Sparse recovery with annihilating filter method. The annihilation equation that the sparse signal should satisfy x(t)μ(t) = 0 is equivalent to a set of discrete convolution equations between uniformly sinusoidal samples and a finite length discrete filter in the Fourier domain. The mask function μ(t), which can be estimated from the given lowpass filtered samples of x(t), vanishes at the position where x(t) is different from zero.