What techniques might one use to estimate the onset time of a sinusoidal tone burst in a noisy signal?
Assume the tone burst has a known fixed frequency (but unknown phase) and a very sharp rise time, and that the goal is to estimate the onset time within better than half the rise time, and/or one period of the frequency of the tone, if possible. How might the estimation techniques change if the S/N ratio is very low (much less than 1)?
Added: Assume the tone burst is of unknown length, but longer than a small multiple of the rise time and the frequency period.
Added: A DFT/FFT shows the very probable existence of a tone. The problem is figuring out exactly precisely where in the FFT window the tone (or perhaps multiple tone bursts of the same frequency) may have started within the FFT window, or determining if the current tone started outside that DFT window, provided I have all that additional time domain data.
Radar pulse detection accuracy is closer to the resolution I need, except I only have an edge, as the tone is of unknown length, and, other than a known rise time, unmodulated. Narrow band pass filters distort the rise time, and thus kill edge arrival estimation resolution.
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