Type of Sampling in Communication Systems

Type of Sampling in Communication Systems are classified as follows

  • Ideal
  • Natural
  • Practical
  • Flat-top(Sample and Hold)

Ideal Sampling ( or Impulse Sampling)
It is accomplished by the multiplication of the signal x(t) by the uniform train of impulses.
Consider the instantaneous sampling of the analog signal x(t)
ideal_pulse
Train of impulse functions select sample values at regular intervals.
See the figure below for ideal sampling
ideal_sampling

Practical Sampling
In practice we cannot perform ideal sampling.
It is not practically possible to create a train of impulses.
Thus a non-ideal approach to sampling must be used.
We can approximate a train of impulses using a train of very thin rectangular pulses as shown below:
practical_sampling

Natural Sampling
If we multiply x(t) by a train of rectangular pulses xp(t), we obtain a gated waveform that approximates the ideal sampled waveform, known as natural sampling or gating.
natural_sampling
From the above graph the sampled signal xs(t) and its Fourier transform Xs(f) are given as:
xstxsf
Each pulse in xp(t) has width Ts and amplitude 1/Ts.
The top of each pulse follows the variation of the signal being sampled.
Xs(f) is the replication of X(f) periodically every fs Hz.
Xs(f) is weighted by Cn Fourier Series Coeffiecient.
The problem with a natural sampled waveform is that the tops of the sample pulses are not flat.
It is not compatible with a digital system since the amplitude of each sample has infinite number of possible values. This problem will be avoided by using the following sampling technique(Flat-Top Sampling).

Flat-Top Sampling
Flat top sampling is used to alleviate the problem occurred in the above natural sampling; here, the pulse is held to a constant height for the whole sample period. This technique is used to realize Sample-and-Hold (S/H) operation.
In S/H, input signal is continuously sampled and then the value is held for as long as it takes to for the A/D to acquire its value.
flatop
The following figures show flat-Top Sampling in time domain and frequency domain.
td
fd

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