Function SCAT

Package

Short description

Usage

    [S, U] = SCAT(x, Wop) 

Input

    x (numeric): The input signal.
    Wop (cell of function handles): Linear operators used to generate a new 
       layer from the previous one.

Output

    S (cell): The scattering representation of x.
    U (cell): Intermediate covariant modulus coefficients of x.

Description

    The signal x is decomposed using linear operators Wop and modulus 
    operators, creating scattering invariants S and intermediate covariant
    coefficients U. 
    Each element of the Wop array is a function handle of the signature
       [A, V] = Wop{m+1}(U),
    where m ranges from 0 to M (M being the order of the transform). The 
    outputs A and V are the invariant and covariant parts of the operator.
    The variables A, V and U are all of the same structure, that of a network
    layer. Specifically, the have one field, signal, which is a cell array
    corresponding to the constituent signals, and another field, meta, which
    contains various information on these signals.
    The scattering transform therefore initializes the first layer of U using
    the input signal x, then iterates on the following transformation
       [S{m+1}, V] = Wop{m+1}(U{m+1});
       U{m+2} = modulus_layer(V);
    The invariant part of the linear operator is therefore output as a scat-
    tering coefficient, and the modulus covariant part V is assigned to the 
    next layer of U.

See also

• wavelet_factory_1d
• wavelet_factory_2d
• wavelet_factory_2d_pyramid