Mathematical Implementation of Hybrid Fast Fourier Transform and Discrete Wavelet Transform for Developing Graphical User Interface Using Visual Basic for Signal Processing Applications

Abstract

In recent years, the application of discrete wavelet transform (DWT) on biosignal processing has made a significant impact on developing several applications. However, the existing user-friendly software based on graphical user interfaces (GUI) does not allow the freedom of saving the wavelet coefficients in .txt or .xls format and to analyze the frequency spectrum of wavelet coefficients at any desired wavelet decomposition level. This work describes the development of mathematical models for the implementation of DWT in a GUI environment. This proposed software based on GUI is developed under the visual basic (VB) platform. As a preliminary tool, the end user can perform "j" level of decomposition on a given input signal using the three most popular wavelet functions — Daubechies, Symlet, and Coiflet over "n" order. The end user can save the output of wavelet coefficients either in .txt or .xls file format for any further investigations. In addition, the users can gain insight into the most dominating frequency component of any given wavelet decomposition level through fast Fourier transform (FFT). This feature is highly essential in signal processing applications for the in-depth analysis on input signal components. Hence, this GUI has the hybrid features of FFT with DWT to derive the frequency spectrum of any level of wavelet coefficient. The novel feature of this software becomes more evident for any signal processing application. The proposed software is tested with three physiological signal — electroencephalogram (EEG), electrocardiogram (ECG), and electromyogram (EMG) — samples. Two statistical features such as mean and energy of wavelet coefficient are used as a performance measure for validating the proposed software over conventional software. The results of proposed software is compared and analyzed with MATLAB wavelet toolbox for performance verification. As a result, the proposed software gives the same results as the conventional toolbox and allows more freedom to the end user to investigate the input signal.

The Best Artificial Neural Network Parameters for Electroencephalogram Classification Based on Discrete Wavelet Transform

“…In this study, DWPT was used to obtain 4 frequency bands of cA7, cD5, cD6, and cD7 levels. The basic relation between the sampling frequency (Fs) of input signal and frequency range of sub bands at any decomposition level (b) was [0−(Fs/2 b+1 )] for approximation coefficient and [(Fs/2 b+1 )−(Fs/2 b )] for detailed coefficients [28]. In this study, the signal was decomposed into a coarse estimate and data feature The assortment of appropriate number of wavelet and decomposition level chosen were 5, 6 and 7, where the frequency ranging from 0 -65 Hz was imperative for the examination.…”

Wavelet Packet Transform Based Driver Distraction Level Classification Using EEG

“…In future, we aim to analyze the significance of PSD through DWPT alone for distraction levels classification. The mathematical derivation of the approximation coefficients (CA 0 , CA 1 , and CA ) is by taking the samples of the input signal and extend it to * = + 2( − 2) + , as is a constant which is equal to 0 for even or 1 for odd [25]. This extension is highly needed to make matching between the numbers of input samples with the wavelet filter coefficients, and this thing should be applied on each input to any level.…”