Int. J. Communications, Network and System Sciences, 2010, 3, 321329
doi:10.4236/ijcns.2010.33041 blished Online March 2010 (
Copyright © 2010 SciRes. IJCNS
Time Domain Signal Analysis Using Wavelet Packet
Decomposition Approach
M. Y. Gokhale1, Daljeet Kaur Khanduja2
1Professor and Head of Department of Mathematics, Maharashtra Institute of Technology, Pune, India
2Assistant Professor Department of Mathematics, Sinhgad Academy of Engineering, Pune, India
Received November 11, 2009; revised December 17, 2009; accepted January 22, 2010
This paper explains a study conducted based on wavelet packet transform techniques. In this paper the key
idea underlying the construction of wavelet packet analysis (WPA) with various wavelet basis sets is elabo-
rated. Since wavelet packet decomposition can provide more precise frequency resolution than wavelet de-
composition the implementation of one dimensional wavelet packet transform and their usefulness in time
signal analysis and synthesis is illustrated. A mother or basis wavelet is first chosen for five wavelet filter
families such as Haar, Daubechies (Db4), Coiflet, Symlet and dmey. The signal is then decomposed to a set
of scaled and translated versions of the mother wavelet also known as time and frequency parameters.
Analysis and synthesis of the time signal is performed around 8 seconds to 25 seconds. This was conducted
to determine the effect of the choice of mother wavelet on the time signals. Results are also prepared for the
comparison of the signal at each decomposition level. The physical changes that are occurred during each
decomposition level can be observed from the results. The results show that wavelet filter with WPA are use-
ful for analysis and synthesis purpose. In terms of signal quality and the time required for the analysis and
synthesis, the Haar wavelet has been seen to be the best mother wavelet. This is taken from the analysis of
the signal to noise ratio (SNR) value which is around 300 dB to 315 dB for the four decomposition levels.
Keywords: WPA, Wavelet Packet Decomposition (WPD), SNR, Haar
1. Introduction
Over the last decade much work has been done in apply-
ing time frequency transforms to the problem of signal
representation and classification. Signals possessing
non-stationary character are not well suited for detection
and classification by traditional Fourier methods. It has
been shown that wavelets can approximate time varying
non-stationary signals in a better way than the Fourier
transform representing the signal on both time and fre-
quency domains [1]. Hence they can easily detect local
features in a signal. Furthermore, wavelet decomposition
allows analyzing a signal at different resolution levels.
The discrete wavelet transform (DWT) provides a very
efficient representation for a broad range of real-world
signals. This property has been exploited to develop
powerful signal de-noising and estimation methods [2]
and extremely low-bit-rate compression algorithms [3].The
discrete wavelet transform (DWT) is usually imple-
mented using an octave-band tree structure. This is ac-
complished by dividing each sequence into a component
containing its approximated version (low-frequency part)
and a component with the residual details (high-frequ-
ency part) and then iterating this procedure at each stage
only on the low-pass branch of the tree [4,5]. The main
drawback of the octave-band tree structure is that it does
not provide a good approximation of the critical subband
decomposition [6]. An alternate means of analysis is
sought, so that valuable time-frequency information is
not lost. The Wavelet Packet Transform (WPT) is one
such time frequency analysis tools. It is a transform that
brings the signal into a domain that contains both time and
frequency information (Wickerhauser, 1991). Thus, analy-
sis of the signal can be done simultaneously in frequency
and time. The most basic way to do time frequency
analysis is by making FFT analysis in short windows.
That has the drawback that the window needs to be short
to find out fast changes in the signal and long to determine
low frequency components. The wavelet packet trans-
form (WPT) offers a great deal of freedom in dealing
with different types of transient signals. Indeed the de-
velopment of the wavelet transform (WT) [79] and
wavelet packets [1012] has sparked considerable activ-
ity in signal representation and in transient and non sta-
tionary signal analysis.[1315].
