General Notation
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Interpretation
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Dyadic scale.  is the level, 1/ or  is the resolution.
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Dyadic translation
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Continuous time
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 or 
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Discrete time
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Pixel
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Signal or image. The signal is a function defined on  or  ; the image is defined on  or  .
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Fourier transform of the function f or the sequence f
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Continuous Time
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Set of signals of finite energy
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Energy of the signal 
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Scalar product of signals  and 
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Set of images of finite energy
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Energy of the image 
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Scalar product of images  and 
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Discrete Time
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Set of signals of finite energy
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Energy of the signal 
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Scalar product of signals  and 
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Set of images of finite energy
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Energy of the image 
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Scalar product of images  and 
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Wavelet Notation
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Interpretation
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Aj
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j-level approximation or approximation at level j
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Dj
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j-level detail or detail at level j
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Scaling function
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Wavelet
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Family associated with the one-dimensional wavelet, indexed by  and 
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Family associated with the two-dimensional wavelet, indexed by
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Family associated with the one-dimensional scaling function for dyadic scales  ; it should be noted that  .
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Family associated with the one-dimensional  for dyadic scales  ; it should be noted that  .
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Scaling filter associated with a wavelet
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Wavelet filter associated with a wavelet
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