Method and apparatus for spectral shaping in signal-point limited transmission systems

A method of lossless spectral shaping or coding of source samples to transmitted samples based on a set of predetermined characteristics of a frequency spectrum, where the allowable signal levels of the transmitted samples are limited to a predescribed set, comprising the steps of:

• a) for each source sample, calculating any one of the following:
• i) an RDS, to obtain a measurement of the DC component of the source sample up to this block;
• ii) a RDFT or RFFT, to obtain a measure of unwanted signal components of the source sample up to this block;
• iii) a Running Filter Sum, to obtain a measure of unwanted signal components of the source sample up to this block;
• b) for every block of a determined plurality (“N”) of source samples, computing an objective function based on the measure obtained from Step a), wherein said objective function shapes the source samples to a predetermined spectrum characterized by a set of filter coefficients associated with a transmitter of said transmitted samples;
• c) for every block of said determined plurality (“N”) of source samples, selecting one of:
• i) at least one redundant sample,
• ii) at least one redundant sign or
• iii) both of at least one redundant sample and at least one redundant sign,
• to optimize the objective function in Step b).

In a transmitter for data communications with a limited number of signal points, a method of spectral shaping transmitted samples, wherein each transmitted sample is either of an unmodified source sample or a dependent sample comprising the steps of:

• a) for each transmitted sample xn, calculating K values of cn(k):
• c n ( k ) = ∑ m = 0 n ⁢ x m ⁢ ⅇ - jω k ⁢ m ⁢ ⁢ ω k = 2 ⁢ π ⁢ ⁢ f k ⁢ T , k = 0 , 1 , … ⁢ , K - 1 , K ≥ 1 ;
• b) calculating a measure of unwanted signal components C n = 1 K ⁢ ∑ k = 0 K - 1 ⁢ [LeftBracketingBar] c n ( k ) [RightBracketingBar] 2 ;
• c) minimizing Cn by selecting at least one dependent sample;
• d) spectrally shaping, using said transmitter, said transmitted samples in accordance with said at least one dependent sample.

In a transmitter for data communications with a limited number of signal points, a method of arbitrary spectral-shaping of transmitted samples according to a predetermined filter characteristics G(z), wherein the transmitted sample is either of an unmodified source sample or a dependent sample, comprising the steps of:

• a) computing a plurality of filter coefficients {ƒm} of the inverse filter of G(z);
• b) for each transmitted sample xn, calculating unwanted signal component measure cn based on c n = ∑ m = 0 n ⁢ x m ⁢ f n - m ;
• c) minimizing cn by selecting at least one dependent sample xn;
• d) spectrally shaping, using said transmitter, said transmitted samples in accordance with said at least one dependent sample xn.