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Ναθαναήλ Στεφανόπουλος
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20 1.8 Paul Mother Wavelet Real Part Imaginary Part Magnitude.6.4 Amplitude t

21 .8.6 Real Part of Three Scaled Wavelets a = 1 a = 5 a = Imaginary Part of Three Scaled Wavelets a = 1 a = 5 a = Magnitude.2.2 Magnitude Time Time

23 .4 Fourier Transform of Paul Wavelet (m=1) Amplitude Frequency

24 .8 Real Part Half Interval Sampled 1.2 Imaginary Part Half Interval Sampled Amplitude 2T ml Amplitude T ml Time (sec) Time (sec)

27 .5 2T ml 2T sp t

33 WW * /a ln a Time (sec.)

34 1 2 Scale where WW * /a is maximized vs. Frequency (Hz) actual calculated scale (a) Input signal (Hz)

36 .8 Real part of Paul Wavelet used as input plotted with peak scaled wavelet Input Signal Peak scaled wavelet Amplitude Time (sec.)

37 .2 Imaginary part of Paul Wavelet used as input plotted with peak scaled wavelet.2 Input Signal Peak scaled wavelet Amplitude Time (sec.)

38 .7 Gaussian Test Function.6.5 Amplitude Time (sec.)

39 W Paul Wavelet ln a Time (sec.)

.7 Gaussian Test Function.6.5 Amplitude.4.3.2.

40 .7 Gaussian Test Function.6.5 Amplitude Time W Paul wavelet ln a Time (sec.)

42 W Paul Wavelet ln a Time (sec.) 1.5

44 1.8 (mother) Paul wavelet with T c marked Real Part Imaginary Part Magnitude.6.4 Amplitude t (nondimensional)

47 1.8 Mother Morlet Wavelet Real Part Imaginary Part Magnitude Amplitude Nondimensional Time

48 1.8 Real Part T c Sampling Points.6 T c.4.2 Amplitude T Nondimensional Time

51 15 Velocity data with mean = 1 5 Velocity (m/s) Time (sec.) 2 Pressure C p Time(sec.)

15 Windowed velocity data with mean = 1 5 Velocity (m/s) 5 1 15 35 4 45 5 55 6 65 Time (sec.

53 15 Windowed velocity data with mean = 1 5 Velocity (m/s) Time (sec.) Wavelet Transform Magnitude ln a Time (sec.)

6 Wavelet Transform Magnitude 6 5 5 4 4 ln a 3 3 2 2 1 1 1 2 3 4 5 6 7 8 Time (sec.

54 6 Wavelet Transform Magnitude ln a Time (sec.) Windowed velocity data with mean = and real scaled Morlet wavelet (a=221) 1 Windowed Signal Scaled Wavelet 5 Velocity (m/s) Time (sec.)

W velocity Paul ln a 5 4.5 4 3.5 3 2.5 2 1.5 1.

55 W velocity Paul ln a Time (sec.) W Paul Wavelet ln a Time (sec.)

56 15 Windowed velocity data with mean = and real scaled Paul wavelet (a=55) Windowed Signal Scaled Wavelet 1 5 Velocity (m/s) Time (sec.)

57 1 Windowed pressure data with mean = 1 2 C p Time sec.

6 Wavelet Transform Magnitude 4 5 4 35 3 25 ln a 3 2 2 1 15 1 5 1 2 3 4 5 6 7 8 Time

58 6 Wavelet Transform Magnitude ln a Time (sec.) 6 Wavelet Transform Magnitude ln a Time (sec.)

59 Windowed Pressure Data mean = & Peak Scale Real Part Morlet Wavelet a=221 Windowed Signal Scaled Wavelet 4 2 C p Time (Sec.)

60 W Paul Wavelet ln a Time (sec.)

61 W Paul Wavelet ln a Time (sec.) 5 Windowed Pressure Data; mean = & Imaginary Part of Paul Scaled Wavelet a = Windowed Signal Scaled Wavelet 2 C p Time (sec.)

64 35 3 Sensativity to window width, Velocity data Paul Wavelet Morlet Wavelet 25 Event Duration (sec.) σ = window width σ ( t = 1)

65 4 35 Paul Wavelet Morlet Wavelet Sensativity to window width, Pressure data 3 Event Duration (sec.) σ = window width σ ( t = 1) Close up of event and two Paul wavelets C p Raw Signal (mean=) Paul T c = 22.6s Paul; T c = 35.s Time (sec.)

68 Raw data from configuration two C p Mean 3*std. dev Time (sec.)

Selectively Sampled Data from configuration two.5 C p (C p C p ).5 1 Peak Begins Peak Ends 1.5 2 89.58 89.6 89.62 89.64 89.

70 Selectively Sampled Data from configuration two.5 C p (C p C p ).5 1 Peak Begins Peak Ends Time (sec.).18 W.16 6 Duration (sec.) Time (sec.)

71 1.5 Windowed peak and Scaled wavelet Windowed Peak Scaled wavelet, T c =.14s.5 C p (C p C p ) Time (sec.).18 W Duration (sec.) Time (sec.)

72 .1 Configuration 1 - Complex peak Configuration 3 - Complex peak C p - (C p - C p ) Time (sec.) C p - (C p - C p ) Time (sec.) Configuration 4 - Complex peak Configuration 6 - Complex peak C p - (C p - C p ) C p - (C p - C p ) Time (sec.) Time (sec.)

79 r:/3cp125.txt C p Time (sec.) r:/14cp225.txt C p Time (sec.) r:/11cp325.txt C p Time (sec.) r:/3cp425.txt C p Time (sec.) r:/3cp625.txt C p Time (sec.) r:/11cp725.txt C p Time (sec.) 1 r:/3cp825.txt C p Time (sec.)

80 Configuration 1 Configuration 2 C p Duration (sec.) C p Duration (sec.) Configuration 3 Configuration 4 C p Duration (sec.) C p Duration (sec.)

81 Configuration 6 Configuration 7 C p Duration (sec.) C p Duration (sec.) -9 Configuration C p duration (sec.)

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