Single channel (univariate) signal - Practical Biomedical Signal Analysis Using MATLAB - page 55

FIGURE 2.16: Illustration of a spectrogram construction. STFT is used to com-
pute the spectrum of a short windowed fragment of the signal. The consecutive spec-
tra are presented as a gray-scale time-frequency map. From the bottom: signal of
increasing frequency, spectra in perspective, time-frequency representation.

Please note that Ψ t , a conserves the overall shape of Ψ, in the sense of number of
zero-crossings, however it is dilated or contracted. The wavelet Ψ should have the
zero mean value. If for scale a 0 1 the wavelet is concentrated in frequency around

f 0 , we can bind the scale and frequency by:

=

f 0
a

f a = (2.93)

The CWT can be interpreted as decomposition of the signal into the time-
frequency atoms, obtained through projection of the signal on the set of waveforms
derived from a single wavelet Ψ by time translations and scaling. In this sense the
CWT is very similar to STFT (2.81), the main difference being that the window
length changes with the scale (or due to (2.93) with the frequency). This property
results in different compromise between the time and frequency resolutions in dif-
ferent frequency bands, i.e., the frequency resolution is fine at low frequencies at the