 1/bw.
        fc (float): The carrier frequency offset in Hz.
        normalize (bool, optional): If True, the pulse is normalized to have
            unit energy. Defaults to True.

    Returns:
        tuple[np.ndarray, np.ndarray]: A tuple containing:
            - t (np.ndarray): Time vector for the pulse in seconds.
            - mag_c (np.ndarray): The complex-valued samples of the pulse.

    Raises:
        AssertionError: If the sample rate is below the Nyquist rate (2 * bw).
    """
    t, mag = uncoded_pulse(sample_rate, bw, normalize=normalize)
    mag_c = np.exp(2j * c.PI * fc * t) * mag
    return t, mag_c

lfm_pulse(sample_rate, bw, T, chirp_up_down, normalize=True)

Generates a baseband Linear Frequency Modulated (LFM) pulse (chirp).

The instantaneous frequency of the pulse varies linearly with time over the pulse duration.

Parameters:

Name	Type	Description	Default
sample_rate	float	The sampling rate in Hz.	required
bw	float	The bandwidth of the frequency sweep in Hz.	required
T	float	The total pulse duration in seconds.	required
chirp_up_down	int	Determines the direction of the frequency sweep. 1 for an up-chirp (frequency increases), -1 for a down-chirp (frequency decreases).	required
normalize	bool	If True, the pulse is normalized to have unit energy. Defaults to True.	True

Returns:

Type	Description
tuple[ndarray, ndarray]	tuple[np.ndarray, np.ndarray]: A tuple containing: - t (np.ndarray): Time vector for the pulse in seconds. - mag (np.ndarray): The complex-valued samples of the LFM pulse.

Raises:

Type	Description
AssertionError	If chirp_up_down is not 1 or -1.

Source code in src/rad_lab/waveform.py

def lfm_pulse(
    sample_rate: float, bw: float, T: float, chirp_up_down: int, normalize: bool = True
) -> tuple[np.ndarray, np.ndarray]:
    """Generates a baseband Linear Frequency Modulated (LFM) pulse (chirp).

    The instantaneous frequency of the pulse varies linearly with time over the
    pulse duration.

    Args:
        sample_rate (float): The sampling rate in Hz.
        bw (float): The bandwidth of the frequency sweep in Hz.
        T (float): The total pulse duration in seconds.
        chirp_up_down (int): Determines the direction of the frequency sweep.
            1 for an up-chirp (frequency increases), -1 for a down-chirp
            (frequency decreases).
        normalize (bool, optional): If True, the pulse is normalized to have
            unit energy. Defaults to True.

    Returns:
        tuple[np.ndarray, np.ndarray]: A tuple containing:
            - t (np.ndarray): Time vector for the pulse in seconds.
            - mag (np.ndarray): The complex-valued samples of the LFM pulse.

    Raises:
        AssertionError: If chirp_up_down is not 1 or -1.
    """
    assert chirp_up_down in [1, -1], "chirp_up_down must be either 1 or -1."
    dt = 1 / sample_rate
    t = np.arange(0, T, dt)
    k = bw / T  # Chirp rate
    phase = chirp_up_down * np.pi * k * (t**2) - chirp_up_down * np.pi * bw * t
    mag = np.exp(1j * phase)

    if normalize:
        mag = mag / norm(mag)

    return t, mag

lfm_waveform(bw, T, chirp_up_down)

Returns a WaveformSample for a Linear Frequency Modulated (LFM) pulse.

Parameters:

Name	Type	Description	Default
bw	float	Bandwidth of the frequency sweep in Hz.	required
T	float	Pulse duration in seconds.	required
chirp_up_down	int	1 for up-chirp, -1 for down-chirp.	required

Returns:

Type	Description
WaveformSample	WaveformSample for use with rdm.gen.

Source code in src/rad_lab/waveform.py

def lfm_waveform(bw: float, T: float, chirp_up_down: int) -> WaveformSample:
    """Returns a WaveformSample for a Linear Frequency Modulated (LFM) pulse.

    Args:
        bw: Bandwidth of the frequency sweep in Hz.
        T: Pulse duration in seconds.
        chirp_up_down: 1 for up-chirp, -1 for down-chirp.

    Returns:
        WaveformSample for use with rdm.gen.
    """
    assert chirp_up_down in [1, -1], "chirp_up_down must be 1 (up) or -1 (down)."
    return WaveformSample(
        type=WaveformType.LFM,
        bw=bw,
        time_bw_product=bw * T,
        pulse_width=T,
        pulse_func=partial(lfm_pulse, bw=bw, T=T, chirp_up_down=chirp_up_down),
    )

random_coded_pulse(sample_rate, bw, nchips, normalize=True)

Generates a baseband pulse with a random binary phase code.

The code consists of a sequence of randomly chosen 1s and -1s.

