Digital Signal Processing Reference
In-Depth Information
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Test signal
Momentary CWT
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Momentary Wavelet
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CWT
Kontinuierliche
WaveletTransformation
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Illustration 64:
Continuous Wavelet Transformation as a “3D Landscape” and sonogram
Top picture: The momentary wavelet which “slides along the signal” produces the momentary continuous
wavelet transformation CWT. For physical reasons the time axis of the momentary CWT is displaced
somewhat in comparison with the time axis of of the signal. For this reason the beginning of the noise
signal appears at the end of the CWT.
Centre picture: The entire CWT is shown here in a 3D representation (“scaling time landscape”) with lin-
ear scaling. The enhanced time resolution accompanying the smaller scaling between the individual signal
segments can be seen very clearly.Bottom Illustration: the good time resolution of the high frequencies
contained in the signal and the relatively poor ones in the case of low frequencies can be seen perfectly in
the sonogram with its isometric representation. The V-shaped funnels to the left and right of the caption,
which are difficult to recognise precisely, show the linear increase in the time resolution with higher
frequencies.
