njit-etd2003-081 - New Jersey Institute of Technology

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where c is a constant. Thus, the bandwidths of the analysis windows are spread
logarithmically with respect to frequency, instead of linearly as with the STFT. This is
illustrated in Figure 3.4.
Figure 3.4 Division of the frequency domain for the STFT and the WT.
What ensures is that the time resolution At becomes arbitrarily good at high
frequencies, and the frequency resolution Af becomes arbitrarily good at low
frequencies. For this reason, wavelet analysis is more effective than Fourier analysis
when the signal of interest is dominated by transient behavior or discontinuities.
Figure 3.5 displays a wavelet function ψ(t)and its dilations for different values
of parameter "a" in the right column along with their short time Fourier transform
equivalent counterpart in the left column. This figure helps to visualize the timefrequency
plane and emphasizes the band pass nature of ψ(t) and its dilations. The
STFT gives fixed resolution (for a given window size), whereas the WT gives variable
resolution, which results in higher frequencies better resolved in time and lower