G=frsynmatrix(F,L);
G=frsynmatrix(F,L) returns the matrix representation G of the frame synthesis operator for a frame F of length L. The frame object F must have been created using frame.
The frame synthesis operator matrix contains all the frame atoms as column vectors. It has dimensions \(L \times Ncoef\), where \(Ncoef\) is the number of coefficients. The number of coefficients can be found as Ncoef=frameclength(L). This means that the frame matrix is usually very large, and this routine should only be used for small values of L.
The action of the frame analysis operator frana is equal to multiplication with the Hermitean transpose of the frame synthesis matrix. Consider the following simple example:
L=200;
F=frame('dgt','gauss',10,20);
G=frsynmatrix(F,L);
testsig = randn(L,1);
res = frana(F,testsig)-G'*testsig;
norm(res)
% Show the matrix (real and imaginary parts)
figure(1); imagesc(real(G));
figure(2); imagesc(imag(G));