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21: Wavelet
3. “Frequency scale factor” text box. Allows you to determine the width of the
wavelets by specifying a fixed ratio between the center frequency [implicitly defined
in the “frequency step” text box (2)] and the wavelet width. The user must make a
tradeoff between frequency and temporal resolution when specifying the fsf value.
4. Sum of power. Displays the sum of power of the wavelets.
5. Sum-of-power graph. Plots the sum of power over the wavelets in the frequency
domain, which enables you to determine if the fsf and frequency step are
appropriately defined for the frequency range. The graph should be flat over the
frequency range of interest.
6. Window Type checkbox and controls. These controls taper the data, smoothing the
discontinuities at the ends of a segment before wavelet analysis is performed.
Following are descriptions of the window types and the Taper Length text box:
• Parzen: a weighted moving-average transformation that smooths the power
values for each frequency by assigning the greatest weight to the observation
being smoothed in the center of the window, and increasingly smaller weights
to values that are farther away from the center.
• Cosinus: sums individual terms to form the window, so that the low-frequency
peaks in the frequency domain combine in such a way as to decrease sidelobe
height. This has the side effect of increasing the mainlobe width.
• Taper Length text box: allows you to specify the amount of data to taper on the
ends of the segment, in terms of seconds. The maximum tapering amount is
one-half the total segment length. If the value entered into this text box is too
large, the Wavelet tool automatically reduces the tapering amount to the
maximum. Figure 21-6 shows how the taper length affects the window shape.
Parzen window
if taper length ≥ one-half segment length
Cosinus window
if taper length ≥ one-half segment length
if taper length = one-fourth segment length
if taper length = one-fourth segment length
Figure 21-6. Effect of the taper length on the shape of the Parzen and Cosinus window
198 Net Station Waveform Tools Technical Manual S-MAN-200-WFTR-001 • December 21, 2006