njit-etd2003-081 - New Jersey Institute of Technology
njit-etd2003-081 - New Jersey Institute of Technology njit-etd2003-081 - New Jersey Institute of Technology
75 Now one can define the basis functions of a Discrete Wavelet Transform as the subset of continuous wavelet function [45 - 48] with the corresponding discrete transform lattices or grids Hence, the discrete wavelet transform basis functions can be expressed as Here m and n are integers. It is intuitively seen that this discrete wavelet family approaches a continuous wavelet family when a 0 —31 b0 ----> 0 It can be shown that the functions of a discrete wavelet transform basis ψmn(t) can form a frame or the sets of m and n parameters are proper for the completeness if the wavelet function (At) satisfies the admissibility condition. Then the frame bounds are constrained by the inequalities [45] 0
76 and the wavelet transform representation of the signal There is a particular interest on a binary or dyadic grid where a0 = 2 and b0 = 1, which leads to the conventional multiresolution concept and the orthogonal discrete wavelet transforms.
- Page 53 and 54: 24 The sympathetic nerve fibers lea
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- Page 59 and 60: 30 Figure 2.6 Autonomic innervation
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- Page 65 and 66: Figure 2.9 The placement of the pos
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- Page 69 and 70: 40 Stage II: Moderate COPD - Worsen
- Page 71 and 72: CHAPTER 3 ENGINEERING BACKGROUND Th
- Page 73 and 74: 44 Two common types of time-frequen
- Page 75 and 76: 46 STFT: Short-Time Fourier Transfo
- Page 77 and 78: 48 3.3 The Analytic Signal and Inst
- Page 79 and 80: 50 The advantage of using equation
- Page 81 and 82: 52 3.5 Covariance and Invariance Th
- Page 83 and 84: where H(f), S(f) are Fourier transf
- Page 85 and 86: 56 Another shortcoming of the spect
- Page 87 and 88: 58 should take the kernel of the WD
- Page 89 and 90: 60 called the cross Wigner distribu
- Page 91 and 92: 62 3.6.3 The Choi-Williams (Exponen
- Page 93 and 94: 64 Figure 3.3 Performance of the Ch
- Page 95 and 96: 66 [-Ω,Ω ], then its STFT will be
- Page 97 and 98: 68 This condition forces that the w
- Page 99 and 100: 70 where c is a constant. Thus, the
- Page 101 and 102: Figure 3.5 The time-frequency plane
- Page 103: 74 The measure dadb used in the tra
- Page 107 and 108: 78 Figure 3.6 Figure depicting the
- Page 109 and 110: 80 The final step to obtain the pow
- Page 111 and 112: 82 It should be noted that if the w
- Page 113 and 114: 84 The normal respiration rate can
- Page 115 and 116: Figure 3.12 Power spectrum of BP II
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- Page 119 and 120: 90 when there is significant correl
- Page 121 and 122: 92 3.12 Partial Coherence Analysis
- Page 123 and 124: 94 after removal of the effects of
- Page 125 and 126: 96 The bulk of the theory and appli
- Page 127 and 128: 98 technique is measurement time. T
- Page 129 and 130: 100 usually attainable. The key poi
- Page 131 and 132: 102 variability exists in the propa
- Page 133 and 134: 104 eXogenous input (ARX) was used
- Page 135 and 136: 106 The baroreflex, an autonomic re
- Page 137 and 138: 108 the principal components are no
- Page 139 and 140: 110 The mathematical solution for t
- Page 141 and 142: 112 3.15 Cluster Analysis The term
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- Page 145 and 146: 116 3.15.5 Squared Euclidian Distan
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- Page 149 and 150: 120 Sneath and Sokal used the abbre
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75<br />
Now one can define the basis functions <strong>of</strong> a Discrete Wavelet Transform as the<br />
subset <strong>of</strong> continuous wavelet function [45 - 48]<br />
with the corresponding discrete transform lattices or grids<br />
Hence, the discrete wavelet transform basis functions can be expressed as<br />
Here m and n are integers. It is intuitively seen that this discrete wavelet family<br />
approaches a continuous wavelet family when a 0 —31 b0 ----> 0<br />
It can be shown that the functions <strong>of</strong> a discrete wavelet transform basis<br />
ψmn(t) can form a frame or the sets <strong>of</strong> m and n parameters are proper for the<br />
completeness if the wavelet function (At) satisfies the admissibility condition. Then the<br />
frame bounds are constrained by the inequalities [45] 0
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