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INTERNATIONAL JOURNAL OF LATEST TECHNOLOGY IN ENGINEERING,
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ISSN 2278-2540 | DOI: 10.51583/IJLTEMAS | Volume XV, Issue V, May 2026
Optimal Choice of mother wavelet for satellite obtained Very Low Frequency radio
wave feature selection
Shivali Verma
Technocrats Institute of Technology, Bhopal -462021, India
DOI: https://doi.org/10.51583/IJLTEMAS.2026.150500226
Received: 27 May 2026; Accepted: 01 June 2026; Published: 18 June 2026
ABSTRACT
Very low frequency (VLF) radio wave signals, frequency range 2 kHz to 20 kHz play imperative role for probing of
ionosphere and magnetosphere. There are three main VLF signals whistlers, chorus and hiss. They all have specific
characteristics with respect time and frequency. Wavelet analysis is a widely used time-frequency analysis method. To
propose a more competent analysis of the VLF signal, the wavelet analysis is deliberated. In wavelet analysis, the best
mother wavelet is chosen for evaluating the signals, as many mother wavelets applied to the signal may yield diverse
results. In this study, we used VLF signals obtained from the DEMETER satellite for wavelet analysis. For the “optimal"
choice of the mother wavelet for such signals, we applied an energy-based quantitative approach at different frequency
levels of VLF signals, which were obtained by Discrete Wavelet Transform (DWT). The results show that Haar and Bior3.5
are the optimum mother wavelets for the analysis of VLF signals.
Keyword Radio wave signals, very low frequency, Mother wavelet
INTRODUCTION
Natural electromagnetic signals, often referred to as "sounds," are detected within the Earth-magnetosphere at Very Low
Frequencies (VLF), ranging from a 2 Hz to 20 Hz. These waves are generated by phenomena such as lightning discharges,
earthquakes, volcanic activity, storms, tornadoes, nuclear explosions, and anthropogenic activities (Barra et al., 2000).
They are significant for subterranean imaging, global communication, and navigation (Cohen et al., 2009). The study of
VLF phenomena has enhanced our understanding of the plasma environment in near-Earth space (Collier 2006). VLF
signals are categorized based on their spectral characteristics (Gallet, 1959), with three primary forms: Whistler, Chorus,
and Hiss emissions (William et al., 1968). These emissions are crucial for several reasons: a) They reveal the properties of
the plasma through which they propagate, serving as effective remote sensing tools. b) Their narrow bandwidth and high
intensity indicate the presence of foreign particles, whose interactions convert the kinetic energy of the charged particles
into coherent electromagnetic radiation. Whistlers are circularly polarized electromagnetic VLF waves generated by
lightning discharge. This energy enters the ionosphere or magnetosphere, where it is guided by the magnetic field lines to
the opposite hemisphere. According to Helliwell (1965), hiss emissions are unstructured and non-dispersive signals
characterized by a broken band of limited signals that produce a hissing sound, with durations ranging from a few
milliseconds to several hours. Chorus emissions are structured and discrete in frequency, typically increasing over time,
known as risers, although they can occasionally decrease, termed falling tones; they may decrease and then increase, known
as hooks, or increase followed by a decrease, termed inverted hooks, or exhibit more complex combinations (Helliwell,
1967; Sazhin and Hayakawa, 1992). Ground-based observations indicate that the typical duration of a chorus event ranges
from 0.5 to 1 h or more (Trakhtengerts, 1999).
Recently, the Wavelet Transform (WT) has emerged in the field of VLF signal processing as an alternative to the well-
known Fourier Transform (FT) and its related transforms. Because VLF signals are inherently non-stationary, wavelet
transformation is particularly suitable for analyzing such signals. Wavelet analysis plays a crucial role, especially in the
automatic detection of these signals through machine learning, which requires precise VLF signal features. This
transformation reveals characteristics hidden within the signal by highlighting changes that occur suddenly and over
extended periods. Therefore, we propose an integrated wavelet-based feature extraction tool for feature extraction. In
wavelet transform, these signals are decomposed into wavelets, meaning that the original function is reconstructed by
adding basic building blocks that maintain a constant shape but vary in size and amplitude. This method allows the design
of a set of basic functions by selecting an appropriate basic wavelet Ψ(t) (mother wavelet) and using its shifted and scaled
versions. A significant challenge in designing a wavelet feature extraction-based VLF recognition system is selecting the
optimal wavelets for these signals, which involves determining the decomposed level within the 1-D wavelet
decomposition (multilevel) and choosing the feature vectors from the wavelet coefficients. The solution to this problem is
revealed in this study.
