PGHI_FINDGAMMA - Find window constant for PGHI and RTPGHI

Usage

gamma = pghi_findgamma({firwinname,gl})
gamma = pghi_findgamma(g,a,M)
gamma = pghi_findgamma(g,a,M,L)
[gamma, Cg] = pghi_findgamma(...)

Input parameters

`gnum`	Window.
`gl`	Length of the support of the window.

Output parameters

`gamma`	Parameter for PGHI and RTPGHI
`Cg`	Window constant

Description

pghi_findgamma({firwinname,gl}) returns parameter gamma, for which the Gaussian window given as:

\begin{equation*} g=exp(-\pi\frac{l^2}{\gamma}) \end{equation*}

is closest to peak-normalized window firwinname from firwin. The parameter is precomputed so the search will not be done.

[gamma,Cg] = pghi_findgamma(...) additionaly returns parameter Cg which is window constant and is used to compute gamma such as:

\begin{equation*} \gamma=C_g \mathit{gl}^2} \end{equation*}

where gl is the length of the window support.

Note that the relationship between gamma and tfr from pgauss is:

\begin{equation*} tfr=gamma/L \end{equation*}

where L is the DGT length.

Additional parameters:

'search' Do the search even for precomputed windows.

References:

Z. Průša and P. L. Søndergaard. Real-Time Spectrogram Inversion Using Phase Gradient Heap Integration. In Proc. Int. Conf. Digital Audio Effects (DAFx-16), Sep 2016.