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Given a band limited signal which over some disjoint intervals of time In behaves as a corresponding linear combination fn(t) of up to N damped sinusoids, we present a method which detects intervals In, determines the number of the sinusoidal components over each interval and estimates their frequencies, with high accuracy and in the presence of noise which can be colored. Intervals In can have very short duration of just a dozen Nyquist rate intervals, hampering the use of the Fourier transform based methods. Our method operates entirely in the time domain; to be applicable, the signal must be sampled at a rate higher than the Nyquist rate. It is based on analyzing local signal behavior using special, numerically robust linear differential operators, called the chromatic derivatives, which were introduced relatively recently, and which hold yet unexplored promise in signal and image processing.