The Design of FIR Digital Filter Using Orthonormal Expansion

This paper presents an algorithm for the design of arbitrary FIR filters, using orthonormal expansion principle in which Hermite-Gaussian functions serve as orthonormal basis set. Since Hermite-Gaussian functions are eigenfunctions of Fourier transform, the orthonormal basis constituted by them bridges between the magnitude and the impulse response, leading to a very simple mapping from the frequency-domain specifications to the time-domain filter coefficients. Experimental result shows our algorithm is more efficient than the referenced Kaiser-window method