In order to perform spectral analysis of nonuniformly sampled time domain signals, algorithms for the Nonuniform-Time Discrete Fourier Transform (NUT-DFT) are developed and evaluated The NUT-DFT takes nonuniform time domain data and produces a uniform sampled spectrum. The proposed algorithms for NUT-DFT are based on approximating the continuous-time Fourier transform by different numerical integration algorithms. Special attention is paid to the ability of the transform to capture signals with frequency components above half the average sampling rate. The performance of the algorithms is studied experimentally by analysing both nonuniformly and uniformly sampled data.