Natural Sampling
Natural Sampling –
It was convenient, for the purpose of introducing some basic ideas, to begin our discussion of time multiplexing by assuming instantaneous commutation and decommutation.
Such instantaneous sampling, however, is hardly feasible.
Even if it were possible to construct switches which could operate in an arbitrarily short time, we would be disinclined to use them.
The reason is that instantaneous samples at the transmitting end of the channel have infinitesimal energy, and when transmitted through a bandlimited channel give rise to signals having a peak value which is infinitesimally small.
We recall that in Fig. I1 = m1 (0) dr.
Such infinitesimal signals will inevitably be lost in background noise.
A much more reasonable manner of sampling, referred to as natural sampling, is shown in Fig.
Here the sampling waveform S(t) consists of a train of pulses having duration τ and separated by the sampling time Ts.
The baseband signal is m(t), and the sampled signal S(t)m(t) is shown in Fig. .
Observe that the sampled signal consists of a sequence of pulses of varying amplitude whose tops are not flat but follow the waveform of the signal m(t).
With natural sampling, as with instantaneous sampling, a signal sampled at
the Nyquist rate may be reconstructed exactly by passing the samples through an ideal low-pass filter with cutoff at
the frequency f where is the highest-frequency spectral component of the signal.
To prove this, we note that the sampling waveform S(t) shown in Fig. is given by A = 1 and T0 = Ts
S(t) = τ / Ts + 2τ / Ts ( C1 cos 2π t/Ts + C2 cos 2 × 2πt/Ts + ……). ….(1)
with the constant Cn given by
Cn = sin ( nπτ/Ts) / nπτ/Ts. ……(2)
This sampling waveform differs from the sampling waveform of Eq. for instantaneous sampling only in that dt is replaced by τ and by the fact that the amplitudes of the various harmonics are not the same.
The sampled baseband signal S(t)m(t) is, for Ts- 1/2Fm
S(t)m(t) = τ / Ts m(t) + 2τ / Ts [m(t)C1 cos 2π(2fm)t + m(t)C2 cos 2π(4fm)t+. …. ] …(3)
Therefore, as in instantaneous sampling, a low-pass filter with cutoff at fm will deliver an output signal s0(t) given by
s0(t) = τ / Ts m(t) ….(4)
which is the same as is given by the first term of Eq. except with dt replaced by τ.
With samples of finite duration, it is not possible to completely eliminate the crosstalk generated in a channel, sharply bandlimited to a bandwidth fc .
If N signals are to be multiplexed, then the maximum sample duration is τ = Ts/N.
It is advantageous, for the purpose of increasing the level of the output signal, to make τ as large as possible.
For, as is seen in Eq. , s0(t) increases with τ.
However, to help suppress crosstalk, it is ordinarily required that the samples be limited to a dura tion much less than Ts/N.
The result is a large guard time between the end of one sample and the beginning of the next.
Multiplying of two 8 bit number–
Addressing modes of 8085 microprocessor
Hi there! I realize this is somewhat off-topic but I
had to ask. Does building a well-established website like yours take a lot of work?
I am completely new to running a blog but I do write in my journal every day.
I’d like to start a blog so I will be able to share my personal
experience and views online. Please let me know if you have any recommendations or
tips for new aspiring blog owners. Appreciate it!
My partner and I absolutely love your blog and find a lot of your post’s to be
exactly what I’m looking for. can you offer guest writers to write content for yourself?
I wouldn’t mind composing a post or elaborating on many of the subjects you write in relation to here.
Again, awesome web site!
Nice post. I learn something totally new and challenging on blogs I stumbleupon every day. It’s always useful to read through content from other writers and practice a little something from other sites.
Dear educationallof.com administrator, You always provide great examples and case studies.
Dear educationallof.com administrator, Your posts are always well researched and well written.
Hello educationallof.com webmaster, Your posts are always well-balanced and objective.
Dear educationallof.com owner, You always provide useful information.
Hi educationallof.com owner, Thanks for the well-organized and comprehensive post!
Dear educationallof.com owner, You always provide clear explanations and step-by-step instructions.
Hello educationallof.com owner, Your posts are always well received by the community.
Dear educationallof.com administrator, Your posts are always insightful and valuable.
Hi educationallof.com administrator, Your posts are always well presented.
Hello educationallof.com webmaster, Your posts are always on topic and relevant.
To the educationallof.com owner, Your posts are always a great read.
Dear educationallof.com owner, Your posts are always well-written and easy to understand.
Dear educationallof.com admin, You always provide useful links and resources.
Dear educationallof.com administrator, Your posts are always well-supported by research and data.
Dear educationallof.com administrator, Thanks for the well-presented post!
Dear educationallof.com owner, Great post!
Hi educationallof.com admin, Excellent work!
Hello educationallof.com webmaster, Thanks for the great post!
Very good article post.Much thanks again. Will read on…
Hello educationallof.com administrator, Good to see your posts!
Hello educationallof.com admin, Thanks for the great post!