Function GRIFFIN_LIM

Package

Short description

Usage

    x = griffin_lim(x_init, x_phi, x_psi_mod, filters, options)

Input

    x_init (numeric): The inital guess for x.
    x_phi (numeric): The lowpass coefficients
    x_psi_mod (cell): The wavelet modulus coefficients.
    filters (struct): The filter bank used to calculate the wavelet transform
        in WAVELET_1D.
    options (struct, optional): Different parameters to the algorithm and to
        WAVELET_1D and INVERSE_WAVELET_1D that are called. Parameters for
        GRIFFIN_LIM are:
            gl_iter (numeric): The number of iterations (default 32).

Output

     x (numeric): The result of the algorithm.

Description

    Given the lowpass coefficients and the modulus of the wavelet 
    coefficients, the Griffin & Lim algorithm attempts to reconstruct the
    original signal by recovering the phase of the wavelet coefficients. To
    do this, it performs an alternating projection on the wavelet reproducing
    kernel (the set of coefficients that are valid wavelet transforms) and
    the set of coefficients of the desired modulus. Since the latter is a 
    non-convex set, the algorithm will not converge. In some applications,
    however, the approximation that it provides is sufficient. For more 
    details, see [1].
 References
    [1] D. W. Griffin and J. S. Lim, “Signal estimation from modified short- 
        time fourier transform,” IEEE Trans. Acoust., Speech, Signal
        Process., vol. 32, no. 2, pp. 236–243, 1984. 

See also

• wavelet_1d
• inverse_wavelet_1d