The classical frequency domain bootstrap (FDB) is investigated and analyzed herein. First some well-known bootstrap consistency results for spectral density functions are revisited and then the article focuses on smooth functions of linear functionals by providing the necessary and sufficient conditions for the validity of the FDB. The authors establish that the FDB is asymptotically valid if and only if the kurtosis of the process is 0 (for instance in the Gaussian case) or if the functional of interest has a centered influence function, which is the case for ratio statistics as well as some Whittle estimators. Then the conditions under which the empirical process in the frequency domain converges to some Gaussian process and when its bootstrap version is valid are provided. Hence it becomes feasible to prove the validity of the bootstrap for large classes of interesting statistics.