[math-fun] Fourier transforms

I hope that this is a trivial question. Fourier analysis can easily separate out the various sinusoidal frequencies in a waveform. Is there an analogous analysis that can separate out various real exponentials in a real waveform? I.e., if a signal is the sum of various real exponentials (i.e., no sinusoidal components), is there a simple analysis that will pull out the coefficients & exponents? Is there a "fast" version analogous to the FFT for this procedure? I recall studying Laplace transforms, but can't recall whether they solve this particular problem. Thanks for any references on this problem.