NWelch uses Welch's method to estimate the power spectra, complex cross-spectrum, magnitude-squared coherence, and phase spectrum of bivariate time series with nonuniform observing cadence. For univariate time series, users can apply the Welch's power spectrum estimator or compute a nonuniform fast Fourier transform-based periodogram. Options include tapering in the time domain and computing bootstrap false alarm levels. Users may choose standard 50%-overlapping Welch's segments or apply a custom-made segmentation scheme. NWelch was designed for Doppler planet searches but may be applied to any type of time series.