Wavelet packet decomposition (WPD) (sometimes
known as just wavelet packets) is a wavelet transform
where the signal is passed through more filters than the
DWT. Wavelet packets are the particular linear combina-
tion of wavelets. They form bases which retain many of
the orthogonality, smoothness, and localization proper-
ties of their parent wavelets. The coefficients in the lin-
ear combinations are computed by a recursive algorithm
making each newly computed wavelet packet coefficient
with the result that expansions in wavelet packet bases
have low computational complexity. In the DWT, each
level is calculated by passing the previous approximation
coefficients through high and low pass filters. However,
in the WPD, both the detail and approximation coeffi-
cients are decomposed. For n levels of decomposition the
WPD producesdifferent sets of coefficients (or nodes)
as opposed to (n+1) sets for the DWT. However, due to
the down sampling process the overall number of coeffi-
cients is still the same and there is no redundancy.
The work presented in this paper contributes a new era
in wavelet packet analysis and synthesis of time domain
signals. Wavelet packet transform techniques have been
used to extract feature from time domain signals. Feature
extraction involves information retrieval from the time
signal [16]. The wavelet packet transform has more im-
portant benefits than the discrete wavelet transform.
Wavelet packet functions comprise a rich family of
building block functions. Wavelet packet functions are
still localized in time, but offer more flexibility than
wavelets in representing different types of signals. In
particular, wavelet packets are better at representing sig-
nals that exhibit oscillatory or periodic behavior. Wave-
let packets are organized naturally into collections, and
each collection is an orthogonal basis for
. It is a
simple, but very powerful extension of wavelets and
multiresolution analysis (MRA). The wavelet packets
allow more flexibility in adapting the basis to the fre-
quency contents of a signal and it is easy to develop a
fast wavelet packet transform. The power of wavelet
packet lies in the fact that we have much more freedom
in deciding which basis function is to be used to repre-
sent the given function. It can be computed very fast, it
demands only O (M log M) time, where M is the number
of data points which is important in particular in real time
applications. It also has compact support in time as well as
in frequency domain and adapts its support locally to the
signal which is important in time varying signals. With
wavelet packets we have a much finer resolution of the
signal and a greater variety of options for decomposing
The paper is organized as follows. In Section 2, brief
background information on Discrete Wavelet transform
and wavelet packet decomposition is discussed. In Sec-
tion 3 the present work is explained. The results are
given in Section 4 and Section 5 gives the conclusions.
2. Background
2.1. Discrete Wavelet Transform
The DWT, which is based on subband coding, is found
to yield a fast computation of Wavelet Transform. It is
easy to implement and reduces the computation time and
resources required. In continuous wavelet transform
(CWT), the signals are analyzed using a set of basis
functions which relate to each other by simple scaling
and translation. In the case of DWT, a time scale repre-
sentation of the digital signal is obtained using digital
filtering techniques. The signal to be analyzed is passed
through filters with different cutoff frequencies at dif-
ferent scales. In the discrete wavelet transform, a signal
can be analyzed by passing it through an analysis filter
bank followed by a decimation operation. When a signal
passes through these filters, it is split into two bands. The
low pass filter, which corresponds to an averaging opera-
tion, extracts the coarse information of the signal. The
high pass filter, which corresponds to a differencing op-
eration, extracts the detail information of the signal. The
output of the filtering operations is then decimated by
two. Filters are one of the most widely used signal proc-
essing functions. Wavelets can be realized by iteration of
filters with rescaling. The DWT is computed by succes-
sive low pass and high pass filtering of the discrete
time-domain signal as shown in Figure 1. This is called
the Mallat algorithm or Mallat-tree decomposition.
At each decomposition level, the half band filters
produce signals spanning only half the frequency band.
This doubles the frequency resolution as the uncertainty
in frequency is reduced by half. In accordance with Ny-
quist’s rule if the original signal has a highest frequency
of ω, which requires a sampling frequency of 2ω radians,
then it now has a highest frequency of ω/2 radians. It can
now be sampled at a frequency of ω radians thus dis-
carding half the samples with no loss of information.
