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Since the canonical algorithm for computing the SNR defined above assumes a solitary frequency spike at the signal frequency superimposed on a smooth background, it can fail here dramatically. Although the eye may be able to pick out the small signal spike riding atop the peaks and valleys, it is difficult to fully automate this discrimination, especially in situations where the signal spike is very near a valley or peak. Fortunately, in this system, for small signal amplitudes, the only change in the spectrum due to the addition of a weak signal is a small spike at the signal frequency. Consequently, we estimate the background spectrum as (Formula presented) in computing the SNR
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Since the canonical algorithm for computing the SNR defined above assumes a solitary frequency spike at the signal frequency superimposed on a smooth background, it can fail here dramatically. Although the eye may be able to pick out the small signal spike riding atop the peaks and valleys, it is difficult to fully automate this discrimination, especially in situations where the signal spike is very near a valley or peak. Fortunately, in this system, for small signal amplitudes, the only change in the spectrum due to the addition of a weak signal is a small spike at the signal frequency. Consequently, we estimate the background spectrum as (Formula presented) in computing the SNR.
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