Thanks to the recent development of sensors and Internet of Things (IoT), it is now common to use mobile application to monitor health status. These applications rely on sensors embedded in the smartphones that measure several physical quantities such as acceleration or angular velocity. However, these data are private information that can be used to infer sensitive attributes. This paper presents a new approach to anonymize the motion sensor data, preventing the re-identification of the user based on a selection of handcrafted features extracted from the distribution of zeros of the Shot-Time Fourier Transform (STFT). This work is motivated by recent works which highlight the importance of the zeros of the STFT Flandrin (IEEE Processing Letters 22:2137-2141, 1) and link them in the case of white noise to Gaussian Analytical Functions (GAF) Bardenet et al. (Applied and Computational Harmonic Analysis 48:682-705, 2) where the distribution of their zeros is formally described. The proposed approach is compared with an extension of an earlier work based on filtering in the time-frequency plane and doing the classification task based on convolutional neural networks, for which we improved the evaluation method and investigated the benefits of gyroscopic sensor’s data. An extensive comparison is performed on a first public dataset to assess the accuracy of activity recognition and user re-identification. We showed not only that the proposed method gives better results in term of activity/identity recognition trade-off compared with the state of the art but also that it can be generalized to other datasets.