**3. Basic joint time / frequency analysis**

106 Advances in Wavelet Theory and Their Applications in Engineering, Physics and Technology

One of the main objectives of developing a surface quality evaluation system was to be able to detect variations in surface quality from time to time which actually may be viewed as discontinuities. Besides detecting if a random or periodic component exists it is also important to determine if the defect is consistent (stationary) or if it changes with time (non-stationary). This can occur in practice from such things as a failure in the feed system or variation in thicknesses of a board being planed. The problem in defining a non-stationary surface is linked to the time frame being observed. A sanding ridge can be considered non-stationary when only a small sample distance is considered (one board), however, if the ridge occurs over numerous boards and all boards are included in the analysis, then the ridge can be considered stationary as far as the process is concerned. Traditional time and frequency analyses cannot distinguish between stationary and non-stationary surfaces. The following section illustrates this shortcoming and discusses some recent developments in **joint time-frequency analysis (JTFA)** that may overcome these shortcomings in surface quality assessment. Figure 4 illustrates the difficulty or shortcomings of traditional frequency analysis. Two significantly

These two examples show the weakness of traditional frequency analysis in the current descriptions of wood surface applications. Though both signals have a similar frequency spectrum, one signal is non-stationary (top – left) where the other one (lower – left) is

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Spatial Frequency (marks per inch) 0 5 10 15 20 25

stationary. This illustrates a need for a more advanced form of frequency analysis.

**2.2.3 Shortcomings of simple time and frequency analysis** 

different surface profiles can result in similar frequency spectra.

Fig. 4. Two types of signals that have similar frequency spectra

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Distance (inches) 0.0 0.5 1.0 1.5 2.0

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