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2. Selection and Formation of Data Set
The VLF signal dataset used in this study was obtained from the DEMETER. The DEMETER microsatellite was launched
in 2004 to detect electromagnetic emissions transmitted from earthquake regions. The scientific payload of this satellite
comprises several instruments capable of recording continuous data related to electric and magnetic field variations during
its passage over seismically active zones (Parrot et al., 2005). The measurement of plasma waves and energetic particles
is also an asset to the operation of this satellite (Lagoutte et al., 2000). The data from the Instrument Champe Electrique
(ICE) payload onboard the DEMETER satellite were used to estimate the electric fields (Parrot, 2006). In our study, we
observed ICE burst mode signals that computed the waveform of one electric component up to 20kHz(Blecki et al.,2009).
The raw data have been withdrawn from the website http://demeter.cnrs-orleans.fr. For the analysis and visualization of
the DEMTER data, fully interactive software named SAWN (Software for Wave Analysis) was used (Lagoutte &
Latermoliere, 1997). We used 100 variations of VLF signals of each emission (chorus, hiss, and whistler), of 1.5 s with a
sampling frequency (Fs) of 40 kHz.
3. Necessity of Selecting an Appropriate Mother Wavelet
For the extraction of features from the VLF signals, as depicted in Figure 1, we employed the Discrete Wavelet Transform
(DWT) to decompose the signal. DWT was selected for this study because of its suitability for real-time applications. In
essence, the Discrete Wavelet Transform (DWT), which underpins sub-band coding, is recognized for facilitating the rapid
computation of the Wavelet Transform. It is straightforward to implement and minimizes the computational time and
resource requirements. The DWT technique iteratively transforms the signal into multi-resolution subsets of coefficients
using filters with varying cutoff frequencies. Consequently, the signal was processed using both low-pass and high-pass
filters to analyse the low and high frequencies, respectively. The input signal was low-pass filtered to yield the approximate
components and high-pass filtered to provide the detailed components. At the first level (A1 and D1), the outputs from
both filters were down sampled by a factor of 2 to obtain the approximation and detail coefficients. The approximate signal
at each stage was further decomposed using the same low-pass and high-pass filters to determine the approximate and
detailed components for the subsequent stage.
Figure 1 Proposed DWT-Based Feature Extraction and Selection Framework for VLF Signal Analysis
Mallat (1989) introduced the concept of multi-resolution analysis, which is performed using the fast discrete wavelet
transform (DWT). During the multi-resolution decomposition of very low frequency (VLF) signals using DWT, two
fundamental questions arise: i) What is the maximum number of decomposition levels used? ii) Which mother wavelet is
selected for the DWT? The answer to the first question is provided by the MATLAB toolbox, which states that the
maximum decomposition level lmax for a signal is given by:
l
max
=fix(log
2
(n/n
w
-1))
where n denotes the length of the signal, and n
w
indicates the length of the decomposition filter associated with the selected
mother wavelet. However, in practice, the maximum decomposition level for wavelet-based feature extraction is chosen
based on convenience and requirements (Debasis, 2013). In our study, the signal frequency range is 2 kHz to 20 kHz, and
the signal length is 60,000. According to MATLAB's rule, the maximum decomposition level is 13, which is not suitable
for this study. This is because, if dyadic decomposition is applied to the VLF signal under consideration, beyond the third
level of decomposition, the VLF range shifts to the extremely low frequency (ELF) range (2 Hz–2 kHz). This can be
verified by Table 1, which demonstrates the bandwidth of each decomposed level.
S.No
Wavelet Decomposition Level
Frequency Range kHz
1
D1
20-10
2
D2
10-5
3
D3
5-2.5
4
A3
2.5-0
Table 1 Frequency Bands Obtained from DWT Decomposition of VLF Signals (Fs=40 kHz)
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For instance, when the decomposition level is set to four, the Discrete Wavelet Transform (DWT) produces the
reconstructed coefficient subsets at the third-level approximation (A4) and the first to third-level details (D1, D2, D3, and
D4), as illustrated in Figure 2(a), (b), and (c). This analysis indicates that the optimal decomposition level for the Very
Low Frequency (VLF) signal is three. Consequently, in our study, we used three detail coefficients and one approximation
coefficient for feature extraction. The primary objective of this study, which addresses the second question, is discussed
in the following section.
(a)
(b)
(c)
Figure 2. Multiresolution decomposition of VLF emissions using the Discrete Wavelet Transform. The original
signal and reconstructed coefficients corresponding to decomposition levels D1, D2, D3, D4, and A4 are illustrated
for representative (a) Hiss, (b) Chorus, and (c) Whistler waveforms.
4. Selection of an Appropriate Mother Wavelet for VLF Signals
The selection of wavelets is a critical task due to the plethora of wavelet functions available for DWT, characterized by
compact support, orthogonality, and biorthogonality, which influence the low-pass and high-pass analysis and synthesis
filters. Among the available wavelet families are Haar, Daubechies (db), Symlets (sym), Coiflets, BiorSplines (bior),
reverse bior, Meyer, and Dmeyer. The Haar, Daubechies, Symlets, and Coiflets are supported by orthogonal wavelets,
whereas the BiorSplines, reverse bior, Meyer, and Dmeyer wavelets are biorthogonal. Wavelets are selected for specific
applications based on their scaling function and signal analysis capability (Daniel and Akio, 1994). Currently, there is no
definitive method for selecting the mother wavelet. However, researchers have developed two approaches based on
different parameters (Ngui et al., 2013). These approaches are as follows:
1. Qualitative Approaches: These depend on similarity, orthogonality, regularity, and compact support.
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2. Quantitative Approaches: These are based on energy and entropy.