Parameters:

Name	Type	Description	Default
sample_rate	float	The sampling rate in Hz.	required
bw	float	The chip bandwidth in Hz. The chip duration is 1/bw.	required
nchips	int	The number of chips in the random code.	required
normalize	bool	If True, the pulse is normalized to have unit energy. Defaults to True.	True

Returns:

Type	Description
tuple[ndarray, ndarray]	tuple[np.ndarray, np.ndarray]: A tuple containing: - t (np.ndarray): Time vector for the pulse in seconds. - mag (np.ndarray): The real-valued, randomly coded magnitude.

Source code in src/rad_lab/waveform.py

def random_coded_pulse(
    sample_rate: float, bw: float, nchips: int, normalize: bool = True
) -> tuple[np.ndarray, np.ndarray]:
    """Generates a baseband pulse with a random binary phase code.

    The code consists of a sequence of randomly chosen 1s and -1s.

    Args:
        sample_rate (float): The sampling rate in Hz.
        bw (float): The chip bandwidth in Hz. The chip duration is 1/bw.
        nchips (int): The number of chips in the random code.
        normalize (bool, optional): If True, the pulse is normalized to have
            unit energy. Defaults to True.

    Returns:
        tuple[np.ndarray, np.ndarray]: A tuple containing:
            - t (np.ndarray): Time vector for the pulse in seconds.
            - mag (np.ndarray): The real-valued, randomly coded magnitude.
    """
    code_rand = np.random.choice([1, -1], size=nchips)
    return coded_pulse(
        sample_rate,
        bw,
        code_rand,
        normalize=normalize,
    )

random_coded_waveform(bw, nchips)

Returns a WaveformSample for a random binary phase-coded pulse.

Parameters:

Name	Type	Description	Default
bw	float	Chip bandwidth in Hz. Chip duration is 1/bw.	required
nchips	int	Number of chips.	required

Returns:

Type	Description
WaveformSample	WaveformSample for use with rdm.gen.

Source code in src/rad_lab/waveform.py

def random_coded_waveform(bw: float, nchips: int) -> WaveformSample:
    """Returns a WaveformSample for a random binary phase-coded pulse.

    Args:
        bw: Chip bandwidth in Hz. Chip duration is 1/bw.
        nchips: Number of chips.

    Returns:
        WaveformSample for use with rdm.gen.
    """
    return WaveformSample(
        type=WaveformType.RANDOM,
        bw=bw,
        time_bw_product=nchips,
        pulse_width=nchips / bw,
        pulse_func=partial(random_coded_pulse, bw=bw, nchips=nchips),
    )

uncoded_pulse(sample_rate, bw, normalize=True)

Generates a simple, baseband rectangular (uncoded) pulse.

Parameters:

Name	Type	Description	Default
sample_rate	float	The sampling rate in Hz.	required
bw	float	The pulse bandwidth in Hz. The pulse duration is 1/bw.	required
normalize	bool	If True, the pulse is normalized to have unit energy. Defaults to True.	True

Returns:

Type	Description
tuple[ndarray, ndarray]	tuple[np.ndarray, np.ndarray]: A tuple containing: - t (np.ndarray): Time vector for the pulse in seconds. - mag (np.ndarray): The real-valued magnitude of the pulse samples.

Raises:

Type	Description
AssertionError	If the sample rate is below the Nyquist rate (2 * bw).

Source code in src/rad_lab/waveform.py

def uncoded_pulse(
    sample_rate: float, bw: float, normalize: bool = True
) -> tuple[np.ndarray, np.ndarray]:
    """Generates a simple, baseband rectangular (uncoded) pulse.

    Args:
        sample_rate (float): The sampling rate in Hz.
        bw (float): The pulse bandwidth in Hz. The pulse duration is 1/bw.
        normalize (bool, optional): If True, the pulse is normalized to have
            unit energy. Defaults to True.

    Returns:
        tuple[np.ndarray, np.ndarray]: A tuple containing:
            - t (np.ndarray): Time vector for the pulse in seconds.
            - mag (np.ndarray): The real-valued magnitude of the pulse samples.

    Raises:
        AssertionError: If the sample rate is below the Nyquist rate (2 * bw).
    """
    assert sample_rate / bw >= 2, "sample rate must be >= 2 * bw (Nyquist)"

    T = 1 / bw
    dt = 1 / sample_rate
    t = np.arange(0, T, dt)
    mag = np.ones(t.size)

    if normalize:
        mag = mag / norm(mag)

    return t, mag

uncoded_waveform(bw)

Returns a WaveformSample for an uncoded rectangular pulse.

Parameters:

Name	Type	Description	Default
bw	float	Pulse bandwidth in Hz. Pulse duration is 1/bw.	required

Returns:

Type	Description
WaveformSample	WaveformSample for use with rdm.gen.

Source code in src/rad_lab/waveform.py

def uncoded_waveform(bw: float) -> WaveformSample:
    """Returns a WaveformSample for an uncoded rectangular pulse.

    Args:
        bw: Pulse bandwidth in Hz. Pulse duration is 1/bw.

    Returns:
        WaveformSample for use with rdm.gen.
    """
    return WaveformSample(
        type=WaveformType.UNCODED,
        bw=bw,
        time_bw_product=1,
        pulse_width=1 / bw,
        pulse_func=partial(uncoded_pulse, bw=bw),
    )