Bandwidth compression of speech by analytic-signal rooting

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 s ½ (t) = Re...

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Bibliographic Details
Published in:Proceedings of the IEEE 1967-01, Vol.55 (3), p.396-401
Main Authors: Schroeder, M.R., Flanagan, J.L., Lundry, E.A.
Format: Article
Language:English
Subjects:
Bandwidth
Computer simulation
Frequency conversion
Frequency modulation
Signal analysis
Signal processing
Speech analysis
Speech processing
Telephony
Vocoders
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Summary: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 s ½ (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 s ½ (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.
ISSN:0018-9219
1558-2256
DOI:10.1109/PROC.1967.5497