For the "optimal" selection of the mother wavelet, we employ an energy-based quantitative approach due to the imperfect
pairing of filters during the frequency band splitting by DWT (Shukla and Tiwari, 2013). To address this, the energy
distribution of the signal is calculated at each decomposition level. This method was utilized by Morsi and Hawary (2008)
for decomposing electric signals. The wavelet that concentrates energy at a particular level more than others is selected as
the mother wavelet. According to Parseval’s theorem, the energy of the distorted signal can be subdivided at different
resolution levels, which is mathematically defined as follows:
Ed
i
=
Ea
i
=
Where i = 1, ..., l represents the wavelet decomposition level, ranging from the first 1to the l-th level. N indicates the
number of details or approximations at each decomposition level. Edi denotes the energy of the detail at decomposition
level i, while Ea
i
represents the energy of the approximation at decomposition level l. In this study, we compared the
wavelet energy at levels D1 to D3 and A3 using Haar (chosen for its conceptual simplicity), db8, db20 (noted for shape
symmetry with the signal and more vanishing moments), bior3.5, and bior6.8 (biorthogonal wavelets). The average energy
distribution for each decomposition level—D1, D2, D3, and A3—was calculated using 50 sets of signals, obtained
separately from chorus, hiss, and whistler, for the mentioned wavelet families, as depicted in Figure 3(a), (b), and (c). It is
predictable that the energy distribution of the analysed signals varies significantly across different groups of VLF signals.
In each case, we observed that the maximum energy distribution for A3 and D3 is achieved with the bior3.5 wavelet.
Similarly, the maximum energy distribution for D1 is found using the Haar wavelet function. This indicates that bior3.5
and Haar are optimal choices for analysing VLF signals at decomposition levels A3, D3, and D1, respectively. However,
at the D2 level, the bior3.5 wavelet yields the maximum energy distribution for hiss only, while Haar shows the maximum
energy distribution for chorus and whistler. Our analysis of the plot reveals that the energy percentage for chorus and
whistler is significantly lower than that for hiss at the D2 level. Furthermore, there is no substantial difference in energy
between Haar and bior3.5 for hiss at this level. Consequently, Haar is selected as the analysis wavelet for the D2 level.
Thus, we conclude that Haar is the superior choice of mother wavelet for D1 and D2 level decomposition, while bior3.5 is
a reliable choice for decomposing D3 and A3 levels for VLF signals. Therefore, we decompose D1 and D2 levels using
the Haar wavelet (Haar, 1910) and D3 and A3 using bior3.5 (Charles, 1992), as they provide maximum energy distribution
at each decomposition level for VLF signals. After performing DWT, we calculated various audio-frequency parameters
concerning time and frequency for each decomposition level and formed a feature vector. The details of the feature
extraction process are published in https://www.ijsr.net/archive/v5i2/NOV161115.pdf. The feature vector curves, shown
in Figure 4, provide different representations of VLF signals (Verma et al., 2016).
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Figure 3. Energy distribution of DWT sub-bands obtained using different wavelet families (Haar, db8, db20,
sym8, bior3.5, and bior6.8) for representative VLF emissions: (a) Hiss, (b) Chorus, and (c) Whistler.
Figure 4. Distribution of feature vectors derived from the selected wavelet-based features for Chorus, Hiss, and
Whistler emissions. The distinct grouping of data points in the feature space demonstrates the suitability of the
extracted features for automatic classification of VLF signal types (adapted from Verma et al., 2016).
CONCLUSION
In this study, we have demonstrated that the primary challenge in wavelet-based feature extraction lies in selecting the
most suitable mother wavelet. To address this, quantitative approaches have been proposed and applied to VLF signals by
calculating the signal's energy. The paper provides a comprehensive analysis of various mother wavelets for feature
extraction of VLF signals. Different mother wavelets were evaluated to determine the most appropriate one for VLF
signals. The bior3.5 wavelet and Haar wavelet, followed by db8, db20, sym8, and bior6.8, emerged as the most suitable
candidates for VLF signals. These wavelets offer rapid computation of wavelet coefficients and are excellent choices for
feature extraction of VLF signals. Regarding VLF signal classification, the Haar and bior3.5 wavelets proved to be the
most appropriate candidates, as they delivered superior performance for VLF signals.
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ACKNOWLEDGEMENT
I sincerely acknowledge my heartfelt thanks to demeter.cnrs-orleans to provide the data.
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