This decimation by 2 halves the time resolution as the
entire signal is now represented by only half the number
of samples. Thus, while the half band low pass filtering
removes half of the frequencies and thus halves the
resolution, the decimation by 2 doubles the scale. The
filtering and decimation process is continued until the
desired level is reached. The maximum number of levels
depends on the length of the signal. The DWT of the
original signal is then obtained by concatenating all the
Copyright © 2010 SciRes. IJCNS
Copyright © 2010 SciRes. IJCNS
Figure 1. Level 3 decomposition using wavelet transform.
2, and
2, Z
Vspan tkkZ
Ospan tkk
coefficients, approximation and details, starting from the
last level of decomposition.
2.2. Multiresolution Analysis
it results from Equations (3) and (4) that .
We then find that for every ,
An orthogonal wavelet decomposition of a signal
 
to coefficients
jkj Z
such that
 
- 2
, 2 2
Wx xttk
22, ,
tkkZj j
jjtkk Z
is an orthonormal basis of
2 2
dt (1)
where the function
is usually referred to as a mother
wavelet and stands for the complex conjugation. The
orthonormal wavelet basis
22, ,
may be built from a multiresolution analysis of
In this case, the approximation of the signal at resolution
can be described by the coefficients 2j
The interest in the QMF filters lies in the efficient
computation of the orthogonal wavelet decomposition
via a two channel filter bank structure. The decomposi-
tion which is useful in emphasizing the local features of
a signal, presents however a limitation, namely its non-
variance in time (or space). This implies that the wavelet
coefficients of
, Txt xtR
 
are gener-
ally not delayed versions of .
 
, 22,
xxt tkk
Z (2) 2.3. Wavelet Packet Decomposition
The wavelet packet method is a generalization of wavelet
decomposition that offers a richer range of possibilities
for signal analysis and which allows the best matched
analysis to a signal. It provides level by level transforma-
tion of a signal from the time domain into the frequency
domain. It is calculated using a recursion of filter-decim-
ation operations leading to the decrease in time resolu-
tion and increase in frequency resolution. The frequency
bins, unlike in wavelet transform, are of equal width,
since the WPT divides not only the low, but also the high
frequency subband. In wavelet analysis, a signal is split
into an approximation and a detail coefficient. The ap-
proximation coefficient is then itself split into a sec-
ond-level approximation coefficients and detail coeffi-
cients, and the process is repeated. In wavelet packet
where the function
is the scaling function. The
mother wavelet and the scaling function then satisfy the
so called two-scale equations:
2 -
2 -
Where and
are respectively the im-
pulse response of lowpass and highpass paraunitary
Quadrature mirror filters (QMF) [17]. If we denote the
vector spaces
analysis, the details as well as the approximations can be
split. This yields more than different ways to en-
code the signal. When the WT is generalized to the WPT,
not only can the lowpass filter output be iterated through
further filtering, but the highpass filter can be iterated as
well. This ability to iterate the highpass filter outputs
means that the WPT allows for more than one basis
function (or wavelet packet) at a given scale, versus the
WT which has one basis function at each scale other than
the deepest level, where it has two. The set of wavelet
packets collectively make up the complete family of pos-
sible bases, and many potential bases can be constructed
from them. If only the lowpass filter is iterated, the result
is the wavelet basis. If all lowpass and highpass filters
are iterated, the complete tree basis results. The top level
of the WPD tree is the time representation of the signal.
As each level of the tree is traversed there is an increase
in the trade off between time and frequency resolution.
The bottom level of a fully decomposed tree is the fre-
quency representation of the signal. Figure 2 shows the
level 3 decomposition using wavelet packet transform.
