Bandwidth compression of speech by analytic-signal rooting
- 1 March 1967
- journal article
- Published by Institute of Electrical and Electronics Engineers (IEEE) in Proceedings of the IEEE
- Vol. 55 (3) , 396-401
- https://doi.org/10.1109/PROC.1967.5497
Abstract
If s(t) is a real, band-limited signal, the corresponding analytic signal is defined as s(t)+js^(t), where s^(t) is the Hilbert transform of s(t). For signals whose spectral width is due primarily to large-index frequency modulation, the "square-rooted" signal, defined as s½(t) = Re [s(t) + js^(t)]½, has approximately only half the bandwidth of s(t). A case of practical interest of a signal having approximately this property is a speech signal filtered to remove all but one formant. In such a case, a close replica of the original signal can be recovered by squaring the analytic signal corresponding to a band-limited version s~½(t) of s½(t): s(t) ≈ Re [s~½(t) + js~½(t)]2. Application of these two processes to the transmission of speech signals over channels of reduced bandwidth is described. Results of computer simulation for a 2-to-1 bandwidth compression are encouraging and suggest that even higher compression factors, using higher roots of the analytic signal, may be feasible.Keywords
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