Getting Started

In this section we will provide a condensed overview of the package. In order to keep this overview concise, we will not discuss any background information or theory here in detail.


To install AutocorrelationShell.jl, start up Julia and type the following code-snipped into the REPL. It makes use of the native Julia package manger.


Additionally, for example if you encounter any sudden issues, or in the case you would like to contribute to the package, you can manually choose to be on the latest (untagged) version.



1D Autocorrelation Wavelet Transform

The following code snippet shows how to obtain the autocorrelation wavelet decomposition of a 1D signal.

using AutocorrelationShell, Wavelets, Plots

H = wavelet(WT.db2)
L = 2
Q = qfilter(H)
P = pfilter(H)

x = zeros(256)
x[128] = 1

decomposition = acwt(x, L=2, P=P, Q=Q)

wiggle(decomposition, Overlap = false)

2D Autocorrelation Wavelet Transform

acwt2D(x; L_row, L_col, P, Q)

The acwt2D function performs a forward wavelet transformation on 2D signals such as images. It returns a 4 dimensional tensor with the dimensions (numrow, numcol, levelsofdecomprow, levelsofdecompcol).


The iacwt2D function is the inverse function of acwt2D. It takes the output of acwt2D(i.e. the wavelet coefficient matrix) and reconstructs the original signal.

The following code snippet shows how to obtain the autocorrelation wavelet decomposition of an image.

H = wavelet(WT.db2)
Q = qfilter(H)
P = pfilter(H)

img = load(../test/pictures/boat.jpg)
img = Float64.(Gray.(img))

decomposition = acwt2D(img, L_row=2, L_col=2, P=P, Q=Q)

# Display the 6th row and column decomposition

# Revert to original signal
reconstruct = iacwt2D(decomposition)

1D Autocorrelation Wavelet Packet Transform

acwpt(x, P, Q)

The acwpt function computes the autocorrelation wavelet packet transform for 1 dimensional signal. It returns a binary tree object where the root node contains the original signal, and each child node contains a vector of 1 dimensional autocorrelation wavelet transform coefficients.

The following code snippet shows how to obtain the autocorrelation wavelet packet transformation of a 1D signal.

using Random, Wavelets, AbstractTrees
rng = MersenneTwister(123);

X₁ = randn(rng, 4); # length 4 random signal
H = wavelet(WT.db2);
Q = qfilter(H);
P = pfilter(H);
decomp = acwpt(X₁, P, Q)

# Print the tree in the console

# Gather all nodes into a vector

Getting Help

To get help on specific functionality you can either look up the information here, or if you prefer you can make use of Julia's native doc-system.

If you encounter a bug or would like to participate in the development of this package come find us on GitHub.