Based on the above analysis, Figure 1 and Figure 2
give the comparison of a three-level wavelet decomposi-
tion and wavelet packet decomposition. It can be seen in
Figure 1 that in wavelet analysis only the approximations
(represented by capital A in the figure) at each resolution
level are decomposed to yield approximation and detail
information (represented by capital D in the figure) at a
higher level. However, in the wavelet packet analysis
[Figure 2], both the approximation and details at a certain
level are further decomposed into the next level, which
means the wavelet packet analysis can provide a more
precise frequency resolution than the wavelet analysis.
The wavelet packet decomposition [4,5,18] is an ex-
tension of the wavelet representation which allows the
best matched analysis to a signal. To define wavelet
packets, we introduce functions of ,
Wt mN
such that
and for all kZ
Wk hWt
21 2
g are the previously de-
fined impulse responses of the QMF filters. If for every
, we define the vector space ,
W t
k Z
then it can be shown that
 
. As a result, if we denote by
P a partition of
into intervals Ij,m = [2-jm,…,2-j(m+1)],
and 0,1,....21
jZ m
, then
jm IP
 
In an equivalent way,
jm IP is an orthonormal basis of
Such a basis is called a wavelet packet. The coefficients
resulting from the decomposition of a signal
tin this
basis are
 
,, 22
jm m
CxxtW tk
By varying the partition P, different choices of wavelet
packets are possible. While a fixed and dyadic parti-
tioning of time frequency domain is imposed in the case
of the wavelet transform, the idea of wavelet packets is
to introduce more flexibility making this partitioning
adaptive to spectral content of the signal.
Figure 2. Level 3 decomposition using wavelet packet transform.
Copyright © 2010 SciRes. IJCNS
In wavelet packet analysis, an entropy-based criterion
is used to select the most suitable decomposition of a
given signal. This means we look at each node of de-
composition tree and quantify the information to be
gained by performing each split [19]. The wavelets have
several families. The most important wavelets families
are Haar, Daubechies, Symlets, Coiflets, and biorthogo-
3. Proposed Work
The block diagram shown in Figure 3 gives the actual
implementation of the method proposed in this paper.
1) Input tim e domain signal
The system described above was simulated on a com-
puter with floating point numbering system. The input
time domain wave is pre-emphasized, low pass filtered
with sampling frequency 8 K to 44.1 KHz range and 1–
10 sec duration samples. The time domain is digitized to
16 bits.
In this block unwanted noise is removed when the
signal gets recorded with the help of various digital filter
such as Low pass filter (LPF) with 3.4 KHz, Notch filter
to remove the line frequency effect i.e. 50 Hz.
Wavelet tr ansforms :
In this block we applied the wavelet filter coefficients
as low and high band and filter the input signal to en-
hance the band energies.
As deals with the multi-rate analysis system the deci-
mation factor helps to enhance the band level informa-
tion from wavelet transform. We consider decimation by
2, 4 etc for our experiments.
Analysi s Subband Feature Vectors:
From the filtering results obtained with the 2 band
system, we have extracted the various features from low
pass and high pass band and then re-arranged with the
desired format for further analysis part.
Interpolation deals with up sampling the inverse wave-
let filtering to reconstruct the original input signal.
Inverse Wavelet transforms:
Analysis of interpolated features is reordered with re-
spect to the 2 bands system to extract the original con-
tents from the feature vector for input signal synthesis
Noise Removal:
Input noisy signal is filtered with band stop filter with
desired cut off frequency. Filtered output is further ap-
plied to post processing.
Post Processing:
Final tuning is done in the post processing block.
2) Testing Setup
Matlab programs were written to implement the struc-
ture shown in Figure 3. Time domain signals in a *.wav
format sampled at 8 KHz were used for all simulations.
Results for different setups are given in the next section.
Several examples of time domain signals of different
sampling frequencies, with five wavelet filter families
are given below.
3) Performance Evaluation
Performance evaluation tests can be done by subjec-
tive quality measures and objective quality measures.
