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Article #1378

Question about Frequency Inversion via Sampling

#1378
From: Dr. Destruction
Date: Sat, 15 Dec 1990 16:52
47 lines
3107 bytes
I am working on a project which requires (among other things) the inversion
of frequencies in a baseband of approximately 1.6kHz. Normally, I am aware,
the easiest method of performing this would be to modulate the baseband
signal (surpressed carrier of course) up to 1.6kHz and then sharply filter
it at 1.6kHz, the result being the inverted spectrum from 0 to 1.6kHz.

Currently, though, I am scrubbing the modulation and performing the
inversion by sampling the baseband signal at 1.6kHz using natural sampling
(ie: gating) with a gate width of approximately 10% of the period (at
1.6kHz). After this is done, the original baseband signal in inverted,
scaled to account for the spectral energy loss due to sampling, and added to
the sampled waveform. The result of this is as follows: the sampled signal
is the typical spectral replication of the baseband (assume it to be
bandlimited at 1.6k) at intervals of 1.6k, scaled by a rather wide sinc
function (due to the convolution with the pulse train -> natural sampling).
The baseband signal, however, is still present. So, in order to achieve the
inversion, the remaining baseband signal is subtracted from the sampled
signal, leaving only spectral replications at 1.6k and higher, which, after
filtering, leaves the inversion and nothing else (theoretically that is :-)

Ok, now: the problem is that it is *very* difficult to attenuate the inverted
baseband signal to *precisely* the correct amplitude to cancel the residual
baseband remaining in the sampled waveform. Failure to subtract the baseband
signal (or subtracting too much for that matter) will of course leave traces
of the baseband signal in the spectrum, which is highly undesirable for me.
My question is that it seems that the result of what I am doing could be
achieved as follows:

	1) Gate (sample) the signal at 90% of the period

	2) Invert it

	3) Filter sharply at 1.6k

This seems to be (thinking in the time-domain here) accomplishing the same
thing as the 10% sampling and subtraction of the baseband. The plus is that
I wouldn't need to subtract anything now! Do you agree with this?? I figured
before I went and tried it I'd get a 2nd (or Nth) opinion. What problems can
you see with this that I am not taking into account? Is there any reason a
system such as this would be difficult to physically realize?

Any feedback (no pun) will be appreciated!

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Frederick True        	true@elbereth.rutgers.edu	ftrue@attmail.att.com
	
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From: true@elbereth.rutgers.edu (Dr. Destruction)
Newsgroups: comp.dsp
Subject: Question about Frequency Inversion via Sampling
Keywords: frequency inversion
Message-ID: <Dec.15.11.52.08.1990.12495@elbereth.rutgers.edu>
Date: 15 Dec 90 16:52:10 GMT
Reply-To: true@elbereth.rutgers.edu (Dr. Destruction)
Lines: 47