Wavelet Packets¶

New in version 0.2.

Version 0.2 of PyWavelets includes many new features and improvements. One of such new feature is a two-dimensional wavelet packet transform structure that is almost completely sharing programming interface with the one-dimensional tree structure.

In order to achieve this simplification, a new inheritance scheme was used in which a BaseNode base node class is a superclass for both Node and Node2D node classes.

The node classes are used as data wrappers and can be organized in trees (binary trees for 1D transform case and quad-trees for the 2D one). They are also superclasses to the WaveletPacket class and WaveletPacket2D class that are used as the decomposition tree roots and contain a couple additional methods.

The below diagram illustrates the inheritance tree:

BaseNode - common interface for 1D and 2D nodes:

Node - data carrier node in a 1D decomposition tree

WaveletPacket - 1D decomposition tree root node

Node2D - data carrier node in a 2D decomposition tree

WaveletPacket2D - 2D decomposition tree root node

BaseNode - a common interface of WaveletPacket and WaveletPacket2D¶

class pywt.BaseNode¶

class pywt.Node(BaseNode)¶

class pywt.WaveletPacket(Node)¶

class pywt.Node2D(BaseNode)¶

class pywt.WaveletPacket2D(Node2D)¶

Note

The BaseNode is a base class for Node and Node2D. It should not be used directly unless creating a new transformation type. It is included here to document the common interface of 1D and 2D node an wavelet packet transform classes.

__init__(parent, data, node_name)¶

Parameters:

parent – parent node. If parent is None then the node is considered detached.
data – data associated with the node. 1D or 2D numeric array, depending on the transform type.
node_name – a name identifying the coefficients type. See Node.node_name and Node2D.node_name for information on the accepted subnodes names.

data¶: Data associated with the node. 1D or 2D numeric array (depends on the transform type).

parent¶: Parent node. Used in tree navigation. None for root node.

wavelet¶: Wavelet used for decomposition and reconstruction. Inherited from parent node.

mode¶: Signal extension mode for the dwt() (dwt2()) and idwt() (idwt2()) decomposition and reconstruction functions. Inherited from parent node.

level¶: Decomposition level of the current node. 0 for root (original data), 1 for the first decomposition level, etc.

path¶: Path string defining position of the node in the decomposition tree.

node_name¶

Node name describing data coefficients type of the current subnode.

See Node.node_name and Node2D.node_name.

maxlevel¶: Maximum allowed level of decomposition. Evaluated from parent or child nodes.

is_empty¶: Checks if data attribute is None.

has_any_subnode¶: Checks if node has any subnodes (is not a leaf node).

decompose()¶: Performs Discrete Wavelet Transform on the data and returns transform coefficients.

reconstruct([update=False])¶

Performs Inverse Discrete Wavelet Transform on subnodes coefficients and returns reconstructed data for the current level.

Parameters:: update – If set, the data attribute will be updated with the reconstructed value.

Note

Descends to subnodes and recursively calls reconstruct() on them.

get_subnode(part[, decompose=True])¶

Returns subnode or None (see decomposition flag description).

Parameters:

part – Subnode name
decompose – If True and subnode does not exist, it will be created using coefficients from the DWT decomposition of the current node.

__getitem__(path)¶

Used to access nodes in the decomposition tree by string path.

Parameters:: path – Path string composed from valid node names. See Node.node_name and Node2D.node_name for node naming convention.

Similar to get_subnode() method with decompose=True, but can access nodes on any level in the decomposition tree.

If node does not exist yet, it will be created by decomposition of its parent node.

__setitem__(path, data)¶

Used to set node or node’s data in the decomposition tree. Nodes are identified by string path.

Parameters:

path – Path string composed from valid node names. See Node.node_name and Node2D.node_name for node naming convention.
data – numeric array or BaseNode subclass.

__delitem__(path)¶

Used to delete node from the decomposition tree.

Parameters:: path – Path string composed from valid node names. See Node.node_name and Node2D.node_name for node naming convention.

get_leaf_nodes([decompose=False])¶

Traverses through the decomposition tree and collects leaf nodes (nodes without any subnodes).

Parameters:: decompose – If decompose is True, the method will try to decompose the tree up to the maximum level.

walk(self, func[, args=()[, kwargs={}[, decompose=True]]])¶

Traverses the decomposition tree and calls func(node, *args, **kwargs) on every node. If func returns True, descending to subnodes will continue.

Parameters:

func –
callable accepting BaseNode as the first param and optional positional and keyword arguments:
```
func(node, *args, **kwargs)
```
decompose – If decompose is True (default), the method will also try to decompose the tree up to the maximum level.

Args:

arguments to pass to the func

Kwargs:

keyword arguments to pass to the func

walk_depth(self, func[, args=()[, kwargs={}[, decompose=False]]])¶

Similar to walk() but traverses the tree in depth-first order.

Parameters:

func –
callable accepting BaseNode as the first param and optional positional and keyword arguments:
```
func(node, *args, **kwargs)
```
decompose – If decompose is True, the method will also try to decompose the tree up to the maximum level.

Args:

arguments to pass to the func

Kwargs:

keyword arguments to pass to the func

WaveletPacket and WaveletPacket tree Node¶

class pywt.Node(BaseNode)¶

class pywt.WaveletPacket(Node)¶

node_name¶

Node name describing data coefficients type of the current subnode.

For WaveletPacket case it is just as in dwt():

a - approximation coefficients
d - details coefficients

decompose()¶

WaveletPacket2D and WaveletPacket2D tree Node2D¶

class pywt.Node2D(BaseNode)¶

class pywt.WaveletPacket2D(Node2D)¶

node_name¶

For WaveletPacket2D case it is just as in dwt2():

a - approximation coefficients (LL)
h - horizontal detail coefficients (LH)
v - vertical detail coefficients (HL)
d - diagonal detail coefficients (HH)

decompose()¶: See also

dwt2() for 2D Discrete Wavelet Transform output coefficients.

expand_2d_path(self, path):

class pywt.WaveletPacket2D(Node2D)¶

__init__(data, wavelet[, mode='symmetric'[, maxlevel=None]])¶

Parameters:

data – data associated with the node. 2D numeric array.
wavelet – Wavelet to use in the transform. This can be a name of the wavelet from the wavelist() list or a Wavelet object instance.
mode – Signal extension mode for the dwt() and idwt() decomposition and reconstruction functions.
maxlevel – Maximum allowed level of decomposition. If not specified it will be calculated based on the wavelet and data length using pywt.dwt_max_level().

get_level(level[, order="natural"[, decompose=True]])¶

Collects nodes from the given level of decomposition.

Parameters:

level – Specifies decomposition level from which the nodes will be collected.
order – Specifies nodes order - natural (natural) or frequency (freq).
decompose – If set then the method will try to decompose the data up to the specified level.

If nodes at the given level are missing (i.e. the tree is partially decomposed) and the decompose is set to False, only existing nodes will be returned.

Wavelet Packets¶

BaseNode - a common interface of WaveletPacket and WaveletPacket2D¶

WaveletPacket and WaveletPacket tree Node¶

WaveletPacket2D and WaveletPacket2D tree Node2D¶

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