Thread View: comp.dsp
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Started by MICHAEL ALEXANDER MCKAY
Sat, 09 Jan 1993 20:36
Imaginary signals
Author: MICHAEL ALEXANDER MCKAY
Date: Sat, 09 Jan 1993 20:36
Date: Sat, 09 Jan 1993 20:36
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Is there a time-domain filter which, given a real signal as input, will output the corresponding imaginary signal? I've tried to make a filter with unity gain and pi/2 phase shift for all frequencies, but with no luck.
Re: Imaginary signals
Author: Armein Langi
Date: Sat, 09 Jan 1993 21:27
Date: Sat, 09 Jan 1993 21:27
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In article 726611777@axe.acadiau.ca, 880840m@axe.acadiau.ca (MICHAEL ALEXANDER MCKAY) writes: > >Is there a time-domain filter which, given a real signal as input, will >output the corresponding imaginary signal? >I've tried to make a filter with unity gain and pi/2 phase shift for >all frequencies, but with no luck. > > I don't really understand what you mean by 'the corresponding imaginary signal'. What I know is that the imaginary part of a signal in defined only on a complex signal space. And, in this case, the imaginary part of a real signal is 0. Thus, the filter is simply a system that produces 0 (am I wrong ?). -Armein
Re: Imaginary signals
Author: Izumi Ohzawa
Date: Sun, 10 Jan 1993 02:21
Date: Sun, 10 Jan 1993 02:21
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In article <C0LvMG.4B4@ccu.umanitoba.ca> langi@ee.umanitoba.ca writes: >In article 726611777@axe.acadiau.ca, 880840m@axe.acadiau.ca (MICHAEL ALEXANDER MCKAY) writes: >> >>Is there a time-domain filter which, given a real signal as input, will >>output the corresponding imaginary signal? >>I've tried to make a filter with unity gain and pi/2 phase shift for >>all frequencies, but with no luck. > >I don't really understand what you mean by 'the corresponding imaginary signal'. Perhaps, he meant "quadrature signal" ? -- Izumi Ohzawa [ $BBg_78^=;(B ] USMail: University of California, 360 Minor Hall, Berkeley, CA 94720 Telephone: (510) 642-6440 Fax: (510) 642-3323 Internet: izumi@pinoko.berkeley.edu (NeXTmail OK)
Re: Imaginary signals
Author: Tim Wilson
Date: Sun, 10 Jan 1993 17:44
Date: Sun, 10 Jan 1993 17:44
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880840m@axe.acadiau.ca (MICHAEL ALEXANDER MCKAY) writes: Is there a time-domain filter which, given a real signal as input, will output the corresponding imaginary signal? I've tried to make a filter with unity gain and pi/2 phase shift for all frequencies, but with no luck. See Oppenheim and Shafer, _Digital Signal Processing_ (1st edition), Section 7.4: "Hilbert Transform Relations for Complex Sequences." In particular, see Section 7.4.1, "Design of Hiblert Transformers." I quote: "...the ideal Hibert transformer or 90-degree phase shifter takes its place alongside the ideal lowpass filter and ideal bandlimited differentiator as valuable theoretical concepts which correspond to noncausal systems and for which the system function exists only in a restricted sense." In the same section, O&S discuss finite-duration approximations of the ideal Hilbert transformer using frequency-sampling, windowing, and equiripple approximations. Finally, they reference B. Gold, A. V. Oppenheim, and C. M. Rader, "Theory and Implementation of the Discrete Hibert Transform," _Proc. Symp. Computer Processing in Communications_, Vol. 19, Polytechnic Press, 1970, New York for a recursive implementation of a 90-degree phase-splitting system. Good luck. -- Tim Wilson Internet: tim@ear-ache.mit.edu UUCP: mit-eddie!mit-athena!tim
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