This paper proposes a method that simultaneously builds the analytic signal from non-uniform samples of a bandpass signal and rejects interferences. The analytic signal is required for many onboard operations in communication satellites. This method operates in the time domain and without preliminary demodulation, using Periodic Non-uniform Sampling of order 2 (PNS2). This non-uniform sampling scheme can be easily implemented with available devices. Exact formulas for the analytic signal construction are derived for an infinite observation window (an infinite number of samples). For practical applications, the formulas should also demonstrate a high convergence rate due to the finite observation window. Formulas with increasing convergence rates are thus derived. The proposed method has been tested through simulations according to the number of available samples, the interference parameters and the filter transfer function regularity.