The separation of multiple signals from their superposition recorded at several sensors is addressed. The methods employ polyspectra of the sensor data in order to extract the unknown signals and estimate the finite impulse response (FIR) coupling systems via a linear equation based algorithm. The procedure is useful for multichannel blind deconvolution of colored input signals with (possibly) overlapping spectra. An extension of the main algorithm, which can be applied for quasiperiodic signal separation, is also given. Simulation results corroborate the applicability of the algorithm.