# Sampling theorem lab experiment

### INTRODUCTION

There is a need to interconnect telephone exchanges and switching centers as economically as possible in all telecommunications networks. Usually the volume of traffic over these routes makes attractive to transmit as much information as possible over each cable. Thus the idea of multiplexing arises.

This idea, basically implemented, converts signals into a number of samples which contain enough information to recreate the original signal. Thus more than one signal can be transmitted on a single cable. However, the number of signals that can be transmitted over one cable is limited by the need to recreate the original signal.

### THE APPARATUS

The apparatus comprises a sampling source, which may be varied in frequency or sample pulse width, a multiplexer and demultiplexer. The multiplexer accept two input channels, samples each, and interleaves the sample. The signals on one of these channels is a waveform containing first and third harmonics of a 1KHz signal the output from the multiplexer may be observed or may be transmitted into the demultiplexer which separates the two channels, and pass the train of each through a low pass filter to reconstitute the original signals.### THE SAMPLING PROCESS THEORY:

In certain communication processes, such as the pulse code modulation system, it is necessary to sample a waveform at regular intervals in order to communicate discreet information rather than continuous information. The process of sampling is equivalent to multiplexing the waveform to be sampled by a series of regularly spaced delta functions.Such a series of delta pulses is termed the sampling function, which has the interesting property that an infinite series of delta pulses in time domain has a spectrum, which is also an infinite delta series in the frequency domain.

We should work in both the frequency and the time domain, and probably the best known rule to do so is the multiplication of waveform in the time domain transforms into convolution of their amplitude spectra in the frequency domain.

If sampling is the multiplication of the analog waveform by a delta series in the time domain the spectrum of the sampled signal is the convolution of the analog waveform with another delta series, as shown in fig 7.7.

If T is the interval between pulses in the time domain i.e. fig 7.2 then the interval between the frequencies, which contain signal energy, is 1/T.

From the figure, it can be seen that provided 1/T > 2 fm then a complete replica of the spectrum of the sampled signal lies below the frequency 1/2T and the low pass filter will restore the original signal unchanged. But if 1/t < 2 fm then overlap of spectra of the sampled signal will occur resulting in distortion.

An analog signal is sampled with pulses, which have a non-zero width.

### TIME DIVISION MULTIPLEXING

The division multiplexing is the process whereby two or more digital streams are combined to facilitate transmission of data over a common highway. There is two basic forms of multiplexing synchronous digital multiplexing which is used when all the digits are exactly the same digit rate, and asynchronous digital multiplexing, when the numbers of digit streams to be combined have nominally the same clock frequency but differ from one another by a few parts per million.### CONCLUSION

- We observe that the amplitude modulation does not affect the frequency.
- After the modulation and demodulation the amplitude will decrease.

## No comments: