Single channel (univariate) signal - Practical Biomedical Signal Analysis Using MATLAB - page 63

2.4.2.2.8 Comparison of time-frequency methods The complex character of
biomedical signals and their importance in health research and clinical practice
brought a wide variety of signal analysis methods into applications in biomedical
research. The most widespread are the spectral methods which make possible the
identification of the basic rhythms present in the signal. Conventional methods of
the analysis assumed stationarity of the signal, in spite of the fact that interesting
processes are often reflected in fast dynamic changes of signal. This implied the
application to the analysis of the signals methods operating in time-frequency space.
The available time-frequency methods can be roughly divided into two categories:

• Those that give directly continuous estimators of energy density in the time-

frequency space

• Those that decompose the signal into components localized in the time-

frequency space, which can be described by sets of parameters, and at the sec-
ond step the components can be used to create the estimators of time-frequency
energy density distribution

An example of time-frequency energy distribution obtained by means of different
methods is shown in Figure 2.21.
In the first category—the Cohen's class of time-frequency distributions—one ob-
tains directly the time-frequency estimators of energy density without decomposing
the signal into some predefined set of simple elements. This allows for maximal flex-
ibility in expressing the time frequency content of the signal. However, there are two
consequences:

• The first consequence is the lack of parametric description of the signals struc-

tures

• The second consequence is that, no matter how much the signal structures are

separated in time or frequency, they interfere and produce cross-terms.

The problem of compromise between time and frequency resolution manifests when
one selects the proper filter kernel to suppress the cross-terms.
In the second category the most natural transition from spectral analysis to the
analysis in time-frequency space is the use of short time Fourier transform (STFT)
and a representation of energy density derived from it—the spectrogram. The pos-
itive properties of this approach are the speed of computations and the time and
frequency shift invariance, which makes the interpretation of the resulting time-
frequency energy density maps easy to interpret. The main drawbacks are: (1) the
apriorifixed compromise between time and frequency resolution in the whole time-
frequency space, which results in smearing the time-frequency representation, (2)
the presence of cross-terms between the neighboring time-frequency structures.
Another common choice in the second category is the CWT. From the practical
point of view the main difference from the STFT relies on another compromise be-
tween the time and frequency resolution. In case of CWT, one sacrifices the time
resolution for the better frequency resolution of low frequency components and vice