11.00C.1
Chapter 11.00B
Physical Problem for Fast Fourier Transform
Chemical Engineering
Signal processing (Fast Fourier transforms (FFT), Power spectral density (PSD)) has
emerged as an important tool to provide improved diagnosis of cardiovascular pathologies.
Cardiovascular disorders are the leading causes of death in the United States, requiring an
enhanced diagnosis to facilitate treatment at an early stage.
An ECG (Electrocardiogram),
which is a measure of the electrical conductivity of the heart, provides clinical information
about the health of the heart.
Parameter extraction from the ECG requires its preprocessing
and analysis to obtain features that have prognostic value and provide a heart disease pattern.
In the current problem, we will use FFT and PSD to differentiate ECG signals of normal
subjects from those having ventricular arrhythmias, who eventually had sudden cardiac
arrest.
The ECG signals are obtained from the database collection provided by
http://www.physionet.org/physiobank
.
The FFT of a signal
)
(
n
x
is given by
nw
N
i
N
n
e
n
x
w
F
2
1
0
)
(
)
(
;
1
,...,
2
,
1
,
0
N
w
If the signal is not exactly periodic, which means that the start and end points of the
signal do not lie at the same point of the cycle, the FFT can have nonzero values even at
nonresonant frequencies.
In such a case, sometimes the peaks of the FFT can become
smeared. This is known as leakage and is a very common situation in any measurement.
To
improve the FFT resolution, the signal is multiplied by a window which forces the signal to
become perfectly periodic.
The power spectral density (PSD) of a signal indicates how the power of a signal is
distributed in the frequency domain, i.e., it gives the energy spectrum of the signal.
It is
defined as the squared modulus of the FFT, scaled by the length of the signal.
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 Spring '08
 Kaw,A
 Cardiology, Cardiac arrest, Normal sinus rhythm

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