A complex Chebyshev approximation algorithm for FIR filter design

We present an algorithm for computing a real coefficient FIR filter that approximates a desired frequency response. The error criterion used is the complex Chebyshev norm of the weighted error function. The procedure is developed by utilizing the characterization theorem for linear complex Chebyshev approximation. Our algorithm is substantially faster than existing approaches and requires O(N/sup 3/) computations, where N represents the filter length. It has been tested in many applications and has been observed to result in the unique optimal solution.<>