The purpose of this software is to provide an educational tool for discrete 1D wavelet transform and its application in the field of digital signal processing. It aims to clearly explain how the wavelet transform works, and uncover the ideas that this transformation offers. The software was designed and developed as a practical part of Peter Nováčik’s bachelor thesis.
The application demonstrates wavelet transform applied to 1D signal. The input signal can be selected and afterwards displayed in the application’s GUI (see Fig.1). It is then transformed and the coefficients of the transformed signal are also displayed. Optionally these coefficients can be modified by the user. Finally, inverse transform is applied on the transformed image and output image is obtained. If the coefficients were not changed, the output image is the same as the input image.
Fig. 1: GUI of the application WTutor1d. It shows input (original) signal, transformed signal (coefficients) and output (modified) signal.
The application provides several tools to demonstrate properties and usefulness of wavelet transform. User can select level of detail, that is number of decomposition level of the wavelet transform, and also family of wavelet filters that are used in the transform (see Fig.2).
Fig. 2: GUI controls provide options to select level of detail and filters to use in the wavelet transform.
It is possible to change the input signal by moving with the sample points in the signal. The coefficients of the transformed signal can be also modified just by dragging them up or down. The corresponding changes in the output signal, that is produced by the inverse transform of the coefficients, are recomputed and visualized immediately.
WTutor1d runs on Microsoft Windows 10 operating system. The application (WTutor1d version 2.0.1 - released in April 2018) can be downloaded here.