Instantaneous Compandors

Mallinckrodt, C. O.

doi:10.1002/j.1538-7305.1951.tb03676.x

Cited by 10 publications

References 7 publications

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On the Recovery of a Band-Limited Signal, After Instantaneous Companding and Subsequent Band Limiting

Landau¹

1960

Bell System Technical Journal

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If f(t) is a band-limited function, with band limit -fl to fl, the result of instantaneously companding f(t) is in general no longer band-limited. Nevertheless, it has been proved that knowledge of merely those frequencies of the compandor output which lie in the band from -fl to (1 is sufficient to recover the original 81,'gnal f( t). A n iteration formula has been proposed that, in theory, performs the desired recovery. In this paper we study in detail some of the practical questions raised by that formula. TVe show that the successive approximations converge to the solution f( t) at a geometric rate, uniformly for all t, and that the iteration procedure is stable. TVe then describe a method of performing the recovery in real time and a successful simulation of it on a general-purpose analog computer. The circuit used in the simulation serves as a first approximation to a practical realization of the recovery scheme. I. INTRODUCTIONWhen a signal, J(t), is transmitted over a channel there is a tendency for the low-amplitude part of J(t) to become masked by the presence of channel noise and for the high-amplitude part of f(t) to become distorted by the nonlinearity of components in those ranges. It would be valuable, therefore, to find a way of assigning to f(t) another signal from which J(t) could be recovered, but which would have the property that its amplitude lay more nearly in the middle ranges than did that of f(t). This second signal is then transmitted, instead of the original jet). One relatively simple way of obtaining such a signal is by instantaneous companding: The signal sent is 1Pl((t)], where lP(x) is a monotonic function (to allow recovery of f(t) from 1Pl(t)]) , which has a large slope around x = 0 so as to magnify signals of low amplitude, and which approaches a constant value for large x so as to cut down on signals of high amplitude. 351

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