**4.4 Signal composed of 2 sinusoids with closely spaced frequencies**

We have also input a signal with 2 very closely spaced frequencies and unity amplitudes. For frequencies {0.3389, 0.3390} we recover the frequencies to machine precision with a 16x1024 mixing matrix. Smaller values of *M* for the mixing matrix yield one root half way between the two frequencies. For frequencies {0.33899,0.33900} mixed with 16x1024 and 32x1024 matrices the OMP part of our algorithm yields a signal with one frequency at 0.338995 and an amplitude of 1.9996. Attempts to find a second frequency yield a badly conditioned matrix for *U***H***WU* and the inversion required to find the 2nd amplitude in eq. (11) fails. For a 64x1024 mixing matrix OMP finds two separated estimates of the frequencies and this allows NLS determination of both frequencies to an accuracy of a few parts in 105. These results are in contrast to those obtained using the "spectral compressive sensing" algorithms that use "a signal model that inhibits closely spaced sinusoids" (Duarte and Baraniuk, 2010).
