Digital Signal Processing For Biomedical Applications Abhishek Murali School of Electrical Engineering VIT University Vellore – 632014, India Email:… [607826]

Digital Signal Processing For Biomedical
Applications

Abhishek Murali
School of Electrical Engineering
VIT University
Vellore – 632014, India
Email: [anonimizat] H.Bharadwaj
School of Electrical Engineering
VIT University
Vellore – 63201 4, India
Email: [anonimizat]

Abstract— Bio medical signals are of extreme importance and
are of vital importance in the field of medicine. Alexander
Muirhead recorded the first ever biomedical signal in 1872,
which was an Electrocardiogram ( ECG) Signal. Since then, a lot
of research has been done in the field of Biomedical Signal
Processing for tackling of real time problems and extending its
applications. In this paper, we discuss the various techniques that
make biomedical signal processing a bit different. We further
recap some new transforms that solve certain issues, and
improved filter designs specially for these purposes.
Index Terms—Transformations, Filtering, Time Complexity
I. INTRODUCTION
Signal processing is a broad topic consisting of analysis of
signals to retrieve useful information from them. The focus of
this paper is to compare the various forms of digital signal
processing techniques used with respect to bio medical
signals. Most practical signals are of analog time dependent
nature which is difficult to gather information about the signal.
The aim of processing these signals is to obtain useful data
such as an encoded message, identifying abnormalities in data,
compression of data and in communication systems which is
harder i n time dependent systems.
Digital signal processing involves multiple stages having
various techniques each with their own advantages and
applications. Signals are first classified on various parameters
so that the ideal method can be chosen. Signals the n need to
be transformed into the required coordinate system. Finally
modulation, filtering, feature extraction and spectral analysis
are performed as required by the application.
This paper investigates transformations of common
biomedical signals such as Electroencephalogram (EEG) and
heart rate. It also explains the time complexity of various
filtering algorithms and their memory requirements to find the
optimum algorithm for the required application.
II. COMPARISON
Electroencephalogram (EEG) signals are o ne of the most
common bio medical signals which require processing. Many
transformation methods exist to extract the features of an EEG
signals [1] such as Fast Fourier Transform (FFT), Wavelet
Transform, Eigenvectors, Time -Frequency Distributions and
Autoregressive method. FFT is a good tool for stationary
narrowband signal and so doesn’t perform well with EEG signals which include localized peaks and is not stationary.
Eigenvector in general is a very strong method used with noisy
signals. There are many types of methods which utilize
eigenvectors such as Pisarenko’s method, MU SIC method and
minimum norm method. Time frequency distribution is a
composite method which allows the signals analysis in both
time and frequency domain allowing the use of window
functions and continuous signal analysis. On the other hand it
is a very sl ow method and is not tolerant to noise. Each of
these methods has a specific advantage and provides certain
level of detail. Thus the required method has to be chosen
based on the signal and application.
Another widely used transformation technique is the discrete
wavelet transform (DWT) to obtain the signal in wavelet
domain with different coefficient values. It is useful to extract
detailed features of a signal and is shown to be effective in
obtaining statistical readings for heart rate variability [2]. In
DWT, the given signal is passed through both high pass as
well as a low pass filter. The samples are sub samples and
passed through their respective filters again as many times as
required to obtain different levels of decomposition. Using
DWT features of the HRV such as energy, entropy , kurtosis
and skewness were extracted. It was shown that DWT of heart
rate variability can be used to detect diabetes.
One of the main concerns regarding the processing of
biomedical signals in their analogous nature when recorded.
Hence, sampling is an i mportant necessity. However, with the
evolution of wearable sensor systems in biomedical domain
such as the pacemaker, battery run time is an important
consideration. Normally, upto four times the signal frequency
is used as sampling frequency to keep sign al quality high and
also as a precaution. As shown in [3], one argument to keep
sampling rate high is to make sure all frequencies in the digital
signal are accounted. Further, without knowledge of the
purpose for which the sensor is being designed, and the
bandwidth properties, a proper sampling rate cannot be chosen.
As a precaution, 4 times the sampling rate is used.
Furthermore, the transition band, where the filter begins to
suppress the desired frequencies but not the aliasing
frequencies can be sol ves using high sampling rate. Phase
distortion is also removed by the high sampling rate. However,
a large number of samples means more RAM and ROM
allocation and a decreased battery life. In Biomedical Signal

Processing, Static RAM is a very rar e resource . The
Bachmann -Ladau Notation was used to determine
computational complexity and its re lation with energy
consumption wa s also shown by the authors [3]. An FIR Filter
shows an O(N2) complexity with N being the sampling rate.
Likewise, various complexities are listed in Table 1.
Table 1:Time Complexities of various algorithms

Algorithm

Complexity

IIR Filter
O(R)

Averaging Filter
O(R2)

Adaptive FIR with LMS
O(R2)

PID Controller
O(R)

STFT with constant Δt
O(R*log 2R)
Lookup Table
O(R)

