Bandwidth and detection limit of a crossing–sampling spectrum analyzer

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Abstract
We report the performance of a spectrum analyzer that determines the Fourier spectrum of an analog input sa(t) using only as data the time locations {ti} where sa(t) intersects with a reference sinusoid r(t)=A cos(2πWt). If A⩽|sa(t)| within the sampling period T, then one crossing exists within each interval Δ=1/2W. The spectrum is computed directly from {ti}, which consists of 2M=T/Δ crossing locations. The theoretical bandwidth and frequency resolution of the analyzer is given by 2W and 1/T, respectively. However, electronic circuits have a finite temporal response and the crossings can only be located with finite accuracy. A trade off, therefore, is expected between the measurement bandwidth and the detection limit in a real crossing-based analyzer. In our design, the accuracy can be varied to increase the bandwidth, through the use of a versatile field programable gate array. The relation between the detection limit, dynamic range, and bandwidth of our device is experimentally studied and analyzed.