Reply by Sebastian Doht●January 23, 20092009-01-23
Chris Bore schrieb:
> This relates to an earlier post - "filter of amplitude versus filter
> of (I,Q)?".
>
> I would like to learn what is the effect in the frequency domain of
> taking the square root of a quantity on the time domain. Also, of
> taking the square (actually magnitude of a complex number) in the time
> domain?
>
> I think I know the second - the magnitude is number*complex_conjugate
> which is autocorrelation of the frequency spectrum - but I dont know
> the first.
>
> Thanks,
>
> Chris
> ==================
> Chris Bore
> BORES Signal processing
> www.bores.com
> chris@bores.com
Hello,
your right on the part with the multiplication. This is basically a
convolution of the signal in the frequency domain with itself. When
using sinoids this has the same effect like a mixer which doubles the
carrier frequency.
However taking the square root is something much more complicated, since
the considered signal neither represents a linear time invariant nor a
linear frequency invariant system and therefore I am afraid there does
not exist a closed form solution for the Fourier Transform. So you have
to do try it numerically or use a linearization operation (taylor
series) for the specific signal.
Greetz,
Sebastian Doht
Reply by Jerry Avins●January 23, 20092009-01-23
Chris Bore wrote:
> This relates to an earlier post - "filter of amplitude versus filter
> of (I,Q)?".
>
> I would like to learn what is the effect in the frequency domain of
> taking the square root of a quantity on the time domain. Also, of
> taking the square (actually magnitude of a complex number) in the time
> domain?
>
> I think I know the second - the magnitude is number*complex_conjugate
> which is autocorrelation of the frequency spectrum - but I dont know
> the first.
I don't have my notes from '55 and I won't do it over, but I can quote a
result that might be relevant.
If you remove one sideband from an ordinary double-sideband signal
(leaving the other sideband and the carrier intact) the demodulated
result will be increasingly distorted as the modulation percentage
increases. One way to achieve low-distortion is increasing the carrier
amplitude ("exalted carrier operation") to reduce the modulation
percentage. A more interesting way is using a square-law detector,
effectively squaring the signal.
To a first order of approximation, removing one of the sidebands
effectively creates the square root of the modulation. (That's not to
imply that using the square root of the modulation will eliminate a
sideband! :-) )
Jerry
--
Engineering is the art of making what you want from things you can get.
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Reply by Chris Bore●January 23, 20092009-01-23
This relates to an earlier post - "filter of amplitude versus filter
of (I,Q)?".
I would like to learn what is the effect in the frequency domain of
taking the square root of a quantity on the time domain. Also, of
taking the square (actually magnitude of a complex number) in the time
domain?
I think I know the second - the magnitude is number*complex_conjugate
which is autocorrelation of the frequency spectrum - but I dont know
the first.
Thanks,
Chris
==================
Chris Bore
BORES Signal processing
www.bores.com
chris@bores.com