In magnetomotive ultrasound, real-time capability is useful for the alignment of magnetic coils and ultrasonic transducers and it is considered as necessary for clinical applications. Since usually a harmonic motion is induced, the magnitude of the displacement is often estimated via Fourier transform of the phase of IQ-data. However, a standard block-by-block processing of IQ-data data can limit estimator performance. Here, hardware-and estimator-parameters are decoupled by implementing a recursive algorithm. Therefore, a sliding windowed infinite Fourier transform was used. The different characteristics of the block-by-block and the sliding processing are demonstrated. A higher performance of the recursive algorithm was shown with simulated data at low signal-to-noise ratios. The implementation on an ultrasound research platform confirmed real-time capability. The presented algorithm is expected to be easily implemented on any ultrasound system. Future work needs to address the optimal parametrization in real-world scenarios.