becomes 



• a-1 



A «" a 



A/X - a 



Simply stated, for b - -1, the ratio of amplitude to wavelength (or 

 height to width) is constant and equal to a at all scales. This 

 condition was termed "self-similarity" by Mandlebrot (1982) and corre- 

 sponds to a fractal dimension of D » 1.5. 



One might visualize the special case b >■ -1 as a signal which 

 appears identical at all scales of observation. In another sense, the 

 signal appears equally "rough" at all scales, the magnitude of roughness 

 being prescribed by the magnitude of a. In cases where -1 < b < 0, the 

 ratio of height to width tends to decrease at longer wavelengths, 

 although the absolute amplitude does Increase. Such signals appear 

 rougher at high frequencies. The converse case of b < - 1, implies that 

 the ratio of height to width increases at longer wavelengths, and there- 

 fore the signal appears smoother at high frequencies. Figure 5-2 sum- 

 marizes these relationships. 



53 



