# Hand Gesture Recognition on Edge Devices:
## 5 Pre-Processing/Signal Processing
### Range-Doppler Map, Range-Angle Map, Doppler-Angle Map  
The RDM is a matrix or an image created by applying the 2D Fourier transform to the received data. In a first step, the raw data is depicted as an array. That creates a matrix of amplitude values. On the x-axis each step corresponds to one data frame. Each frame corresponds to one pulse or chirp. The data along the y-axis represents the values gathered within one frame. Thus, each step on the y-axis is a time step of the sample frequency. The Fourier transforms for range are in the direction of slow-time and for Doppler in the fast-time direction. Doppler means the frequency shift through Doppler effect caused by an object that moves towards or away from a frequency source. Angle is estimated by evaluating the phase shifts between several receiving antennas. As the distance among them and the distance between receivers and sender are known this allows to calculate the direction of an object. A segmented sample of an ultrasonic push-pull gesture is depicted in Figure 12, where the z-axis corresponds to the amplitude values. The same data is plotted in 2D in Figure 13. Figure 14 shows the full sample. We can see that the segment zooms into a part in the middle, bottom of it. Figure 7 is derived through application of one Fourier transform in the fast time direction. That means along each pulse. Finally, Figure 15 shows the actual RDM. As the input to the Fourier transform is real data, the image is symmetrical. Micro-Doppler maps are spectrograms. Both represent frequency components of a signal over time. This type of pre-processing is used to evaluate smaller displacements sometimes on top of a large movement with higher granularity.  
How closely related the topics of radar and ultrasound-based HGR are shows in the interrelation of papers [8; 47; 48; 49]. Ref. [47] is an extension of [48], which is based on [49]. And [49] uses the same features as the authors in this FMCW radar application [8]. The features were selected according to a feature selection algorithm described in [8]. All systems are based on pulsed actuation. In case of radar the pulse consists of a sweep, for  
Figure 11: 8 ultrasound sender at \(\frac{3}{2}\) spacing, 24.5 kHz frequency, 45\({}^{\circ}\) steering.  
ultrasound one constant frequency of 40 kHz is being sent. In all cases the first step is to calculate the RDM. This pre-processing consists of several steps. First, the amplitude values are divided in the pulse trains and stacked such that the pulse trains are represented in x-direction and the y-direction ticks are steps from one pulse train to the next. Therefore, the x-direction is called fast time and the y-direction slow time. The following steps are an FFt in x- and in y-direction. The change in frequency along fast-time represent velocity of an object perpendicular to the sender, while changes in frequency among consecutive pulses represent distance changes. The creation of a RDM is explained in more detail in Section 5.5. A range-doppler image of ultrasound sensor data is depicted in Figure 15. As one of these maps can be created per sensor, stacking temporarily connected maps creates a data cube. Differences between the maps of several sensors add information about the location and direction of travel of objects in the field of view.  
Figure 12: Raw ultrasound data sample in 3D.  
Figure 13: Raw ultrasound data sample in 2D only segmented part plotted.