dct-toolkit 0.5.0

DCT/FFT-based convolutional statistics for Cartesian and polar data

DCT-Toolkit: Convolutional Statistics

dct_toolkit provides DCT-based smoothing and normalized-convolution statistics for data with gaps. The current publication-prep track is intentionally focused on the convolution/statistics surface.

Current Scope (Stats-First)

• DCT-based smoothing for 1D/N-D Cartesian data.
• Polar smoothing with adaptive azimuth kernels.
• Reflective boundaries via DCT and periodic azimuth boundaries via real FFT.
• Robust local statistics (dct_mean, dct_variance, dct_std, dct_count) with NaN support.

Installation

pip

pip install .

When the package is published on PyPI, installation will be:

pip install dct-toolkit

from source

git clone <your-repo-url>
cd dct_toolkit
pip install .

conda (planned)

Conda-forge packaging is in preparation. Until the feedstock is published, you can install with pip inside a conda environment.

conda create -n dct-toolkit python=3.11 -y
conda activate dct-toolkit
pip install dct-toolkit

Quick Start

1) Robust Mean with Missing Data

import numpy as np
import dct_toolkit as dct

data = np.sin(np.linspace(0, 10, 200))
data[70:110] = np.nan

mu = dct.dct_mean(data, width=10.0)

1b) Prefill Before Full-Field Smoothing

prefilled = dct.dct_prefill(data, width=10.0, max_iter=3)
smoothed = dct.dct_smooth(prefilled, width=10.0)

2) Polar Smoothing with Periodic Azimuth

smoothed = dct.dct_smooth(
    radar_data,
    width=5.0,
    coordinates="polar",
    az_boundary="periodic",
    az_res_deg=1.0,
)

3) Local Variability Estimates

var = dct.dct_variance(data, width=10.0)
std = dct.dct_std(data, width=10.0)

Public API (Top Level)

• dct_smooth
• dct_count
• dct_mean
• dct_prefill
• dct_variance
• dct_std
• smooth_cartesian
• smooth_polar
• get_dct_transfer_function
• dct_convolve_1d

Notes on Gap Filling

Gap-filling methods remain in the repository for internal research, but they are de-scoped from the top-level public API for the initial convolution/statistics release.

Documentation

• docs/MATHEMATICAL_BASIS.md
• docs/API_REFERENCE.md

License

MIT. See LICENSE.