Objective measures provide a measure that can be easily
implemented and reliably reproduced. Objective meas-
ures are based on mathematical comparison of the origi-
nal and processed time domain signals. The majority of
objective quality measures quantify time domain quality
of the signal in terms of a numerical distance measure.
The signal to noise ratio is the most widely used method
to measure time domain signal quality. It is calculated as
the ratio of the signal to noise power in decibels.
 
10 2
10 logˆ
SNR sn sn
where s(n) is the clean time domain signal and ŝ(n) is the
processed time domain signal.
Analysis subband
Wavelet Packet Decimation Preprocessing
Inverse Wavelet
Packet Transform
Filter for noise
Post processing
Time domain
Signal + Noise
An alys is
Figure 3. Block diagram of time domain signal using wavelet packet transform.
opyright © 2010 SciRes. IJCNS
4. Results
We have tested the 10 input samples with sampling fre-
quency of 8 K on various wavelet filtering bank i.e. Haar,
Db4, Symlet, dmey, etc. as shown in Tables 1, 3, 4, 7.
We observe that SNR for wavelet packet analysis and
synthesis after filtering is around 120 dB to 320 dB for
level 1 decomposition, level 2 decomposition 120 dB to
310 dB, level 3 decomposition 115 dB to 310 dB and
level 4 decomposition 115 dB to 305 dB.
From Tables 2, 4, 6, 8 as per timing consideration the
total time for analysis and synthesis is tabulated. We
observe that total time for analysis and synthesis using
wavelet filtering is around 8 sec to 25 sec.
Table 1. SNR calculation for various mother wavelet level 1
Sample Haar Db4 Sym5 dmey Coif5
T1 315.64 244.16 247.86 122.32 165.94
T2 315.58 244.16 247.86 122.28 165.95
T3 315.53 244.16 247.86 122.35 165.94
T4 315.55 244.16 247.86 122.34 165.94
T5 315.55 244.16 247.86 122.34 165.94
T6 315.53 244.16 247.86 122.35 165.94
T7 315.53 244.16 247.86 122.30 165.95
T8 315.53 244.16 247.86 122.35 165.94
T9 315.55 244.17 247.87 122.25 165.95
T10 315.54 244.16 247.86 122.32 165.95
Figure 4. Graphical presentation of SNR for various mo-
ther wavelets.
Table 2. Total time calculation (in seconds) for analysis and
synthesis using wavelet filtering for level 1.
Sample Haar Db4 Sym5 dmey Coif5
T1 8.10 8.31 9.15 9.40 8.96
T2 8.90 10.56 9.17 11.01 9.28
T3 8.53 9.43 9.32 13.45 10.40
T4 8.85 9.34 9.06 12.31 10.20
T5 8.39 9.01 8.59 11.90 9.29
T6 10.73 11.37 12.45 13.10 11.90
T7 11.48 12.03 13.07 13.28 13.18
T8 8.65 9.23 10.46 12.57 9.62
T9 9.59 10.65 10.20 11.40 11.26
T10 9.32 9.64 9.67 13.29 10.11
Table 3. SNR calculation of various mother wavelets for
level 2 decomposition.
SampleHaar Db4 Sym5 dmey Coif5
T1 310.41 232.64 247.31 121.37 165.81
T2 310.41 232.64 247.31 121.34 165.82
T3 310.40 232.64 247.31 121.36 165.81
T4 310.41 232.64 247.31 121.39 165.81
T5 310.38 232.64 247.31 121.36 165.81
T6 310.40 232.64 247.31 121.42 165.81
T7 310.40 232.64 247.31 121.33 165.82
T8 310.39 232.64 247.31 121.42 165.81
T9 310.40 232.65 247.31 121.25 165.82
T10 310.41 232.64 247.31 121.34 165.82
Figure 5. Graphical presentation of SNR for various mo-
ther wavelets.
Table 4. Total time calculation (in seconds) for analysis and
synthesis using wavelet filte r ing for level 2.
