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and Section 3 presents the fundamental theory de-
scribing the model, which is used as the main ap-
proach for the realization of the proposed system.
Section 4 introduces the methods used for the design
of experiments and simulations used throughout the
paper. Section 5 deals with the system simulation and
discusses the dynamics of the presented algorithm.
Section 6 discusses the overall system efficiency and
derives the parameters for an optimum noise reduc-
tion. Section 7 introduces the realized hardware and
Section 8 concludes the paper.
2 RELATED WORK
There have recently been many attempts to remove
random noise from various types of signals using sta-
tistical inference methods mostly based on wavelet
statistical models and Bayesian estimation, (Sameni
et al., 2007). A survey of theoretical and practi-
cal aspects of hardware implementation of wavelet–
based denoising filters is presented in (Gavrincea
et al., 2007). Traditional filter implementations deal
with cutting of unwanted frequency components, typ-
ically using low–pass, high–pass, or band–pass filter-
ing configurations. Since the frequency range of ran-
dom noise covers the entire frequency bandwidth of
the processed signal, using the conventional pass/cut–
based filtering method will also cut and distort the de-
sired signal while processing. The signal averaging
technique is an ideal solution to this essential prob-
lem, which recovers signal while quickly averaging
out random noise components.
The recursive semi-digital signal averaging
(RSDA) technique presented here bears also some
limitations compared to non–recursive or finite im-
pulse response (FIR) filters. Mainly, it can introduce
phase shifts cause also bandwidth limitations due to
the existence of feedback structures. This charac-
teristic can limit its applicability to measurements
involving very high frequency signal reconstruction
tasks. On the other hand, a non–recursive filter will
generally use more memory and CPU resources
for its applications, which makes its use difficult
in real–time applications, and more costly as well.
Though most medical signal measurements operate
with narrow–band signals, narrow–band filtering is
not considered by RSDA, however, (Choi and Cho,
2002) proposes a useful algorithm for the suppression
of narrow-band interference in direct sequence spread
spectrum systems, based on the open–loop adaptive
IIR notch filtering.
The application of signal averaging techniques
are relatively old but steadily shows up in different
applications, algorithms, and modifications. For
example, as early as, (Bogdanov, 1997) has presented
a comparison of discrete and continuous average
techniques applied to multi–component force trans-
ducers. Most statistical algorithms are CPU–intensive
and require more memory usage. An algorithm for
robust weighted averaging with automatic adjustment
of insensitivity parameter is introduced in (Leski and
Gacek, 2004), where also the ensemble averaging
and weighted averaging techniques are discussed in
some context. The weighted signal averaging method
(Laciar and Jane, 2001), different from the sample–
based averaging presented here, is also sensitive to
the presence of outliers in the measurement data,
however, it has to perform intensive computations
in order to estimate the noise variance in all signal
cycles.
Adaptive filtering, which has been a popu-
lar research field for decades, is suitable for the
reconstruction of periodic signals with very low
frequencies. Though its efficiency is mainly based on
the recursive estimation of error–free denoising and
signal tracking parameters (Tichavsky and Handel,
1995), an adaptive filter can be effective for batch
processing, but relatively inefficient in real–time
applications compared to the semi–digital averager
presented here.
Often, adaptive filtering gives good performance
in low–amplitude signal measurements, e.g., an
adaptive scheme for ECG enhancement is presented
in (Almenar and Albiol, 1999). Influence of low
frequency noise in adaptive estimation using the
LMS algorithm is discussed in (Brito et al., 2009).
A relatively computation–intensive approach is pre-
sented in (Laguna et al., 1992). A noise–constrained
least mean fourth adaptive algorithm focusing on the
learning speed of the adaptive algorithm is discussed
in a newer work (Zerguine et al., 2011). Approaches
given in (Momot, 2009) deals with a comprehensive
study of weighted averaging of electrocardiogram
(ECG), which applies Bayesian inference to the
analysis of filter performance. Regarding the
electrocardiography, an alternative noise reduction
algorithm used for rhythmic and multitrial biosignals
is presented in (Celka et al., 2008).
Wavelet–based denoising using (soft) thresh-
olding involves several steps (Donoho, 1995); (1)
performing a linear forward wavelet transform of the
noisy data, (2) obtaining and performing a soft thresh-
olding of the wavelet coefficients where the threshold
depends on the noise variance, and (3) the coefficients
obtained from step (2) are then used to obtain the
signal estimate for the reconstruction of the signal
(linear inverse wavelet transform). Obviously, this
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