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Julia code for the time-frequency analysis

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[![Licence](http://img.shields.io/badge/license-GPLv2-blue.svg?style=flat)](http://www.gnu.org/licenses/gpl-2.0.html)
[![arXiv](http://img.shields.io/badge/arXiv-1603.02898-green.svg?style=flat)](http://arxiv.org/abs/1603.02898)
[![arXiv](http://img.shields.io/badge/arXiv-1810.00334-green.svg?style=flat)](http://arxiv.org/abs/1810.00334)
[![ascl](http://img.shields.io/badge/ascl-1702.003-red.svg?style=flat)](http://ascl.net/1702.003)

Julia codes for time-frequency analysis. I started to import the Wigner distribution, the pseudo-Wigner distribution, and the short-time Fourier transform from MATLAB GPL programs, tftb-0.2 and modified them and added other techniques. Regarding tftb, visit http://tftb.nongnu.org/. The modification and new additions include the zero-padding FFT, the non-uniform FFT, the adaptive algorithm by Stankovic, Dakovic, Thayaparan 2013, the S-method, the L-Wigner distribution, the polynomial Wigner-Ville distribution, extraction of instantaneous frequency, mode tracking, time-frequency distributions of the Stokes parameters for the spectrogram, the Wigner-Ville distribution, the S-method. Juwvid was initially developed for the paper on a characterization method of Earth-like exoplanets, [Kawahara (2016)](http://arxiv.org/abs/1603.02898) (TFA in general). It was extended for the paper on the gravitational wave of core-collapse supernovae [Kawahara et al. (2018)](http://arxiv.org/abs/1810.00334) (polarization and IF tracking). If you want to refer juwvid, consider citing those papers because the detailed description is given in them, depending on topics though. Recently, Julia 1.0 was released. I plan to update juwvid to match Julia 1.0. Until this, use Julia 0.6. Sorry for the inconvenience.

## Current Stable Version

[Juwvid 0.6](https://github.com/HajimeKawahara/juwvid/releases/tag/v0.6)

## Gallery

Visit [wiki](https://github.com/HajimeKawahara/juwvid/wiki) for various samples

## Available

- Wigner-Ville distribution w/ NUFFT
- Cross Wigner-Ville distribution w/ NUFFT
- Pseudo Wigner-Ville distribution w/ zero-padding FFT and NUFFT and Adaptive Algorithm
- Short-time Fourier Transform w/ NUFFT
- S-method w/ NUFFT
- L-Wigner distribution w/ NUFFT
- polynomial Wigner-Ville distribution w/ NUFFT
- Stokes parameters for the Short-time Fourier Transform (spoectrogram-type Stokes)
- Stokes parameters for the Wigner-Ville distribution
- Stokes parameters for the pseudo Wigner-Ville distribution
- Stokes parameters for the S-method (S-type Stokes)

## Requirements and Install

- Julia v0.6 (VERSION<0.6 does not work now.)

#### Julia Packages

- DSP
- PyPlot
- Distributions, IJulia (just for tutorials)

To install, use Pkg.add in the julia console, such as

```
Pkg.add("DSP")
```

Set JULIA_LOAD_PATH as 
```
setenv JULIA_LOAD_PATH /Users/kawahara/juwvid
```
for csh/tcsh or 
```
export JULIA_LOAD_PATH=/Users/kawahara/juwvid
```
for bash.

#### Julia Bindings of non-uniform FFT (NUFFT)

Juwvid has the Julia bindings of parts of [CMCL/NUFFT](http://www.cims.nyu.edu/cmcl/nufft/nufft.html) version 1.3.3 (but currently only for nufft1d2). The original Fortran code of NUFFT is from [CMCL/NUFFT](http://www.cims.nyu.edu/cmcl/nufft/nufft.html). The source files in the nufft_src directory are BSD licensed, and the Julia bindings are GPLv2.

Edit Makefile and type

```
make
```

to generate a shared library file, libnufft.so. Change the path of ccall in jnufft.jl.

#### Features

- Various TFDs
- Dense frequency sampling using NUFFT
- Thinning out the time grid for large dataset
- TFDs for polarization

## Tutorials

See ipython notebooks in the ipynb directory.

- Wigner Ville Distribution with FFT, zero-padding FFT, and NUFFT.ipynb
- Pseudo Wigner Ville Distribution for the nonlinear IF using FFT and NUFFT.ipynb
- Adaptive algorithm for window selection of the pseudo WV.ipynb
- S-Method.ipynb
- S-Method with NuFFT.ipynb
- L-Wigner Distribution and Polynomial Wigner Ville Distribution.ipynb
- Polynomial Wigner Ville distribution with NuFFT.ipynb
- Stokes Distribution.ipynb
- Application to LIGO data.ipynb

#### References 
- Cohen, L. 1995, Time-Frequency Analysis (PTR-PH)
- Stankovic, L., Dakovi ́c, M., & Thayaparan, T. 2013, Time-frequency signal analysis with applications (Artech House)
- Boashash, B. 2015, Time-Frequency Signal Analysis and Processing, 2nd Edition A Comprehensive Reference (Elsevier)
- Kawahara, H. 2016, Frequency Modulation of Directly Imaged Exoplanets: Geometric Effect as a Probe of Planetary Obliquity, ApJ 822, 112 
- Kawahara, H. et al. 2018, A Linear and Quadratic Time-Frequency Analysis of Gravitational Waves from Core-Collapse Supernovae, accepted for publication in ApJ

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