SampleHaar Db4 Sym5 dmey Coif5
T1 8.29 8.73 10.11 12.85 9.20
T2 10.10 11.06 11.57 14.64 11.21
T3 9.60 9.56 10.06 12.51 10.43
T4 8.93 10.43 9.48 13.95 11.67
T5 8.42 10.18 8.89 11.92 10.85
T6 11.82 13.51 12.48 15.62 13.00
T7 10.70 12.64 13.11 16.84 13.40
T8 9.45 10.53 9.82 13.28 10.56
T9 9.21 10.09 9.81 12.18 11.04
T10 10.75 10.98 11.09 14.25 10.71
Table 5. SNR calculation of various mother wavelets for
level 3 decomposition.
SampleHaar Db4 Sym5 dmey Coif5
T1 307.15 230.59 241.56 115.85 159.86
T2 307.15 230.60 241.56 115.84 159.86
T3 307.13 230.59 241.56 115.84 159.86
T4 307.12 230.59 241.56 115.86 159.86
T5 307.14 230.59 241.56 115.85 159.86
T6 307.14 230.59 241.56 115.88 159.86
T7 307.16 230.60 241.56 115.83 159.87
T8 307.15 230.59 241.56 115.87 159.87
T9 307.15 230.60 241.57 115.77 159.87
T10 307.14 230.60 241.56 115.83 159.86
Copyright © 2010 SciRes. IJCNS
Figure 6. Graphical presentation of SNR for various Mot-
her wavelets.
Table 6. Total time calculation (in seconds) for analysis and
synthesis using wavelet filtering for level 3.
Sample Haar Db4 Sym5 dmey Coif5
T1 9.45 9.42 9.76 12.46 9.40
T2 10.35 11.70 10.57 15.64 11.01
T3 10.17 11.53 13.28 14.98 12.07
T4 10.11 11.48 12.21 16.54 12.40
T5 10.00 10.89 10.04 12.89 11.57
T6 11.84 13.73 13.21 18.04 14.68
T7 12.65 12.12 12.76 20.37 13.60
T8 10.53 11.20 10.87 15.43 11.86
T9 9.56 10.00 11.59 14.32 11.96
T10 10.32 10.48 11.96 16.68 13.42
Table 7. SNR calculation of various mother wavelets for
level 4 decomposition.
Sample Haar Db4 Sym5 dmey Coif5
T1 304.74 226.62 241.29 115.31 159.79
T2 304.74 226.62 241.29 115.29 159.79
T3 304.74 226.62 241.29 115.33 159.79
T4 304.73 226.62 241.29 115.37 159.79
T5 304.73 226.62 241.29 115.32 159.79
T6 304.73 226.62 241.29 115.37 159.79
T7 304.74 226.62 241.29 115.27 159.80
T8 304.75 226.62 241.29 115.36 159.79
T9 304.74 226.62 241.29 115.21 159.80
T10 304.74 226.62 241.29 115.30 159.80
Figure 7. Graphical presentation of SNR for various Mot-
her wavelets.
Table 8. Total time calculation (in seconds) for analysis and
synthesis using wavelet filtering for level 4.
SampleHaar Db4 Sym5 dmey Coif5
T1 9.95 10.90 10.76 14.92 12.26
T2 12.01 12.59 13.48 19.46 14.84
T3 12.12 12.81 14.79 22.09 12.53
T4 11.03 12.79 11.98 20.34 14.73
T5 11.34 12.37 12.54 16.79 13.09
T6 13.25 15.59 16.37 25.25 19.20
T7 14.51 15.40 17.39 25.89 17.98
T8 11.90 13.14 11.96 19.57 13.15
T9 12.09 13.17 12.51 20.01 15.48
T10 13.09 13.28 14.57 21.75 15.35
From Table 9, entropy which is a common measure of
the efficiency of a signal transform is calculated using
wavelet packet analysis is matched before decomposition
and reconstruction.
