Studies of bandwidth reduction techniques applicable to amplitude-modulated signals
Gordon B. Lockhart · Spiral (Imperial College London) · 1970
The problem of reducing the bandwidth of envelope detectable signals is studied.Bandwidth reduction systems are classified according to whether effective reduction is achieved in the sense of spectral concentration or strict reduction where bandwidth is halved In comparison with conventional amplitude modulation.A study is made of the structure and generation by combined amplitude/phase modulation of the bandlimited minimum phase signal which is central in the theory of effective bandwidth reduction.An upper bound on the spectrum of this signal is obtained and compared with the corresponding bound for conventional amplitude modulation.An expansion is determined which reveals some important properties of the minimum phase signal in an explicit form.A theory of combined amplitude/phase modulation is presented and applied to the study of a number of commercial "compatible single sideband" systems.It is concluded that, with reservations, these systems can achieve effective bandwidth reduction but not strict reduction.Signals generated by strict bandwidth reduction systems are interpreted as approximations to Logan and Schrooder9 s "Ideal Signal" which possesses no envelope distortion within the bandwidth of the information signal.An alternative to Logan and Schroeder 9 s scheme for synthesising this signal which enables standard S.S.B. technology to be employed is proposed and termed "Direct S.S.B. Recursion".Theoretical analyses follow Sandberg 9 s formulation in application of the Fixed Point Contraction Mapping Theorem.Computer-generated examples areemployed to demonstrate that Direct S.S.B. recursion can operate satisfactorily at realistically high depths of modulation.It is shown that for the important practical case of a single iteration all second order distortion is eliminated from the envelope of the transmitted signal.A general definition of signal efficiency is introduced and applied.Apparatus is described with which it was possible to verify that the performance of a Direct S.S.B. Recursion scheme for a singletone input was obtainable in practice.