SSB-carrier mismatch detection from speech characteristics: Extension beyond the range of uniqueness

In certain radio-surveillance applications, speech signals with uncertain carrier frequencies may be detected. Beyond other disturbances, carrier mismatches distort the demodulated SSB signals by frequency shifts Δ_f. Recently, a detection and correction of such errors was presented [1], exploiting the harmonic structure of voiced speech with a fundamental (or "pitch") frequency f_p. Noise-robust, modified pitch-detection methods [2, 3] were shown to be applicable, together with an iteratively corrected "coherentsuperposition" algorithm [4, 5]. Thereby, carrier errors are removed reliably [1] though only within an a-priori uniqueness range |Δ_f| <; f_p/2. In the following, the extension beyond this limitation is presented. It emerges from a closer, statistical analysis of the measurement errors: The measurement statistics within this range are interpreted as a conditional probability density function (pdf) p_Δf(x|y) conditioned on the actual pitch frequency, its combination with the (measurable) pitch-frequency pdf P_fp (y) yields the joint pdf P_Δf,_fp(x,y), and its integration gives the marginal pdf P_Δf(x). Its evaluation leads to an even narrower reliability range |Δ_f| <; f_p/23, first. The interpretation of the uniqueness range as one period of an Ip-periodic repetition of the measurement statistics, however, leads to the solution: After the same steps as sketched above, the marginal pdf P_Δf(x) shows a strong peak at the true value Δf without a (theoretical) restriction. The resulting algorithm was successfully tested with simulated and real data.