In Table 10, Band stop filtered signal is tabulated which
removes the line frequency noise from the signal, it
shows a reasonable SNR of 40–46 dB.
Figure 8 shows the tree diagram associated with a
depth-3 WPT. It reflects the structure of its correspond-
ing hierarchical filter bank, such as the structure shown
in Figure 2. Moving from top to bottom in the diagram
Table 9. Entropy for 4 levels.
T1 21937
T2 32511
T3 29809
T4 34655
T5 29145
T6 49058
T7 51218
T8 32971
T9 34857
T10 37040
Table 10. SNR after removing noise.
T1 44.16
T2 44.41
T3 41.29
T4 44.52
T5 44.47
T6 44.85
T7 44.58
T8 40.39
T9 46.36
T10 41.89
opyright © 2010 SciRes. IJCNS
of Figure 8, frequency is divided into ever smaller seg-
ments. Each line that emanates down and to the left of a
node represents a lowpass filtering operation (h0), and
each line emanating down and to the right a highpass
filtering operation (h1). The nodes that have no further
nodes emanating down from them are referred to as ter-
minal nodes, leaves, or subbands. We refer to the other
nodes as non-terminal, or internal nodes. As such, the
tree node labeling scheme provides a simple mechanism
for indicating the nodes in the tree that we can work with
when imparting modifications on the signal.
For the node (j,k), j denotes the depth within the
transform (tree) and k the position. For example, at node
(0,0) no filtering has taken place, and we simply have the
original sequence of time samples. Lowpass filtering this
will produce node (1,0) and highpass filtering with pro-
duces (1,1). These filtering operations are equivalent to
finding the correlation of the signal with the scaling
function for node (1,0) and the correlation of the signal
with the wavelet function for node (1,1). Going down the
tree to the next depth, we see that (2,0) and (2,1) emanate
from (1,0). From the filter perspective, the samples at
(1,0) are applied to the filters and. Multiresolution is ach-
ieved because the coefficients at (1,0) have been down
sampled by two to achieve critical sampling. From the
wavelet and scaling function perspective, the correlations
between both and the samples of (1,0) are determined
through this operation.
Figure 9 shows how the block diagram wise analysis
and synthesis is carried out.
Figure 8. Wavelet packet tree for level 3 of decomposition.
Figure 9. Input sample: (a) t7.w av; (b) For Haar wave let; (c)
For Db4 wavelet; (d) For Sym5 wavelet; (e) For dmey wave-
let; (f) line freq filter.
Copyright © 2010 SciRes. IJCNS
Please add units to Figure 9(a)-(f)
-time (sec) or (min) or (hour)?
Copyright © 2010 SciRes. IJCNS
5. Conclusions
We have presented a method for analysis and synthesis
of time signals using wavelet packet filtering techniques.
From this study we could understand and experience the
effectiveness of wavelet packet transform in time signal
analysis and synthesis. The performance of wavelet
packet is appreciable while comparing with the discrete
wavelet transform decomposition technique since wave-
let packet analysis can provide a more precise frequency
resolution than the wavelet analysis. It also has compact
support in time as well as in frequency domain and adapts
its support locally to the signal which is important in time
varying signal. With wavelet packets we have a greater
variety of options for decomposing the signal. The
method presented is used for time as well as frequency
analysis of time varying signals. From the results we
conclude that the wavelet filtering find applications in
the time domain analysis and synthesis era. In terms of
signal quality, Haar wavelet has been seen to be the best
mother wavelet. This is taken from the analysis of the
signal to noise ratio (SNR) value around which is quite
satisfactory for time varying signals. The system has
been tested with various sampling frequencies for time
domain samples which gave satisfactory output. Taking
into consideration the signal quality and the time for
analysis and synthesis it can be concluded that Haar
wavelet is the best mother wavelet. Hence we conclude
that the system will behave stable with wavelet packet
filter and can be used for time signal analysis and syn-
thesis purpose.
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