Trapezoidal stratified Monte Carlo integration
SIAM Journal on Numerical Analysis
Randomized Signal Processing
Spectral analysis of randomly sampled signals: suppression of aliasing and sampler jitter
IEEE Transactions on Signal Processing
Random sampling of deterministic signals: statistical analysis of Fourier transform estimates
IEEE Transactions on Signal Processing
Wideband spectrum sensing technique based on random sampling on grid: Achieving lower sampling rates
Digital Signal Processing
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We estimate the Fourier transform of continuous-time signals on the basis of N discrete-time nonuniform observations. We introduce a class of antithetical stratified random sampling schemes and we obtain the performance of the corresponding estimates. We show that when the underlying function f(t) has a continuous second-order derivative, the rate of mean square convergence is 1/N5, which is considerably faster that the rate of 1/N3 for stratified sampling and the rate of 1/N for standard Monte Carlo integration. In addition, we establish joint asymptotic normality for the real and imaginary parts of the estimate and give an explicit expression for the asymptotic covariance matrix. The theoretical results are illustrated by examples for low-pass and high-pass signals.