Kernel Functions

This library supports two primary ways to define spectral graph filters: pre-defined analytical filters and fully custom filters using Vector Fitting.

Analytical Filters

For common signal processing tasks, three analytical filters are provided as methods on the convolution context.

lowpass(X, scales): Smooths the signal by attenuating high-frequency components.
bandpass(X, scales): Isolates components within a specific frequency band.
highpass(X, scales): Emphasizes sharp transitions by attenuating low-frequency components.

The scales parameter is a list of floating-point values that control the cutoff frequencies of the filters. Larger scales correspond to lower frequencies.

from sgwt import Convolve, impulse
from sgwt import DELAY_TEXAS as L

X = impulse(L, n=600)
scales = [0.1, 1.0, 10.0]

with Convolve(L) as conv:
    # Returns a list of filtered signals, one for each scale
    Y_lp = conv.lowpass(X, scales)
    Y_bp = conv.bandpass(X, scales)
    Y_hp = conv.highpass(X, scales)

Custom Kernels via Vector Fitting

For advanced use cases, you can define arbitrary filter shapes using the VFKernel class. This approach uses a rational approximation (poles and residues) to model the desired frequency response, a technique known as Vector Fitting.

The library includes several pre-computed kernels. You can use them by passing the kernel object to convolve().

from sgwt import Convolve, impulse, VFKernel
from sgwt import DELAY_USA as L
from sgwt import MODIFIED_MORLET

# Load a pre-computed Vector Fitting kernel
K = VFKernel.from_dict(MODIFIED_MORLET)
X = impulse(L, n=35000)

with Convolve(L) as conv:
    # Apply the custom kernel
    Y = conv.convolve(X, K)

This powerful feature allows you to implement specialized filters, such as the Modified Morlet wavelet used in the Vector Fitting Kernels example.