@book{CrochiereRabiner1983,
  author    = {Ronald E. Crochiere and Lawrence R. Rabiner},
  title     = {Multirate Digital Signal Processing},
  publisher = {Prentice Hall},
  address   = {Englewood Cliffs, New Jersey},
  year      = {1983}
}

@book{Vaidyanathan1993,
  author    = {P. P. Vaidyanathan},
  title     = {Multirate Systems and Filter Banks},
  publisher = {Prentice Hall},
  address   = {Englewood Cliffs, New Jersey},
  year      = {1993}
}

@book{VetterliKovacevic1995,
  author    = {Martin Vetterli and Jelena Kova\v{c}evi\'{c}},
  title     = {Wavelets and Subband Coding},
  publisher = {Prentice Hall},
  address   = {Englewood Cliffs, New Jersey},
  year      = {1995}
}

@book{StrangNguyen1996,
  author    = {Gilbert Strang and Truong Nguyen},
  title     = {Wavelets and Filter Banks},
  publisher = {Wellesley Cambridge Press},
  address   = {Wellesley, Massachusetts},
  year      = {1996}
}

@book{Daubechies1992,
  author    = {Ingrid Daubechies},
  title     = {Ten Lectures on Wavelets},
  series    = {CBMS NSF Regional Conference Series in Applied Mathematics},
  volume    = {61},
  publisher = {Society for Industrial and Applied Mathematics},
  address   = {Philadelphia},
  year      = {1992}
}

@book{Mallat2009,
  author    = {St\'{e}phane Mallat},
  title     = {A Wavelet Tour of Signal Processing},
  edition   = {Third},
  publisher = {Academic Press},
  address   = {Burlington, Massachusetts},
  year      = {2009}
}

@article{CohenDaubechiesFeauveau1992,
  author  = {Albert Cohen and Ingrid Daubechies and Jean Christophe Feauveau},
  title   = {Biorthogonal bases of compactly supported wavelets},
  journal = {Communications on Pure and Applied Mathematics},
  volume  = {45},
  number  = {5},
  pages   = {485{\textendash}560},
  year    = {1992},
  doi     = {10.1002/cpa.3160450502}
}

@article{Sweldens1996,
  author  = {Wim Sweldens},
  title   = {The lifting scheme: A custom design construction of biorthogonal wavelets},
  journal = {Applied and Computational Harmonic Analysis},
  volume  = {3},
  number  = {2},
  pages   = {186{\textendash}200},
  year    = {1996},
  doi     = {10.1006/acha.1996.0015}
}

@article{DaubechiesSweldens1998,
  author  = {Ingrid Daubechies and Wim Sweldens},
  title   = {Factoring wavelet transforms into lifting steps},
  journal = {Journal of Fourier Analysis and Applications},
  volume  = {4},
  number  = {3},
  pages   = {247{\textendash}269},
  year    = {1998},
  doi     = {10.1007/BF02476026}
}

@article{CoifmanWickerhauser1992,
  author  = {Ronald R. Coifman and Mladen Victor Wickerhauser},
  title   = {Entropy based algorithms for best basis selection},
  journal = {IEEE Transactions on Information Theory},
  volume  = {38},
  number  = {2},
  pages   = {713{\textendash}718},
  year    = {1992},
  doi     = {10.1109/18.119732}
}

@article{MallatHwang1992,
  author  = {St\'{e}phane Mallat and Wen Liang Hwang},
  title   = {Singularity detection and processing with wavelets},
  journal = {IEEE Transactions on Information Theory},
  volume  = {38},
  number  = {2},
  pages   = {617{\textendash}643},
  year    = {1992},
  doi     = {10.1109/18.119727}
}

@article{GottliebShu1997,
  author  = {David Gottlieb and Chi-Wang Shu},
  title   = {On the Gibbs phenomenon and its resolution},
  journal = {SIAM Review},
  volume  = {39},
  number  = {4},
  pages   = {644{\textendash}668},
  year    = {1997},
  doi     = {10.1137/S0036144596301390}
}

@article{DeVore1998,
  author  = {Ronald A. DeVore},
  title   = {Nonlinear approximation},
  journal = {Acta Numerica},
  volume  = {7},
  pages   = {51{\textendash}150},
  year    = {1998},
  doi     = {10.1017/S0962492900002816}
}

@article{Donoho1999,
  author  = {David L. Donoho},
  title   = {Wedgelets: Nearly minimax estimation of edges},
  journal = {The Annals of Statistics},
  volume  = {27},
  number  = {3},
  pages   = {859{\textendash}897},
  year    = {1999},
  doi     = {10.1214/aos/1018031261}
}

@article{CandesDonoho2004,
  author  = {Emmanuel J. Cand\`es and David L. Donoho},
  title   = {New tight frames of curvelets and optimal representations of objects with piecewise smooth singularities},
  journal = {Communications on Pure and Applied Mathematics},
  volume  = {57},
  number  = {2},
  pages   = {219{\textendash}266},
  year    = {2004},
  doi     = {10.1002/cpa.10116}
}

@book{AmbrosioFuscoPallara2000,
  author    = {Luigi Ambrosio and Nicola Fusco and Diego Pallara},
  title     = {Functions of Bounded Variation and Free Discontinuity Problems},
  publisher = {Oxford University Press},
  address   = {Oxford},
  year      = {2000}
}

@book{Zygmund2002,
  author    = {Antoni Zygmund},
  title     = {Trigonometric Series},
  edition   = {Third},
  publisher = {Cambridge University Press},
  address   = {Cambridge},
  year      = {2002}
}

@book{Smith1969,
  author    = {Phillip H. Smith},
  title     = {Electronic Applications of the Smith Chart},
  publisher = {McGraw Hill},
  address   = {New York},
  year      = {1969}
}

@misc{DLMFGibbs,
  author = {{National Institute of Standards and Technology}},
  title = {{NIST Digital Library of Mathematical Functions}, Section 6.16(i): The Gibbs Phenomenon},
  year = {2026},
  howpublished = {\url{https://dlmf.nist.gov/6.16.i}},
  note = {Version 1.2.8, released 15 September 2026. Equations 6.16.1--6.16.4. Accessed 20 October 2026}
}