It can be concluded that the algorithm selected must grow
at O(R) rate to achieve an equilibrium between signal quality
and optimized usage of SRAM
Determining the frequency content in the signal is o f utmost
importance for filtering applications etc. The Fast Fourier
Transform (FFT) is still widely used for this purpose. However,
this only gives a global spectrum and doesn’t contain any
temporal information. [4] This is solved by usage of the Short
Time Fourier Transform (STFT) which uses a moving window
over which F ourier Transform is computed to give the local
spectra. The Window used commonly is the Gaussian Window.
Window length must be chosen carefully to avoid poor time
resolution and poor frequency resolution. In order to resolve
this, an S transform (ST) is us ed which is derived from the
STFT where the window length depends upon the frequency.
However, the ST is very computationally intensive and even
for small sample signals, takes longer time than the STFT. It is
thus not useful in time sensitive biomedical a pplications. Like
the Fast Fourier Transform, a Fast S Transform is also
developed but the calculations are still intensive and introduce
error that cannot be neglected. A Discrete Orthonormal S
Transform is a fast algorithm but uses a sinc window, which i s
also not fast generally. A typical fast S transform can be given
by equation 1.

Equation 1: S Transform When applied with 2 times oversampling and using band
pass filters with pre -calculated windows gives a time
complexity O( Nlog 2N) which when compared to the normal S
transform having O(N2log 2N) and Discrete Orthonormal S
Transform having O(N2) shows that the time complexity is
greatly reduced. This fast S Transform(FST) combined with
the improved algorithm can be used in time critical
applications such as acute stroke treatment, and in the analysis
of 3D MRI, digital X -ray, ECG and EEG signals.
Another reason the Fourier Transform doesn’t solve all
issues is that it maps a time series or function into a frequency
spectrum. Whi le maintain perfect frequency information, it
doesn’t provide any time information. This means that there is
no information on when these frequenci es appear in a given
signal. [5] This is again only useful in the in stationary signals
and cannot provide localized time information. Time
frequency is of paramount importance in analysis of non –
stationary signals where spectral properties change with time.
It is importa nt for the time frequency techniques to detect
different components (P and T waves and importantly, the
QRS complex) to get proper diagnostics. The STFT is a
popular technique for non -stationary signals, using a window
which moves with time. When sufficien tly narrow, it can be
seen as a stationary signal over which FT can be applied.
Results obtained show that the time frequency analysis
describes how a heart beats: normal people with have a
smooth profile with moderate frequency, and with the same
smooth profile but with high frequency. However, a patient
suffering from arrhythmia will show roughness with different
frequencies. Time frequency analysis detection of arrhythmia
can be done by using the frequency information in QRS
complex chunk, and variatio ns in its magnitude.
Kalman filtering is a widely used technique for a variety of
applications. It’s a robust technique which is used to remove
statistical noise by conducting successive measurements over
time and estimates the error. It finds application in camera
based photoplethysmography [6] which is a noninvasive
technique used to measure heart rate. A rough estimate of heart
rate was made using FFT and an autoregressive model was
implemented within a Kalman filter framework to improve the
SNR and reliability of the signal. Kalman filter has the ability
to track short -time stationary signals as well as real time
capabilities.
III. CONCLUSION
Digital Signa l Processing for Bio medical application is a
well-established field with a lot of available techniques. The
most important aspects of digital signal processing in
biomedical applications involve the transformation and filtering
of signals into the require d domain. This can be achieved using
the techniques discussed in this paper such as Fast Fourier
Transform (FFT), Wavelet Transform, Eigenvectors, Time –
Frequency Distributions and Autoregressive method. Design
and computational complexity of filters such a s IIR, averaging,
adaptive and kalman filters were discussed. There is a lot of
scope for improvement in the existing algorithms with respect
to accuracy and memory requirement and continuous research

in this field is required to improve the quality of bio medical
systems.

IV. REFERENCES
[1] A. S. Al -Fahoum and A. A. Al -Fraihat, “Methods of
EEG Signal Features Extraction Using Linear
Analysis in Frequency and Time -Frequency
Domains,” ISRN Neurosci. , vol. 2014, pp. 1–7, 2014.
[2] U. Rajendra Acharya, K. S. Vidya, D. N. Ghista, W. J.
E. Lim, F. Molinari, and M. Sankaranarayanan,
“Computer -aided diagnosis of diabetic subjects by
heart rate variability signals using discrete wavelet
transform method,” Knowledge -Based Sy st., vol. 81,
pp. 56 –64, 2015.
[3] A. Tobola et al. , “Sampling rate impact on energy
consumption of biomedical signal processing
systems,” 2015 IEEE 12th Int. Conf. Wearable
Implant. Body Sens. Networks , pp. 1 –6, 2015.
[4] R. a Brown and R. Frayne, “A fast discrete S –
transform for biomedical signal processing.,” Conf.
Proc. IEEE Eng. Med. Biol. Soc. , vol. 2008, pp. 2586 –
2589, 2008.
[5] A. Dliou, E. Nationale, and E. Nationale, “Arrhythmia
ECG Signal Analysis using Non Parametric Time –
Frequency Techniques,” vol. 41, no. 4, pp. 25 –30,
2012.
[6] F. Andreotti, A. Trumpp, H. Malberg, and S.
Zaunseder, “Improved heart rate detection for camera –
based photoplethysmography by means of Kalman
filtering,” 2015 IEEE 35th Int. Conf. Electron.
Nanotechnology, ELNANO 2015 – Conf. Proc. , pp.
428–433, 2015.