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The present invention comprises a method of obtaining coefficients for a transmit filter such that the power spectral density of the output for the different frequencies comes close to but does not exceed a maximum power spectral density of a communication(s) standard. By first doing a convex optimi

The present invention comprises a method of obtaining coefficients for a transmit filter such that the power spectral density of the output for the different frequencies comes close to but does not exceed a maximum power spectral density of a communication(s) standard. By first doing a convex optimization procedure to obtain the autocorrelation coefficients for the filter and then using the autocorrelation coefficients to determine the filter coefficients, a low-order filter that closely approximates the desired output power spectral densities can be produced.

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1. A digital transmit filter for a communication system having a maximum prescribed output power spectral density, the digital transmit filter having filter coefficients selected such that the output power spectral density of the system is below the maximum output power spectral density of the commu

1. A digital transmit filter for a communication system having a maximum prescribed output power spectral density, the digital transmit filter having filter coefficients selected such that the output power spectral density of the system is below the maximum output power spectral density of the communication system, the filter coefficients being selected from optimized autocorrelation coefficients for the filter in a convex optimization procedure. 2. The digital transmit filter of claim 1 wherein spectral factorization is used to determine the filter coefficients from the autocorrelation coefficients. 3. The digital transmit filter of claim 2 wherein spectral factors of the spectral factorization are found using a root finding method. 4. The digital transmit filter of claim 1 wherein the system includes an interpolating filter that affects affects the total output power spectral density of the system. 5. The digital transmit filter of claim 1 wherein a discrete approximization of an upper bound constraint is done in the convex optimization procedure. 6. The digital transmit filter of claim 1 wherein the digital transmit filter is implemented with different coefficients for upstream and downstream directions. 7. The digital transmit filter of claim 1 wherein the digital transmit filter has fewer than one hundred coefficients. 8. The digital transmit filter of claim 1 wherein the digital transmit filter has thirty-two or fewer coefficients. 9. A method of determining filter coefficients for a digital transmit filter of a communication system having a maximum prescribed output power spectral density, comprising optimizing autocorrelation coefficients for the digital transmit filter in a convex optimization procedure; and determining the filter coefficients from the autocorrelation coefficients. 10. The method of claim 9 wherein the filter coefficients are determined from the autocorrelation coefficients using spectral factorization. 11. The method of claim 10 wherein the spectral factorization is done using a root finding method. 12. The method of claim 9 wherein a discrete approximization of an upper bound constraint of the autocorrelation coefficients is done in the convex optimization procedure. 13. The method of claim 9 wherein the digital transmit filter is for a DSL system. 14. The method of claim 13 wherein the digital transmit filter is for a high-bit DSL system. 15. The method of claim 9 wherein the digital transmit filter has fewer than one hundred coefficients. 16. The method of claim 9 wherein the digital transmit filter has thirty-two or fewer coefficients.