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Mathematical Conventions
This chapter and the reference pages use certain mathematical conventions.

General Notation
Interpretation 

Dyadic scale. is the level, 1/ or is the resolution.

Dyadic translation

Continuous time
or
Discrete time

Pixel

Signal or image. The signal is a function defined on or ; the image is defined on or .

Fourier transform of the function f or the sequence f
Continuous Time


Set of signals of finite energy

Energy of the signal

Scalar product of signals and

Set of images of finite energy

Energy of the image

Scalar product of images and
Discrete Time


Set of signals of finite energy

Energy of the signal

Scalar product of signals and

Set of images of finite energy

Energy of the image

Scalar product of images and

Wavelet Notation
Interpretation
 Aj
j-level approximation or approximation at level j
 Dj
j-level detail or detail at level j
phi
Scaling function
psi
Wavelet

Family associated with the one-dimensional wavelet, indexed by and

Family associated with the two-dimensional wavelet, indexed by



Family associated with the one-dimensional scaling function for dyadic scales ; it should be noted that .

Family associated with the one-dimensional for dyadic scales ; it should be noted that .

Scaling filter associated with a wavelet

Wavelet filter associated with a wavelet


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