hilbert-toolkit 0.1.4

This package provide several implementations of the discrete Hilbert transform (DHT).

Hilbert - Discrete Hilbert Transform Implementations

Hilbert is a project that will contain numerous implementations of the Hilbert transform for discrete data. This will hopefully enable users to compare different implementation, such as the newly introduced LeDHT (see below).

arXiv manuscript on a learned-matrix approach to the DHT (LeDHT): https://arxiv.org/abs/2204.00666

• Jupyter notebooks to recreate the main and supplemental text figures (and data) are included in the Examples folder

Currently Implemented

• Discrete Fourier Transform-based

  • Henrici [1]

  • Marple (SciPy and MATLAB’s hilbert implementation) [2]

  • Haar wavelet-based (similar to Zhou-Yang [3])

• Learned-matrix approach to the DHT (LeDHT) [4] - Data and code from the arXiv manuscript is available in the Examples folder as a Jupyter Notebook

References

[1]

P. Henrici, Applied and Computational Complex Analysis Vol III (Wiley-Interscience, 1986).

[2]

L. Marple, “Computing the discrete-time “analytic” signal via FFT,” IEEE Trans. Signal Process. 47(9), 2600–2603 (1999).

[3]

C. Zhou, L. Yang, Y. Liu, and Z. Yang, “A novel method for computing the Hilbert transform with Haar multiresolution approximation,” J. Comput. Appl. Math. 223(2), 585–597 (2009).

[4]

C. H. Camp Jr., “Raman Signal Extraction from CARS Spectra Using a Learned-Matrix Representation of the Discrete Hilbert Transform,” arXiv: 2204.00666 (2022).

Coming Soon

• Implementations

  • B-splines implementation (Bilato)

  • Sinc / Whittaker Cardinal

  • and more!

• Documentation

Dependencies

• Python 3.* (Tested on 3.8)

• NumPy (Tested on 1.19)

• SciPy (Tested on 1.5)

• Scikit-learn (Tested on 1.0)

Installation

NOTE: The Examples/ folder (and data) are not included in the pip installation. You will need to download the file from the GitHub repo manually.

Using pip

# If this fails, try hilbert_toolkit
pip install hilbert-toolkit

Using pip (soft install, i.e. can update with git)

# Make new directory for hilbert-toolkit and enter it
# Clone from github
git clone https://github.com/usnistgov/hilbert .

pip install -e .

# To update in the future
git pull

Usage

import numpy as np
import matplotlib.pyplot as plt
from hilbert_toolkit import hilbert_fft_marple as dht
from hilbert_toolkit import hilbert_pad_simple

dht_pad = lambda x: hilbert_pad_simple(x, dht, 1)

n = np.arange(-500,501)

sig_analytical = -2 / (n + 1j*50)
plt.plot(n,sig_analytical.real, label='Real Part')
plt.plot(n,sig_analytical.imag, label='Imag Part')
plt.plot(n,dht(sig_analytical.real), label='DHT{Real Part}')
plt.plot(n,dht_pad(sig_analytical.real), label='DHT-Pad{Real Part}')
plt.legend()
plt.xlabel('n')
plt.ylabel('Amplitude (au)')
plt.show()

Citing This Software

C. H. Camp Jr., “Raman Signal Extraction from CARS Spectra Using a Learned-Matrix Representation of the Discrete Hilbert Transform”, arXiv:2204.00666 (2022).

LICENSE

This software was developed by employees of the National Institute of Standards and Technology (NIST), an agency of the Federal Government. Pursuant to title 17 United States Code Section 105, works of NIST employees are not subject to copyright protection in the United States and are considered to be in the public domain. Permission to freely use, copy, modify, and distribute this software and its documentation without fee is hereby granted, provided that this notice and disclaimer of warranty appears in all copies.

THE SOFTWARE IS PROVIDED ‘AS IS’ WITHOUT ANY WARRANTY OF ANY KIND, EITHER EXPRESSED, IMPLIED, OR STATUTORY, INCLUDING, BUT NOT LIMITED TO, ANY WARRANTY THAT THE SOFTWARE WILL CONFORM TO SPECIFICATIONS, ANY IMPLIED WARRANTIES OF MERCHANTABILITY, FITNESS FOR A PARTICULAR PURPOSE, AND FREEDOM FROM INFRINGEMENT, AND ANY WARRANTY THAT THE DOCUMENTATION WILL CONFORM TO THE SOFTWARE, OR ANY WARRANTY THAT THE SOFTWARE WILL BE ERROR FREE. IN NO EVENT SHALL NIST BE LIABLE FOR ANY DAMAGES, INCLUDING, BUT NOT LIMITED TO, DIRECT, INDIRECT, SPECIAL OR CONSEQUENTIAL DAMAGES, ARISING OUT OF, RESULTING FROM, OR IN ANY WAY CONNECTED WITH THIS SOFTWARE, WHETHER OR NOT BASED UPON WARRANTY, CONTRACT, TORT, OR OTHERWISE, WHETHER OR NOT INJURY WAS SUSTAINED BY PERSONS OR PROPERTY OR OTHERWISE, AND WHETHER OR NOT LOSS WAS SUSTAINED FROM, OR AROSE OUT OF THE RESULTS OF, OR USE OF, THE SOFTWARE OR SERVICES PROVIDED HEREUNDER.

Portions of this package include source code edited from the sklearn’s project template, which requires the following notice(s):

Copyright (c) 2016, Vighnesh Birodkar and scikit-learn-contrib contributors All rights reserved.

THIS SOFTWARE IS PROVIDED BY THE COPYRIGHT HOLDERS AND CONTRIBUTORS “AS IS” AND ANY EXPRESS OR IMPLIED WARRANTIES, INCLUDING, BUT NOT LIMITED TO, THE IMPLIED WARRANTIES OF MERCHANTABILITY AND FITNESS FOR A PARTICULAR PURPOSE ARE DISCLAIMED. IN NO EVENT SHALL THE COPYRIGHT HOLDER OR CONTRIBUTORS BE LIABLE FOR ANY DIRECT, INDIRECT, INCIDENTAL, SPECIAL, EXEMPLARY, OR CONSEQUENTIAL DAMAGES (INCLUDING, BUT NOT LIMITED TO, PROCUREMENT OF SUBSTITUTE GOODS OR SERVICES; LOSS OF USE, DATA, OR PROFITS; OR BUSINESS INTERRUPTION) HOWEVER CAUSED AND ON ANY THEORY OF LIABILITY, WHETHER IN CONTRACT, STRICT LIABILITY, OR TORT (INCLUDING NEGLIGENCE OR OTHERWISE) ARISING IN ANY WAY OUT OF THE USE OF THIS SOFTWARE, EVEN IF ADVISED OF THE POSSIBILITY OF SUCH DAMAGE.

Contact

Charles H Camp Jr: [e-mail]

Contributors

• Charles H Camp Jr