This paper discusses the derivative x(z) in which the order z is an arbitrary complex number. Earlier research [2,3] and patented inventions by the author [5,6,7] employ the derivative x(α), where α is a real number and discuss its application to condition monitoring and active vibration control. The results obtained here indicate that x(z) can also be used for this purpose and that in certain
... [Show full abstract] cases it provides a more reliable picture of the condition of a machine than do the signals based on x(α).