Single channel (univariate) signal - Practical Biomedical Signal Analysis Using MATLAB - page 64

FIGURE 2.21: Comparison of energy density in the time-frequency plane ob-
tained by different estimators for a signal e): a) spectrogram, b) discrete wavelet
transform, c) Choi-Williams transform, d) continuous wavelets, f) matching pursuit.
Construction of the simulated signal shown in (e), the signal consisting of: a sinusoid,
two Gabor functions with the same frequency but different time positions, a Gabor
function with frequency higher than the previous pair, an impulse. From [Blinowska
et al., 2004b].
versa for higher frequency components; also the change of the frequency of a struc-
ture leads to the change of the frequency resolution.
STFT and CWT can be considered as atomic representations of the signal, and as
such give a certain parametric description of the signals. However, the representation
in not sparse; in other words there are too many parameters; hence they are not very
informative.
The sparse representation of the signal is provided by DWT and MP, which leads to
efficient parameterization of the time series. The DWT can decompose the signal into
a base of functions, that is a set of waveforms that has no redundancy. There are fast
algorithms to compute the DWT. Similar to CWT, the DWT has poor time resolution
for low frequencies and poor frequency resolution for high frequencies. The DWT
is very useful in signal denoising or signal compression applications. The lack of
redundancy has a consequence in the loss of time and frequency shift invariance.
DWT may be appropriate for time-locked phenomena, but much less for transients
appearing in time at random, since parameters describing a given structure depend