| Hi-index | 35.68 |
The authors propose the use of transition bands and transition functions in the ideal amplitude frequency response to allow the analytical design of optimal least-squared-error FIR digital filters with an explicit control of the transition band edges. Design formulas are derived for approximations to ideal frequency responses which use pth-order spline transition functions. A mixed analytical and numerical method for zero-error weight in the transition bands and passband and stopband error weighting functions with an integral squared error approximation are derived. A variable-order spline transition function is developed, and a method for choosing the optimal order to minimize the integral squared approximation error is given