NSIGT_REAL - Nonstationary Gabor synthesis for real signals
Usage
fr = nsigt_real(c,g,shift,M,Ls)
Input parameters
c | Cell array of nonstationary Gabor coefficients |
g | Cell array of synthesis windows |
shift | Vector of time shifts |
M | Number of frequency channels (vector/scalar) |
Ls | Length of the analyzed signal |
Output parameters
fr | Synthesized real-valued signal (Channels are stored in the columns) |
Description
Given the cell array c of nonstationary Gabor coefficients, a set of windows g and time shifts shift, this function computes the corresponding real-valued nonstationary Gabor synthesis. Let N=numel(g) and \(P(n)=\sum_{l=1}^{n} shift(l)\) , then the complex valued synthesis formula reads:
for \(l=0,\cdots,Ls-1\) . In practice, the synthesis formula is realized by ifft and overlap-add. In the real valued case, ifftreal provides the missing frequency content normally given by the coefficients c{n}(m) for \(m \geq floor(M(n)/2)\) .
If a nonstationary Gabor frame was used to produce the coefficients and g is a corresponding dual frame, this function should perfectly reconstruct the originally analyzed signal to numerical precision.
Note that nsigt_real requires the input parameter M to guarantee that the vectors used in the overlap-add process are of the correct length.
Multichannel output will save each channel in a column of fr.
References:
P. Balazs, M. Dörfler, F. Jaillet, N. Holighaus, and G. A. Velasco. Theory, implementation and applications of nonstationary Gabor Frames. J. Comput. Appl. Math., 236(6):1481-1496, 2011.