Spectrum estimation of uniformly sampled data can be performed using conventional methods. However, astronomical and atmospheric data signals are usually obtained at non-regular intervals of time. The spectral analysis of such non-uniformly sampled data becomes challenging. The spectrum being sparse and the presence of additive noise further worsens the situation. The present study aims at spectral analysis of such signals using two sparse spectrum estimation algorithms called Iterative Adaptive Approach (IAA) and Sparse/Semi-Parametric Iterative Covariance based Estimation (SPICE). The application of these algorithms in cognitive radio scenario for spectrum sensing and estimation using lesser number of received samples is also proposed in the present study. The semi-parametric methods show superior performance than the conventional periodogram based technique for spectrum estimation. © Research India Publications.