Re: Differences between laplace transform, z transform and fourier transform
- From: "Me" <invalid@xxxxxxxxxxxxxxx>
- Date: Thu, 16 Jul 2009 14:36:12 +0100
Sorry, I was misled by your original reply. Thinking further on the
matter, there is no sin(x)/x anomaly, because what I proposed is
just a scaling of the amplitude by a factor of T (or 1/T depending which
way you look at it), but with no change of shape.
I was /am positing a reperesentation of scaled Unit Impulses.
The issue of integration is not relevant.
Even if sin(x)/x were involved, then in the linear systems which we
discuss, it does not matter what the ordre of analysis is, whether
the sin(x)/x is considered at the beginning or at the end.
In my approach, it is considered at the end because it is not introduced
at the start. Sure, we start off with a sampling pulse of the form
U(nT) - U((n+1)T) in which sin(x)/x might be relevant, but by the
simple conversion to T.d(t) it is definitely not relevant.
NO. If youuse the representation that I suggest you do NOT have
to consider the distortion because it ain't there.
"John Monro" <johnmonro@xxxxxxxxxxxxxxx> wrote in message
news:4a5edbea$0$4046$afc38c87@xxxxxxxxxxxxxxxxxxxxxxx
There would be a disagreement if there were only two choices:
1. Represent the signal as a series of pulses of duration T sec.
2. Represent the signal as a series of infinite-amplitude, zero-width
pulses.
In fact there is a third choice. It seems I failed to make it clear that I
think it is useful to represent the sampled signal as a series of pulses
of finite ampilitude and non-zero duration. The values of the amplitude
and duration are not defined (and don't need to be defined). Only the
integral over a very short period of time is defined. (I claim no
originality for this thought :=).
Regarding the sin(x)/x distortion, simple reconstruction by holding each
sample for one full sample-period does indeed give the same sin(x)/x
distortion as the scheme you are siggesting, but the distortion occurs at
the last step in the reproduction process and we don't have to worry about
distortion before then.
If we use the representation you suggest, we either have to agree to
ignore the distortion that is (conceptually) introduced right at the
sampling stage, or we include the distortion, which messes up the
representation. Neither seems very satisfactory to me.
Regards,
John
.
- Follow-Ups:
- References:
- Differences between laplace transform, z transform and fourier transform
- From: somanath17
- Re: Differences between laplace transform, z transform and fourier transform
- From: Tim Wescott
- Re: Differences between laplace transform, z transform and fourier transform
- From: Me
- Re: Differences between laplace transform, z transform and fourier transform
- From: John Monro
- Re: Differences between laplace transform, z transform and fourier transform
- From: Me
- Re: Differences between laplace transform, z transform and fourier transform
- From: John Monro
- Differences between laplace transform, z transform and fourier transform
- Prev by Date: Re: AM demodulation-envelope detection method
- Next by Date: Re: AM demodulation-envelope detection method
- Previous by thread: Re: Differences between laplace transform, z transform and fourier transform
- Next by thread: Re: Differences between laplace transform, z transform and fourier transform
- Index(es):
Relevant Pages
|
