Signals

The primary input for all filtering operations is a signal defined on the vertices of the graph. This signal should be provided as a NumPy array.

Format and Memory Layout

The signal array X can be either:

• 1D: Shape (n_vertices,) for a single signal

• 2D: Shape (n_vertices, n_timesteps) for multiple signals

where n_vertices is the number of vertices (nodes) in the graph, matching L.shape[0], and n_timesteps is the number of independent signals or time samples to be processed concurrently.

When a 1D signal is passed, the output will also be 1D (squeezed accordingly).

For optimal performance with 2D signals, it is highly recommended to create the signal array with column-major (Fortran) ordering by specifying order='F'. This memory layout aligns with the underlying C-based CHOLMOD library, avoiding costly data re-ordering during computation.

import numpy as np
from sgwt import DELAY_USA as L

n_vertices = L.shape[0]

# 1D signal (single signal)
X_1d = np.random.randn(n_vertices)

# 2D signal (multiple signals)
n_signals = 10
X_2d = np.random.randn(n_vertices, n_signals).astype(np.float64)
X_2d = np.asfortranarray(X_2d)

# Verify the memory order for 2D
assert X_2d.flags['F_CONTIGUOUS']

See also

Graph Laplacian

For the definition of vertex-domain functions.

Creating Test Signals with impulse

For testing and examples, the library provides the impulse() helper function to quickly generate a Dirac impulse (a value of 1 at one vertex and 0 everywhere else).

from sgwt import impulse
from sgwt import DELAY_TEXAS as L

# Create a signal with a single impulse at vertex 600
X_impulse = impulse(L, n=600)

print(X_impulse.shape)
# Output: (2000, 1)