Realization Calculus

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1 @book{CrochiereRabiner1983,
2   author    = {Ronald E. Crochiere and Lawrence R. Rabiner},
3   title     = {Multirate Digital Signal Processing},
4   publisher = {Prentice Hall},
5   address   = {Englewood Cliffs, New Jersey},
6   year      = {1983}
7 }
8 
9 @book{Vaidyanathan1993,
10   author    = {P. P. Vaidyanathan},
11   title     = {Multirate Systems and Filter Banks},
12   publisher = {Prentice Hall},
13   address   = {Englewood Cliffs, New Jersey},
14   year      = {1993}
15 }
16 
17 @book{VetterliKovacevic1995,
18   author    = {Martin Vetterli and Jelena Kova\v{c}evi\'{c}},
19   title     = {Wavelets and Subband Coding},
20   publisher = {Prentice Hall},
21   address   = {Englewood Cliffs, New Jersey},
22   year      = {1995}
23 }
24 
25 @book{StrangNguyen1996,
26   author    = {Gilbert Strang and Truong Nguyen},
27   title     = {Wavelets and Filter Banks},
28   publisher = {Wellesley Cambridge Press},
29   address   = {Wellesley, Massachusetts},
30   year      = {1996}
31 }
32 
33 @book{Daubechies1992,
34   author    = {Ingrid Daubechies},
35   title     = {Ten Lectures on Wavelets},
36   series    = {CBMS NSF Regional Conference Series in Applied Mathematics},
37   volume    = {61},
38   publisher = {Society for Industrial and Applied Mathematics},
39   address   = {Philadelphia},
40   year      = {1992}
41 }
42 
43 @book{Mallat2009,
44   author    = {St\'{e}phane Mallat},
45   title     = {A Wavelet Tour of Signal Processing},
46   edition   = {Third},
47   publisher = {Academic Press},
48   address   = {Burlington, Massachusetts},
49   year      = {2009}
50 }
51 
52 @article{CohenDaubechiesFeauveau1992,
53   author  = {Albert Cohen and Ingrid Daubechies and Jean Christophe Feauveau},
54   title   = {Biorthogonal bases of compactly supported wavelets},
55   journal = {Communications on Pure and Applied Mathematics},
56   volume  = {45},
57   number  = {5},
58   pages   = {485{\textendash}560},
59   year    = {1992},
60   doi     = {10.1002/cpa.3160450502}
61 }
62 
63 @article{Sweldens1996,
64   author  = {Wim Sweldens},
65   title   = {The lifting scheme: A custom design construction of biorthogonal wavelets},
66   journal = {Applied and Computational Harmonic Analysis},
67   volume  = {3},
68   number  = {2},
69   pages   = {186{\textendash}200},
70   year    = {1996},
71   doi     = {10.1006/acha.1996.0015}
72 }
73 
74 @article{DaubechiesSweldens1998,
75   author  = {Ingrid Daubechies and Wim Sweldens},
76   title   = {Factoring wavelet transforms into lifting steps},
77   journal = {Journal of Fourier Analysis and Applications},
78   volume  = {4},
79   number  = {3},
80   pages   = {247{\textendash}269},
81   year    = {1998},
82   doi     = {10.1007/BF02476026}
83 }
84 
85 @article{CoifmanWickerhauser1992,
86   author  = {Ronald R. Coifman and Mladen Victor Wickerhauser},
87   title   = {Entropy based algorithms for best basis selection},
88   journal = {IEEE Transactions on Information Theory},
89   volume  = {38},
90   number  = {2},
91   pages   = {713{\textendash}718},
92   year    = {1992},
93   doi     = {10.1109/18.119732}
94 }
95 
96 @article{MallatHwang1992,
97   author  = {St\'{e}phane Mallat and Wen Liang Hwang},
98   title   = {Singularity detection and processing with wavelets},
99   journal = {IEEE Transactions on Information Theory},
100   volume  = {38},
101   number  = {2},
102   pages   = {617{\textendash}643},
103   year    = {1992},
104   doi     = {10.1109/18.119727}
105 }
106 
107 @article{GottliebShu1997,
108   author  = {David Gottlieb and Chi-Wang Shu},
109   title   = {On the Gibbs phenomenon and its resolution},
110   journal = {SIAM Review},
111   volume  = {39},
112   number  = {4},
113   pages   = {644{\textendash}668},
114   year    = {1997},
115   doi     = {10.1137/S0036144596301390}
116 }
117 
118 @article{DeVore1998,
119   author  = {Ronald A. DeVore},
120   title   = {Nonlinear approximation},
121   journal = {Acta Numerica},
122   volume  = {7},
123   pages   = {51{\textendash}150},
124   year    = {1998},
125   doi     = {10.1017/S0962492900002816}
126 }
127 
128 @article{Donoho1999,
129   author  = {David L. Donoho},
130   title   = {Wedgelets: Nearly minimax estimation of edges},
131   journal = {The Annals of Statistics},
132   volume  = {27},
133   number  = {3},
134   pages   = {859{\textendash}897},
135   year    = {1999},
136   doi     = {10.1214/aos/1018031261}
137 }
138 
139 @article{CandesDonoho2004,
140   author  = {Emmanuel J. Cand\`es and David L. Donoho},
141   title   = {New tight frames of curvelets and optimal representations of objects with piecewise smooth singularities},
142   journal = {Communications on Pure and Applied Mathematics},
143   volume  = {57},
144   number  = {2},
145   pages   = {219{\textendash}266},
146   year    = {2004},
147   doi     = {10.1002/cpa.10116}
148 }
149 
150 @book{AmbrosioFuscoPallara2000,
151   author    = {Luigi Ambrosio and Nicola Fusco and Diego Pallara},
152   title     = {Functions of Bounded Variation and Free Discontinuity Problems},
153   publisher = {Oxford University Press},
154   address   = {Oxford},
155   year      = {2000}
156 }
157 
158 @book{Zygmund2002,
159   author    = {Antoni Zygmund},
160   title     = {Trigonometric Series},
161   edition   = {Third},
162   publisher = {Cambridge University Press},
163   address   = {Cambridge},
164   year      = {2002}
165 }
166 
167 @book{Smith1969,
168   author    = {Phillip H. Smith},
169   title     = {Electronic Applications of the Smith Chart},
170   publisher = {McGraw Hill},
171   address   = {New York},
172   year      = {1969}
173 }
174 
175 @misc{DLMFGibbs,
176   author = {{National Institute of Standards and Technology}},
177   title = {{NIST Digital Library of Mathematical Functions}, Section 6.16(i): The Gibbs Phenomenon},
178   year = {2026},
179   howpublished = {\url{https://dlmf.nist.gov/6.16.i}},
180   note = {Version 1.2.8, released 15 September 2026. Equations 6.16.1--6.16.4. Accessed 20 October 2026}
181 }

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