Theoretical and experimental methods of correlation processing of the speckle signals formed by a single-fiber multimode interferometer are investigated and demonstrated. These methods are based on (1) a photographic filter, (2) a standard computer, and (3) analog computing approaches. All of these methods enable the transformation modulation of the speckle pattern to be either optical or electrical signals, which linearly depend on correlation coefficients of reference and current speckle patterns. The functional dependence of the correlation coefficient on the value of the length of the interferometer is studied, enabling quantitative measurements of the length. Standard optical and electrical components are utilized, making the methods suitable for industrial use.