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This article presents a method for digital acquisition of low-frequency signals immersed in high-frequency noise when noise frequency is higher than the sampling one. This method uses no antialiasing filters, but random sampling and filtering instead. Its formulation is developed for JRS (jitter random sampling) and finite impulse response (FIR) filters. The proposed method is experimentally tested on three FIR filters: moving average, windowed linear phase, and constrained least square.