#### Analysis and processing of vibration signals (Signal Processing)

###### In the case of rotating machines, the use of vibration signals such as acceleration, speed and displacement because these signals contain dynamic information about the state of the machine; It is effective in identifying and distinguishing between various defects. Methods of analysis and troubleshooting in rotating machines with the help of vibrating signals can be divided into the following three categories:

###### • Time domain analyzes

###### • Frequency domain analyzes

###### • Time-frequency domain analyzes

###### Time domain analyzes are directly based on time waveform. Traditional time domain analysis calculates characteristic features in the form of statistical descriptions of time waveform signals. Features such as mean, peak, crest coefficient, and high-order statistics such as root mean square, skewness, kurtosis, and more. These features, mostly called time domain features, are used with limited ability to detect local defects. Common time domain analytical approaches, such as simultaneous averaging, and the self-reversing model, are widely used to troubleshoot rotary machines.

###### Frequency domain analyzes or spectral analyzes are generally performed by Fourier transform. Fourier analysis converts a time domain signal f (t) to a frequency domain; So that the generated spectrum F (ω) includes all the signal frequency content (base and harmonic) which is defined as the following relation:

###### But the most important drawback of FFT is its inability to provide information about the time conditions of the signal spectrum; So that the results are averaged over the entire signal range. This will cause problems in the analysis of non-static signals. In such cases, having a relationship between the time and the frequency content of the signal can be useful. This severe limitation of FFT has led to the use of time-frequency signal analysis tools such as "Fourier transform short time" (STFT), or "Winger Ville distribution" (WVD) and so on. The STFT method converts a signal into a two-dimensional function of time and frequency. The short-time Fourier transform, or STFT, performs a "time-localized" Fourier transform on the x (t) signal sequentially, using a slider window function g (t) to temporally centered. As a result, changes in the frequency content of the signal contained within the time window function appear. This process can be seen in the following figure: