What is meant by "arbitrary" in the context of digital filter design? I try to understand the 'arbitrary' what does it meant?
I had read many references ,such a one it is 'begin the process with a transfer function of your choice' ,in other reference :related by the starting point,

In other hand i read about Chebyshev approximation with arbitrary magnitude,
how can i find the better design with arbitrary magnitude ?
any method of design have a criteria ,the 'arbitrary' related by the method of design or related by the transfer function?
The term "arbitrary" in this context refers to the desired frequency response, and what it means is that the respective design method accepts any desired response. So unlike required by many standard design routines, the magnitude response does not need to be piecewise constant or linear, and, more importantly,  the phase response need not be linear or minimum-phase. The corresponding design problem is a complex approximation problem because the desired frequency response which must be approximated is a complex-valued function.