gt=wilorth(M,L); gt=wilorth(g,M); gt=wilorth(g,M,L);
| g | Auxiliary window window function (optional). |
| M | Number of modulations. |
| L | Length of window (optional). |
| gt | Window generating an orthonormal Wilson basis. |
wilorth(M,L) computes a nice window of length L generating an orthonormal Wilson or WMDCT basis with M frequency bands for signals of length L.
wilorth(g,M) computes a window generating an orthonomal basis from the window g and number of channels M.
The window g may be a vector of numerical values, a text string or a cell array. See the help of wilwin for more details.
If the length of g is equal to \(2\times M\), then the input window is assumed to be a FIR window. In this case, the orthonormal window also has length of \(2\times M\). Otherwise the smallest possible transform length is chosen as the window length.
wilorth(g,M,L) pads or truncates g to length L before calculating the orthonormal window. The output will also be of length L.
The input window g must be real whole-point even. If g is not whole-point even, the computed window will not generate an orthonormal system (i.e. reconstruction will not be perfect). For a random window g, the window closest to g that satisfies these restrictions can be found by
g_wpe = real(peven(g));
All Gabor windows in the toolbox satisfies these restrictions unless clearly stated otherwise.