By J. Eells
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Extra resources for Complex Analysis. Proc. Summer School, Trieste, 1980
Wavelet Transforms in Image Processing 29 struction. It then shows how this leads to a number of commonly used wavelets, and discusses their lack of shift invariance. 3 introduces our complex wavelet transform (CWT), designed to overcome this problem, and describes some important features when the CWT is extended to two dimensions, in particular the directional selectivity of the 2-D filters. 4 briefly describes how we have applied the CWT to motion estimation and de-noising and gives some results from this work.
20). Within 1. 9. 5 f-··· ;. 2 : ; ... f· ·· ·- ·· · ········· ····· 1\ \ ! 3 .. · ! J. 10. Cross-sections through the mesh diagram of wavelet amplitude (upper graph) and differential phase (lower graph) for a constant amplitude harmonic of fixed frequency 18 David E. ; NO =32768 "iii "5 a. 5 time I seconds; sampling freq. ::::,_j 10 ~ 20 window min. J 20 40 60 window max. 11. Six notes of a hymn tune played on the oboe stop of a pipe organ: time history (top view), frequency composition (below), transform windows (below), and specimen analysing wavelet (bottom view) this band, which straddles the center frequency w0 , it varies linearly with frequency n.
One end was tapped lightly in a direction perpendicular to the flat side of the beam. The hammer had a soft tip designed so that only low frequency vibrations were generated (up to about 1 kHz). An accelerometer attached to the beam close to the point of impact measured beam response and this data was captured by a data logger. The sampling frequency was 4096 Hz and so the Nyquist frequency was 2048Hz. This signal, a short length of which is reproduced in Fig. 4, is interesting because it disguises the passage backwards and forwards along the beam of bending waves of different frequencies.
Complex Analysis. Proc. Summer School, Trieste, 1980 by J. Eells