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Measurement of external magnetic fields provides information on electric current distribution inside an object. For example, in magnetoencephalography modern measurement devices sample the magnetic field produced by the brain in several hundred distinct locations around the head. The signal space separation (SSS) method creates a fundamental linear basis for all measurable multichannel signal vectors of magnetic origin. The SSS basis is based on the fact that the magnetic field can be expressed as a combination of two separate and rapidly converging expansions of harmonic functions with one expansion for signals arising from inside of the measurement volume of the sensor array and another for signals arising from outside of this volume. The separation is based on the different convergence volumes of the two expansions and on the fact that the sensors are located in a source current-free volume between the interesting and interfering sources. Individual terms of the expansions are shown to contain uncorrelated information of the underlying source distribution. SSS provides a stable decomposition of the measurement into a fundamental device-independent form when used with an accurately calibrated multichannel device. The external interference signals are elegantly suppressed by leaving the interference components out from the reconstruction based on the decomposition. Representation of multichannel data with the SSS basis is shown to provide a large variety of applications for improved analysis of multichannel data.