The Parks-McClellan algorithm offers an optimum FIR filter design technique that attempts to design the best filter possible for a given number of coefficients. Such a design reduces the adverse effects at the cutoff frequencies. It also offers more control over the approximation errors in different frequency bands control that is not possible with the window method.
Using the Parks-McClellan algorithm to design FIR filters is computationally expensive. This method, however, produces optimum FIR filters by applying time-consuming iterative techniques.