Equiripple FIR Filter Design By The FFT Algorithm - IEEE Signal Processing Magazine

he Fast Fourier Transform (FFT) algorithm has been used in a variety of applications in signal and image T processing [1-51. In this article, a simple procedure for designing Finite-extent Impulse Response (FIR) discretetime filters using the FFT algorithm is described. The zerophase (or linear phase) FIR filter design problem is formulated here to altemately satisfy the frequency domain constraints on the magnitude response bounds and time domain constraints on the impulse response support 16-81, The design scheme is iterative in which each iteration requires two FFT computations. The resultant filter is an equiripple approximation to the desired frequency response. The main advantage of the FFT-based design method is its implementational simplicity and versatility. Furthermore, the way the algorithm works is intuitive and any additional constraint can be incorporated in the iterations, as long as the convexity property of the overall operations is preserved [6]. In one-dimensional cases, the most widely used equiripple FIR filter design algorithm is the Parks-McClellan algorithm [7]. This algorithm is based on linear programming, and it is computationally efficient. However, it caninot be generalized to higher dimensions. Extension of om design method to higher dimensions is straightforward. In this case two Multi-Dimensional (M-D) FFT computations are needed in each iteration [8].