Patent ID: 6885713

Claim:
A method of designing a filter for a multiple access communications system which minimizes crosstalk between channels comprising the step of identifying signals s 2 (t) having a first property of which an autocorrelation function associated with said s 2 (t) signals decay rapidly from a central lobe at a higher than 1/x rate which is typical of a wavelength division multiplexing communications system and having a second property in which the zero points of the autocorrelations function have high order multiplicities, the method,—further comprising the steps of: (a) choosing a signal s(t) which is periodically orthogonal to its translates; (b) determining a first autocorrelation function associated with s(t); (c) denoting the Fourier transform of s(t) to be S(f); (d) denoting the Fourier transform of said first autocorrelation function of s(t) as H(f); (e) determining said Fourier transform, H(f), of said first autocorrelation function of s(t) in accordance with the equation H(f)=|S(f)| 2 ; (f) forming the Fourier transform of a second autocorrelation function by convolving H(f) with itself; (g) determining said convolution according to the equation G(f)=Conv(H(f), H(f)), wherein G(f) is a new autocorrelation function by convolving H(f) with itself; (h) determining the square root of G(f); (i) denoting said square root of G(f) as S 2 (f); and (j) taking the inverse Fourier transform of S 2 (f).