This work addresses the problem of reconstruction of spectra F(ω) from the irregular sampling of autocorrelation functions f(t). We assume that F(ω) has bounded support [-π, π] : The number 2L of sampling times is such that the variation of F(ω) on intervals of length π/L is small enough to lead to a good interpolation of this function. Reconstruction formulas are based on PNS (Periodic Nonuniform Sampling) plans. They allow reconstructions not demanding periodic resampling and suppress two stages in classical computations. The method can also be easily generalized to spectra in symmetric frequency bands (bandpass signals).

This paper proposes a method for selective digital-to-analog conversion of a stationary band-pass random process submitted to interference. This method simultaneously performs the signal digital-to-analog conversion and the interference rejection from the observed process samples: it does not require any preliminary demodulation of the bandpass observed process and the filtering is performed in the time domain using an explicit expression of the filter taps. The method uses a particular non uniform sampling scheme called Periodic Non-uniform Sampling of order 2 (PNS2). The PNS2 sampling scheme uses two interleaved sample sequences. Appropriate formulas are derived to reconstruct the signal from its non-uniform samples while removing the interference by a selective filtering. The reconstruction from an infinite observation window (an infinite number of samples) is exact. However, in practical applications, the digital-to-analog conversion is generally performed in real time using a finite sliding observation window (a finite number of samples). Thus the reconstruction formulas should also demonstrate a high convergence rate. This paper proposes reconstruction formulas with increasing convergence rates using filters with increasingly regular transfer functions. The proposed method has been tested through simulations according to experimental parameters.