Function CONV_SUB_1D

Package

Short description

Usage

    y_ds = CONV_SUB_1D(xf, filter, ds)

Input

    xf (numeric): The Fourier transform of the signal to be convolved.
    filter (*numeric OR struct*): The analysis filter in the frequency
       domain. Either Fourier transform of the filter or the output of
       OPTIMIZE_FILTER.
    ds (int): The downsampling factor as a power of 2 with respect to xf.

Output

    y_ds (numeric): the filtered, downsampled signal, in the time domain.

Description

    This function is at the foundation of the wavelet transform in 1D. It
    performs an element-wise product of a signal and a filter in the
    frequency domain, equivalent to a convolution in the time domain.
    The filter argument may either be:
       * a DFT real vector, or
       * an optimized filter structure from OPTIMIZE_FILTER
    In the latter case, different methods are used to speed up the calcula-
    tion, such as storing the filter at different resolutions or only storing
    the Fourier transform coefficients that are non-zero. These are obtained
    when defining the filter bank using the filt_opt.filter_format parameter. 
    See FILTER_BANK for more information.
    Multiple signals can be convolved in parallel by specifying them as dif-
    ferent columns of xf. If many signals need to be convolved at the same
    time, this is often much faster than performing calling CONV_SUB_1D on
    each signal separately.

See also

• conv_sub_2d
• wavelet_1d