Generalized linear prediction based on analytic signals

The conventional theory of linear prediction (LP) is renewed and extended to form a more flexible algorithm called generalized linear prediction (GLP). There are three new levels of generalization available. On the first level (I) the predictor FIR is replaced with a generalized FIR constructed out of allpass sections having complex coefficients. On the second level (II) the allpass filters have distributed coefficients, i.e., they are unequal, and on the third and the most general level (III) the filter sections may have different characteristics. The theory of GLP is presented and the algorithm is tested with speech signals. The results show that GLP works as desired: nonuniform frequency resolution can be achieved and the resolution is controlled by the choice of the allpass parameters. On level I, the angle of the pole-zero-pair of the allpass sections defines the highest resolution area while the radius of the pole controls the degree of the resolution improvement. The GLP prediction error decreases rapidly with the order of the predictor. Its normalized RMS value falls off exponentially and its spectral flatness improves efficiently. On the average the results are clearly better than those of conventional LP. Levels II and III are only briefly discussed