🚀 go-pugleaf

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