## 1 Introduction  
Global aging is a phenomenon known to have resulted from increasing longevity. Every year, the proportion population aged over 65 is growing [1, 2]. The aging process is characterized by unfavorable changes in the body's systems and organs, which may cause impaired coordination and loss of balance during changes in body position. These changes increase the chance of falls. Falls are the most common cause of accidents among the elderly [3] and are responsible for various injuries, including serious injuries that frequently lead to functional dependencies. The most common such injury is hip fracture. One of the circumstances influencing the severity of fall consequences in the elderly is the length of time for which the victim is waiting, immobile on the ground, for help. Less time spent waiting for help is related to less-severe health consequences and a higher chance of successful recovery and return to normal life.  
Consequently, experts are increasingly working toward the development of effective fall detection systems and techniques. Several fall detection systems have recently been proposed in the literature [4, 5]. Most studies divide fall detectors into two main categories: wearable and non-wearable. Wearable devices [4, 5, 6] are inexpensive but have some significant disadvantages, including the need to remember to wear the device. An elderly person may forget to put on the device or refuse to wear it for comfort reasons. Moreover, push-button devices are battery-operated and require the individual to be able to press the button after a fall. Fall detection systems that are non-wearable seem to be more promising than those that are wearable, because they do not require additional effort from the individual after the system has been installed at the user's home.  
Non-wearable fall detection methods are non-obtrusive and can be optical (e.g., video-based) [4; 7] or non-optical, based on ultrasonic [8], pressure [9] or vibration sensors [10], among others. In this work, we focus on fall detection based on millimeter-wave (MMW) radar.  
Recent technological developments have resulted in MMW radar becoming an increasingly commercialized and applicable technology. This radar is employed as a detection measure in many applications, such as in collision avoidance radars in automobiles [11] and in stand-off remote sensors in homeland security applications [12; 13; 14]. Detection of a person using Doppler MMW radar has several advantages compared to other remote sensing technologies. Due to its high transmission frequency, the transmission power is low, its dimensions are small and the transmission angle is wide.  
The micro-Doppler signature of a moving person is a time-varying frequency shift caused by the relative movement of separate parts of the body; it can be studied to extract additional information on an individual's movement characteristics [13]. Several works exploiting micro-Doppler signatures for human identification have been published [13; 15; 16]. To enable the detection of a fall incident, we started with the development of motion classification algorithms. These provide the system with knowledge regarding various types and forms of motion and enable it to identify specific patterns and detect anomalies. This paper is concerned with practical issues involving efficient algorithm system implementations. The goal of this study was to develop a motion classifier and build a fall detection application that can be further developed and deployed in users' homes.  
This paper is organized as follows: In Section 2, we describe the principles of continuous-wave micro-Doppler radar operation. In Section 3, we explain how to create an optimal spectrogram using short-time Fourier transform. The experimental setup is presented in Section 4. In Section 5, we describe the method of fall detection using spectral signatures and present the experimental results. In Section 6, we summarize and conclude the paper.