1. Introduction

Signal processing applied to vibration signals involves many techniques allowing the investigation of the machine reality through the signal representation.Among all, the time waveform  and spectral representations are the most popular.

Each one of these has its own advantages and disadvantages that we list in the following table:

A simple reading of the above table shows that the disadvantages of each technique are compensated by the advantages of the other.

Here comes the utility and the originality of the Time frequency representation, it combines the time waveform and the spectral representations and thus eliminates all the disadvantages.

2. Challenge

The challenge is a competition between time waveform, spectral, and Time Frequency representations to recognize a combination of 4 numbers typed on a telephone keypad.

The frequency representation allows us to pinpoint the frequencies containing the energy of the signal - recognize the used keys, while the time waveform representation gives us the time duration of each event (0.2s).

The time-frequency spectrogram combines these two points in the following table:

The spectrogram in this case is the only technique understanding the reality of the phenomenon.

Can you tell which are the used keys in order? Leave your answer in a comment below.

3. Vibration case study:

Original Signal measured on a bearing with an outer ring defect BPFO= 96.4Hz

3.1 Wavelet Recursive filters

4.Results