## 4 Vibroarthrography of the Knee Joint
### VAG Signal Preprocessing and Filtration  
Signal processing and filtering is another key step in VAG signal analysis. Its purpose is to prepare data for further analysis by eliminating interference and improving the signal quality. The signal is preprocessed to minimise measurement artifacts that can negatively affect the accuracy of signal analysis. The most common artifacts are random noise, muscle contraction interference (MCI), baseline wander, and low-frequency motion artifacts [116; 42; 117]. Thermal effects of electronic components in the measuring system and semiconductor defects in medical instruments can also generate random noise [118]. MCI is a disturbance resulting from muscle activity or, more precisely, mechanical vibrations of muscles near the knee joint. The resulting acoustic waves interfere with the signal from the joint movement, making it difficult to distinguish the muscle signal from the joint signal. Baseline wander is caused by the patient's body movements resulting from pain during the movement. Low-frequency motion artifacts are caused by improperly attached sensors, a lack of stability during measurement, and external body movements. VAG signal filtration is based on two main types of filters, which include fixed and adaptive filtering. Fixed filtering includes band-pass filters and low- and high-pass filters. Band-pass filters are used to pass signals in a specific frequency range. The VAG signal removes higher and lower frequency components that are important for signal analysis. The frequency of the vibroarthrographic signal is usually in the range of 10 Hz to 2 kHz, which corresponds to the natural vibrations of the knee joint. A fourth-order digital Butterworth band-pass filter with cut-off frequencies between 50 Hz and 1000 Hz was used in the work of [PERSON] et al. [100]. Low-pass filtering attenuates higher frequencies than a set threshold and is used to remove interference that may come from external sources. An example of a low-pass filter is the 20 th-order cascade moving average filter, which is used to remove the baseline wander artifact in the work of [PERSON] et al. [119]. This is a type of digital filter that performs multistage filtering based on a moving average. Its purpose is to smooth the signal while suppressing higher frequencies. The filter structure consists of stages (cascades), each of which increases the accuracy and improves the filtering efficiency. Cascading the filter allows for more effective smoothing of the signal while maintaining its key features [120]. Low-pass filtering was also used in the work of [PERSON] et al. [121]. A finite impulse response (FIR) moving average filter was used to locally smooth the signal and thereby remove its noise [122]. Another filter belonging to this type of filtration is the Butterworth filter used by [PERSON] et al. [88]. It removed frequencies above 100 Hz, after which a notch filter was used to remove power line interference (PLI) at 50 Hz. [PERSON] et al. [11] used semi-automatic segmentation using a relative angular signal to extract the extension and flexion cycles from the VAG signals. The analogue signal was then low-pass filtered using an RC filter with a cutoff frequency of 4.5 Hz. The aim of the filtering was to suppress signals originating from small muscle movements or tremors. Cycles with a variance exceeding twice the variance of the entire segment were excluded. Cycles shorter than one second were also excluded as they did not comply with the measurement protocol. Cycles with values at the border of the analogue-to-digital converter saturation were also rejected because the cycles of the VAG signals without artifacts were below this limit. [PERSON] et al. [108] implemented the cascaded moving average filter (CMA) to evaluate and remove baseline wander from the raw VAG signal. The principle of its operation is based on cascading several moving average filters, which allows for better smoothing of signals.