In pulsed radar and sonar systems, the target return has unknown phase, and also unknown frequency, if the target is moving. In unspecified non-Gaussian noise, optimal detectors are unavailable, and current single sensor, noncoherent techniques rely on the frequency being known. When frequency estimates are substituted for the unknown frequency in these latter detectors, they fail completely because their thresholds do not take into account the uncertainty of the frequency estimator. In this contribution, we propose a detector based on the peak of the finite Fourier transform and the bootstrap. The bootstrap is a statistical method for estimating the sampling distribution of a statistic from the sample data itself. In this way, modeling assumptions about the noise and signal are relaxed. This advantage of using the bootstrap is seen from theoretical results and simulations presented. We demonstrate that a constant false alarm rate is achievable even for heavily skewed interference, while detection rates of 99% are possible for data sizes as low as 100 samples and -5 dB signal-to- noise ratio. Some asymptotic properties of the detector are given. In the simulations, we also present a comparison of the detector with the classical detectors based on least squares regression and based on uniform random phase. It is seen that our proposed method compares favorably with these methods in that, when the frequency is known, the proposed method is only slightly less powerful than the classical detectors for Gaussian noise. It continues to do well for heavy-tailed and skewed non-Gaussian noise such as t- distributed and Gaussian mixture noise. For unknown frequency, it is still able to obtain a high detection rate when the classical detectors fail completely.