## 3 Results and Discussion
### The Influence of the Measured Signal's Oscillation  
This section examines how the oscillation of the measured signal affects the error in the numerical integration used to calculate the total impulse. It is well understood that the issues to be considered in thrust measurement during static testing are the resonant vibration characteristics between the mounting structure and the installed rocket motor [1]. The oscillation in the signal measured by the load cell during static rocket motors tests can result from a combination of factors. Among the most common are mechanical vibrations induced by the motor's operation, such as gas flow turbulence, which are transmitted to the load cell and cause signal oscillations. This phenomenon is typical in static tests due to the strong interaction between the motor and the test stand. Another relevant factor is structural resonance, which occurs when the test stand or the motor itself operates at a frequency close to its natural resonance frequency. This amplifies vibrations and consequently affects the thrust measurement. Additionally, electronic noise can influence the load cell's signal, caused by electromagnetic interference from cables and other equipment at the test site. Inadequate sampling frequency can also lead to distortions. If the data acquisition rate is not high enough to accurately capture the load cell's response, phenomena such as aliasing may occur, resulting in apparent signal oscillations. Finally, dynamic coupling between the motor and the load cell may introduce additional forces resulting from lateral or angular movements, leading to undesirable signal oscillations. To mitigate these effects, some solutions include applying digital filters, such as the low-pass filter, which attenuates high-frequency oscillations, and the notch filter, which eliminates specific frequencies, such as resonances and electromagnetic interference. Another approach is to use vibration dampers, shock absorbers, or isolating supports between the motor and the load cell, as well as analyze and adjust the natural frequencies of the test structure, thus avoiding unwanted resonances. These factors directly impact the accuracy of the total impulse calculation, as signal oscillations can distort the result of the thrust integral over time. Properly controlling these variables is essential to ensure reliable measurements. In this study, we apply digital signal filters to mitigate the oscillation. To evaluate how the application of a digital filter affects the numerical integration of the thrust signal in obtaining the total impulse, we will conduct a case study based on a thrust signal acquired during the static firing test of a rocket motor in the Army Technology Center's laboratory. Figure 5 shows the profile of this signal. The reference signal exhibits an oscillatory behavior that can impact measurement accuracy, particularly in applications such as numerical thrust integration. Using MATLAB R2024b software, we analyzed the frequency distribution of the reference signal through a Fast Fourier Transform--FFT--to identify frequency components contributing to the observed oscillatory characteristics. This technique enables a clear examination of the signal's frequency distribution, aiding in the identification of components that contribute to the oscillations. With this information, we can select and adjust an appropriate digital filter to effectively attenuate unwanted oscillations, enhancing the thrust signal quality and achieving more precise total impulse measurements. Figure 6 illustrates the frequency spectrum of the normalized thrust signal. The frequency spectrum analysis of the reference signal revealed oscillations at 47 Hz, 77 Hz, 180 Hz, 300 Hz, and 360 Hz. Two types of digital filters were applied to filter out these unwanted oscillations: first, third-order notch filters at 47 Hz and 77 Hz, followed by a low-pass filter with a 100 Hz cutoff frequency to mitigate the inherent oscillations in the thrust signal.