Abstract
Abstract. The real and imaginary parts of baseband signals are obtained from a real narrow-band signal by quadrature mixing, i.e. by mixing with cosine and sine signals at the narrow band's selected center frequency. We address the consequences of a delay between the outputs of the quadrature mixer, which arise when digital samples of the quadrature baseband signals are not synchronised, i.e. when the real and imaginary components have been shifted by one or more samples with respect to each other. Through analytical considerations and simulations of such an error on different synthetic signals, we show how this error can be expected to afflict different measurements. In addition, we show the effect of the error on actual incoherent scatter radar data obtained by two different digital receiver systems used in parallel at the EISCAT Svalbard Radar (ESR). The analytical considerations indicate a procedure to correct the error, albeit with some limitations due to a small singular region. We demonstrate the correction procedure on actually afflicted data and compare the results to simultaneously acquired unafflicted data. We also discuss the possible data analysis strategies, including some that avoid dealing directly with the singular region mentioned above.
Highlights
An analog baseband receiver processes the complete spectral information in the input signal by mixing to baseband and lowpass filtering before sampling to eliminate the redundant upper sidebands and for bandwidth matching
We address the consequences of this error on the spectrum of incoherent scatter signals using first theoretical considerations; we show the effect of the error on simulated incoherent scatter signals; we deliberately replicate the error on unafflicted real-life data, and compare it to data taken in parallel with a different receiver that inadvertently had the error; we describe a way to correct for the error, and demonstrate it on the real-life afflicted data; we discuss different ways to deal with the error when analysing data for plasma physical parameters
The top left panel shows data taken in the MIDAS-W system, unafflicted by the 1-sample shift, while the bottom right panel shows the corresponding data obtained in the standard EISCAT Svalbard Radar (ESR) digital receiver, where the imaginary part of the signal was inadvertently advanced by 1 sample, corresponding to a delay of −20 μs
Summary
When such receivers are realised in analog hardware, common problems are mismatches in phase or gain between the two signal paths. For τ =0 and zero frequency, the effect is likewise nil, but as the frequency of the tone increases, the phase shift of the imaginary part increases, and when ωsτ =π/2, the phase difference between the real and imaginary parts has increased to π, which means that the real and imaginary parts have exactly opposite phase This is equivalent to a purely real signal and it has a symmetric spectrum. If the tone frequency is increased to ωsτ =π , the phase difference between the real and imaginary parts is 3π/2, which corresponds to a signal e−iωst , where all the signal power has moved over from ωs to −ωs It should be clear from this simple picture that advancing or delaying either part of the signal has the same effect on the observed spectra. Afterwards, more realistic synthetic signals can be studied subjected to the same relative delay
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