Stated more than 20 years ago by C. Heil, J. Ramanathan, and P. Topiwala, the HRT conjecture is about the linear independence of a collection of finitely many time-frequency shifts of an arbitrary nonzero square integrable function. Despite the simplicity of its statement, the conjecture is still open for the general case. In this talk the author will present results based on a paper by Dr. J. Benedetto and the author. The paper proves HRT conjecture for a class of functions with certain behavior at infinity. This class includes some square integrable functions built by combining polynomial, exponential, and logarithmic functions. For example, we prove HRT for any finite collection of time-frequency shifts of e{-|x|}.