Function CONCATENATE_FREQ

Package

Short description

Usage

    Y = CONCATENATE_FREQ(X, fmt)

Input

    X (struct or cell): The scattering layer to process, or a cell array of
       such scattering layers. Often S or U outputs of SCAT.
    fmt (char, optional): Either 'table' or 'cell'. Describes how grouped
       coefficients are assembled. See Description for more details (default
       'table').

Output

    Y (struct or cell): The same scattering layers, with all coefficients 
       that only differ by first frequency lambda1 grouped together.

Description

    In order to perform operations along frequency, or in the time-frequency
    plane, scattering coefficients need to be grouped together and concate-
    nated along the first frequency axis, lambda1. Specifically, all coef-
    ficients that have the same frequencies lambda2, lambda3, etc are grouped
    together. For the first order, this means that we only have one group,
    whereas in the second order, we have one group for each lambda2, and so
    on.
    Each signal in the input is of the form Nx1xK, where N is the number of
    time samples and K is the number of signals that are processed simulta-
    neously. Consider one group as described above, containing P coeffi-
    cients, with all coefficients having the same number of time samples. 
    This is the case, for example, when the input X is a scattering transform
    output S. Here, the coefficients can be concatenated into a single table
    of dimension NxPxK. If the fmt parameter is set to 'table', this is in-
    deed what happens. The P coefficients in X are therefore replaced by
    one table in Y of the dimension described above. If fmt equals 'cell',
    a cell array is created instead of a table, containing each of the sig-
    nals in the group. In both cases, frequencies lambda1 are arranged in 
    order of decreasing frequency (increasing scale).
    To preserve the meta fields of the original coefficients, they are copied
    into the output structure. They are ordered in order of increasing group
    index, so that if the first group contains P coefficients, the first
    P columns of a given meta field corresponds to the coefficients of the 
    first group, and so on. Within each group, the columns are ordered in 
    order of decreasing lambda1, just like within the groups themselves.

See also

• scat_freq