## 1 Introduction
Noticeably, these devices perform better than other types of contactless sensors, e.g., Laser Doppler devices [11]. However, a potential shortcoming of the RAR technique is that the motion of the soil the RAR system is installed on is combined with the motion of the building, so that the relative motion between the building and the RAR device may be unknown and/or blurred on the recorded signals. Nevertheless, the structural response clearly enhances the modal frequencies of the building, thus making their identification and isolation easy in the RAR recorded signals using advanced methods for signal analysis--narrow band pass Butterworth filtering, in our case. This issue would be particularly relevant if measurements were taken during strong ground motion due to great earthquakes, since the device's base is not fixed, and the ground motion would be important. Considering these effects, up-to-date RAR devices incorporate an accelerometer, allowing RAR operators to properly address this issue. In any case, the RAR device used in the case study shown in this article may not be suitable for use during great earthquakes. As this method is also intended to be used after damaging earthquakes, in these cases, people with responsibilities for emergency management, usually including firemen, civil protection personnel and other authorities, should identify buildings that require study and suggest proper locations that are stable, safe and proper for the easy and fast installation of the equipment in front of the buildings/structures to be surveyed. The use of the RAR to determine the dynamic properties of buildings is a present and actual issue [12; 13]. Remote RAR measurements have been widely and successfully used for monitoring large civil structures including bridges and towers [14; 15; 16; 17; 18], wind turbines [19; 20], chimneys [21; 22; 23; 24], and heritage and high-rise buildings [25; 26; 27; 28]. However, combined accelerometric- and RAR-based applications to damaged low- and mid-rise conventional buildings are not so frequent nor so successful, mainly because of the low periods (high frequencies) and very low displacements involved, which may compromise the ability of techniques based on RAR technology to help in these cases. In this article, both methods are applied to a mid-rise building that was severely damaged during an actual earthquake, providing insight into the ability of RAR to properly address these kinds of problems. Extending the use of RAR to mid-rise buildings is of great importance, not only because this typology of buildings represents a large amount of the structures built in the world but also because it is among the most vulnerable structures in seismic scenarios. The signal analysis techniques often used to analyze the acceleration and displacement-time histories are the power spectral density (PSD), periodogram, and peak picking method (PPM). In this article, other methods such as the cross power spectral density (CPSD) and the magnitude-squared coherence (MSC) are investigated. These advanced methods may help to overcome issues from high noise amplitudes compared to the very low amplitudes of the building displacements, significantly improving the resolution and the quality of the obtained results. Finally, joint synchronous analyses of the acceleration-time histories will allow us to identify not only the main modal frequencies but also the type of motion involved, which, in our case, are rotation and translation, respectively, for the first and second modes of vibration. In addition, the joint analysis of the synchronous displacement-time histories of the Rhins, corresponding to microwaves reflected at different heights of the building, will indicate the ability of RAR measurements dealing with the corresponding modal shape. In this study, the use of RAR for the identification of fundamental frequencies in a building that suffered severe damage during the May 11 th 2011 earthquake is analyzed and discussed.