Skip to content

discrete_wavelet

Bases: object

Base class for discrete wavelet functions.

This class provides a framework for implementing various discrete wavelet functions with scaling and translation parameters.

Attributes:

Name Type Description
name str

The name of the wavelet.
a float

The scaling parameter, must be > 1.
b float

The translation parameter, must be > 0.

Methods:

Name Description
psi

Abstract method for wavelet function definition.
forward

Apply the wavelet transformation to the input signal.
__call__

Perform wavelet transformation via call.
Source code in tinybig/koala/signal_processing/wavelet.py 
 16
 17
 18
 19
 20
 21
 22
 23
 24
 25
 26
 27
 28
 29
 30
 31
 32
 33
 34
 35
 36
 37
 38
 39
 40
 41
 42
 43
 44
 45
 46
 47
 48
 49
 50
 51
 52
 53
 54
 55
 56
 57
 58
 59
 60
 61
 62
 63
 64
 65
 66
 67
 68
 69
 70
 71
 72
 73
 74
 75
 76
 77
 78
 79
 80
 81
 82
 83
 84
 85
 86
 87
 88
 89
 90
 91
 92
 93
 94
 95
 96
 97
 98
 99
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
class discrete_wavelet(object):
    """
    Base class for discrete wavelet functions.

    This class provides a framework for implementing various discrete wavelet functions with scaling and translation parameters.

    Attributes
    ----------
    name : str
        The name of the wavelet.
    a : float
        The scaling parameter, must be > 1.
    b : float
        The translation parameter, must be > 0.

    Methods
    -------
    psi(tau: torch.Tensor)
        Abstract method for wavelet function definition.
    forward(x: torch.Tensor, s: int, t: int)
        Apply the wavelet transformation to the input signal.
    __call__(x: torch.Tensor, s: int, t: int)
        Perform wavelet transformation via call.
    """
    def __init__(self, name: str = 'discrete_wavelet', a: float = 1.0, b: float = 1.0, *args, **kwargs):
        """
        Initialize the discrete wavelet class.

        Parameters
        ----------
        name : str, optional
            Name of the wavelet. Default is 'discrete_wavelet'.
        a : float, optional
            Scaling parameter. Must be > 1. Default is 1.0.
        b : float, optional
            Translation parameter. Must be > 0. Default is 1.0.
        *args, **kwargs
            Additional parameters.
        """
        if a < 1 or b < 0:
            raise ValueError('a must be > 1 and b mush > 0...')

        self.name = name
        self.a = a
        self.b = b

    @abstractmethod
    def psi(self, tau: torch.Tensor):
        """
        Abstract method for wavelet function definition.

        Parameters
        ----------
        tau : torch.Tensor
            Transformed input values.

        Returns
        -------
        torch.Tensor
            Wavelet values for the input.
        """
        pass

    def forward(self, x: torch.Tensor, s: int, t: int):
        """
        Apply the wavelet transformation to the input signal.

        Parameters
        ----------
        x : torch.Tensor
            Input signal.
        s : int
            Scaling factor.
        t : int
            Translation factor.

        Returns
        -------
        torch.Tensor
            Transformed signal.
        """
        tau = x/(self.a**s) - t*self.b
        return 1.0/math.sqrt(self.a**s) * self.psi(tau=tau)

    def __call__(self, x: torch.Tensor, s: int, t: int):
        """
        Perform wavelet transformation via call.

        Parameters
        ----------
        x : torch.Tensor
            Input signal.
        s : int
            Scaling factor.
        t : int
            Translation factor.

        Returns
        -------
        torch.Tensor
            Transformed signal.
        """
        return self.forward(x=x, s=s, t=t)

__call__(x, s, t)

Perform wavelet transformation via call.

Parameters:

Name Type Description Default
x Tensor

Input signal.

 required
s int

Scaling factor.

 required
t int

Translation factor.

 required

Returns:

Type Description
Tensor

Transformed signal.
Source code in tinybig/koala/signal_processing/wavelet.py 
100
101
102
103
104
105
106
107
108
109
110
111
112
113
114
115
116
117
118
def __call__(self, x: torch.Tensor, s: int, t: int):
    """
    Perform wavelet transformation via call.

    Parameters
    ----------
    x : torch.Tensor
        Input signal.
    s : int
        Scaling factor.
    t : int
        Translation factor.

    Returns
    -------
    torch.Tensor
        Transformed signal.
    """
    return self.forward(x=x, s=s, t=t)

__init__(name='discrete_wavelet', a=1.0, b=1.0, *args, **kwargs)

Initialize the discrete wavelet class.

Parameters:

Name Type Description Default
name str

Name of the wavelet. Default is 'discrete_wavelet'.

 'discrete_wavelet'
a float

Scaling parameter. Must be > 1. Default is 1.0.

 1.0
b float

Translation parameter. Must be > 0. Default is 1.0.

 1.0
*args

Additional parameters.

 ()
**kwargs

Additional parameters.

 ()
Source code in tinybig/koala/signal_processing/wavelet.py 
40
41
42
43
44
45
46
47
48
49
50
51
52
53
54
55
56
57
58
59
60
def __init__(self, name: str = 'discrete_wavelet', a: float = 1.0, b: float = 1.0, *args, **kwargs):
    """
    Initialize the discrete wavelet class.

    Parameters
    ----------
    name : str, optional
        Name of the wavelet. Default is 'discrete_wavelet'.
    a : float, optional
        Scaling parameter. Must be > 1. Default is 1.0.
    b : float, optional
        Translation parameter. Must be > 0. Default is 1.0.
    *args, **kwargs
        Additional parameters.
    """
    if a < 1 or b < 0:
        raise ValueError('a must be > 1 and b mush > 0...')

    self.name = name
    self.a = a
    self.b = b

forward(x, s, t)

Apply the wavelet transformation to the input signal.

Parameters:

Name Type Description Default
x Tensor

Input signal.

 required
s int

Scaling factor.

 required
t int

Translation factor.

 required

Returns:

Type Description
Tensor

Transformed signal.
Source code in tinybig/koala/signal_processing/wavelet.py 
79
80
81
82
83
84
85
86
87
88
89
90
91
92
93
94
95
96
97
98
def forward(self, x: torch.Tensor, s: int, t: int):
    """
    Apply the wavelet transformation to the input signal.

    Parameters
    ----------
    x : torch.Tensor
        Input signal.
    s : int
        Scaling factor.
    t : int
        Translation factor.

    Returns
    -------
    torch.Tensor
        Transformed signal.
    """
    tau = x/(self.a**s) - t*self.b
    return 1.0/math.sqrt(self.a**s) * self.psi(tau=tau)

psi(tau) abstractmethod

Abstract method for wavelet function definition.

Parameters:

Name Type Description Default
tau Tensor

Transformed input values.

 required

Returns:

Type Description
Tensor

Wavelet values for the input.
Source code in tinybig/koala/signal_processing/wavelet.py 
62
63
64
65
66
67
68
69
70
71
72
73
74
75
76
77
@abstractmethod
def psi(self, tau: torch.Tensor):
    """
    Abstract method for wavelet function definition.

    Parameters
    ----------
    tau : torch.Tensor
        Transformed input values.

    Returns
    -------
    torch.Tensor
        Wavelet values for the input.
    """
    pass