  Nonstationary signals are commonly analyzed and processed in the
time-frequency (T-F) domain that is obtained by the discrete Gabor transform
(DGT). The T-F representation obtained by DGT is spread due to windowing, which
may degrade the performance of T-F domain analysis and processing. To obtain a
well-localized T-F representation, sparsity-aware methods using $\ell_1$-norm
have been studied. However, they need to discretize a continuous parameter onto
a grid, which causes a model mismatch. In this paper, we propose a method of
estimating a sparse T-F representation using atomic norm. The atomic norm
enables sparse optimization without discretization of continuous parameters.
Numerical experiments show that the T-F representation obtained by the proposed
method is sparser than the conventional methods.

Signal Processing