Function SPEC_FREQ_AVERAGE

Package

Short description

Usage

    spec = SPEC_FREQ_AVERAGE(x, filters, options)

Input

    x (numeric): The signal to be transformed.
    filters (cell): The set of filters used to calculate the spectrogram
       and the frequency averaging.
    options (struct): Various options to the function:
       options.oversampling (int): The amount of oversampling with respect to
          the critical bandwidth, as a power of 2 (default 1).

Output

    spec (numeric): The frequency-averaged spectrogram, arranged in as a 
       first-order scattering transform.

Description

    First, the spectrogram of x is computed with respect to the second-order
    lowpass filter filters{2}.phi, if it is present, otherwise filters{1}.phi
    is used. Once a spectrogram is obtained, the filters in filters{1}.psi are
    averaged with the spectrogram to each yield a time-varying coefficient.
    The resulting signals are arranged in spec in the format of a first-order
    scattering transform. As a result, spec{1}.signal is empty, since no 
    zeroth-order coefficients are present. However, spec{2}.signal contains 
    the frequency-averaged spectrogram coefficients, arranged in order of 
    decreasing frequeny.
    The accompanying meta structure is also analogous to the scattering 
    transform. Notably, spec{2}.meta.order is equal to 1 for each coefficient
    and spec{2}.meta.j gives the index of the filter used to compute the
    frequency averaging.

See also

• morlet_filter_bank_1d
• wavelet_factory_1d