September 2022 - ece4uplp

Introduction:-

Communications refer to sending, receiving and processing of information by electrical means, that is it means exchanging information between transmitter and receiver.

In early 1840’s the type of communication used was Wire telegraphy later on the forms are as telephony, Radio communication (possible with the invention of triode tube, Satellite communications and fibre optics(with the invention of transistors and IC’s and semi-conductor devices), that means communications become more advanced with increasing emphasis on computer and other data communications.

A modern communication system is concerned with

before transmission:-

sorting:- sorting for the right message.
Processing:- processing is to make that message more suitable for transmission.
storing:- storing that message before transmission.

then the actual transmission of that message takes place (processing and filtering noise)

at the receiver:-

decoding:-decoding the original message.
storage:-storing a copy of that message.
interpretation:-and analyzing for the correctness of that message.

the different forms of modern communication systems includes Mobile communications,Computer communications, Radio telemetry etc.

to become familiar with communication systems one needs to know about amplifiers and oscillators that means fundamentals of electronic circuits must be known, with these concepts as a background the every day communication concepts like noise, modulation and information theory as well as various types of systems may be studied.

The most general form of Communication system ( one or two blocks may differ) is shown in the figure basic terminology used in Communication systems is message signal /information/data,channel,noise,modulation, encoding and decoding. Communication system is meant for communicating messages between Transmitter and Receiver (or) source & destination.

source:-

source or information source is the primary block in communication system which generates original message / actual message.

i.e, selecting one message (actual message) from a group of messages itself is called as sorting data (or) information. Source generates message which may be in any form like words, code , symbols, sound signal, images, videos etc.among these the desired message has been selected and conveyed.

A transducer is one which converts one form of energy into electrical energy because the message from information source may not be always in electrical form, a transducer is used in between source and transmitter as a separate block sometimes (or) may be a part of Tx ^r.

Transmitter:-

Tx^r is meant for the following tasks

restriction of range of audio frequencies (i.e, limiting the bandwidth of the message signal).
Amplification.
Modulation.

In general modulation is said to be the main function of the transmitter.

Channel:-

The medium that exists between transmitter and receiver is called as channel. The function of channel is to provide connection between transmitter and receiver, two types of channels are there wired/point to point and wireless/broadcasting channels.

Point to point channels are generally wired channels(i.e, a physical medium exists) like Microwave links, optical fibre links etc.

Microwave links:- these links are used in telephone transmission.In these type of links guided EM waves are used to transmit from Tx^r to Rx^r.

optical fibre links:- used in low-loss high speed data transmission and uses optical fibers as the medium .

Broadcast channels:- the medium or channel is wireless here, in broadcasting a single transmitter can send information to many receivers simultaneously, satellite broadcasting system is one such system.

during the process of transmission and reception, the signal gets distorted due to noise in the channel, noise may interfere with the signal at any point but noise in the channel has greatest effect on the signal.

Receiver:-

The main function of the receiver is to reproduce the message signal in electrical form from the distorted received signal. This reproduction process is called demodulation (or) detection , in general this demodulation may be assumed as the reverse process of modulation carried out in transmission.

there are a great variety of receivers in communication systems, the type of receiver chosen depends on type of modulation, operating frequency ,its range and type of destination required. Most common receiver is superheterodyne receiver .

so many types of receivers are available from a very simple crystal receiver with headphones to radar receiver etc.

Destination:- It is the final stage of any communication system. it would be a loud speaker / a display device/simply a load etc depending up on the requirement of the system.

Reconstruction filter(Low Pass Filter)

Reconstruction filter (Low Pass Filter) Procedure to reconstruct actual signal from sampled signal:-

Low Pass Filter is used to recover original signal from it’s samples. This is also known as interpolation filter.

An LPF is that type of filter which passes only low frequencies up to cut-off frequency and rejects all other frequencies above cut-off frequency.

For an ideal LPF, there is a sharp change in the response at cut-off frequency as shown in the figure.

i.e, Amplitude response becomes suddenly zero at cut-off frequency which is not possible practically that means an ideal LPF is not physically realizable.

i.e, in place of an ideal LPF a practical filter is used.

In case of a practical filter, the amplitude response decreases slowly to zero (this is one of the reason why we choose $f_{s}>2f_{m}$ )

This means that there exists a transition band in case of practical Low Pass Filter in the reconstruction of original signal from its samples.

Signal Reconstruction (Interpolation function):-

The process of reconstructing a Continuous Time signal x(t) from it’s samples is known as interpolation.

Interpolation gives either approximate (or) exact reconstruction (or) recovery of CT signal.

One of the simplest interpolation procedures is known as zero-order hold.

Another procedure is linear interpolation. In linear interpolation the adjacent samples (or) sample points are connected by straight lines.

We may also use higher order interpolation formula for reconstructing the CT signal from its sample values.

If we use the above process (Higher order interpolation) the sample points are connected by higher order polynomials (or) other mathematical functions.

For a Band limited signal, if the sampling instants are sufficiently large then the signal may be reconstructed exactly by using a LPF.

In this case an exact interpolation can be carried out between sample points.

Mathematical analysis:-

A Band limited signal x(t) can be reconstructed completely from its samples, which has higher frequency component f_m Hz.

If we pass the sampled signal through a LPF having cut-off frequency of f_m Hz.

From sampling theorem

$g(t) = x(t).\delta _{T_{s}}(t)$ .

$g(t)=\frac{1}{T_{s}}\left \{ 1+2\cos \omega _{s}t+2\cos 2\omega _{s}t+2\cos 3\omega _{s}t+..... \right \}$ .

g(t) has a multiplication factor $\frac{1}{T_{s}}$ . To reconstruct x(t) (or) X(f) , the sampled signal must be passed through an ideal LPF of Band Width of $f_{m}$ Hz and gain $T_{s}$ .

$\left | H(\omega ) \right |=T_{s} \ for \ -\omega _{m}\leq \omega \leq \omega _{m}$ .

$h(t) = \frac{1}{2\pi } \int_{-\omega _{m}}^{\omega _{m}}T_{s}e^{j\omega t}\ d\omega$ .

$h(t) = 2f_{m}T_{s} \ sinc(2\pi f_{m}t)$ .

If sampling is done at Nyquist rate , then Nyquist interval is $T_{s} = \frac{1}{2f_{m}}$ .

therefore $h(t) = \ sinc(2\pi f_{m}t)$ .

h(t) = 0. at all Nyquist instants $t= \pm \frac{n}{2f_{m}}$ , when g(t) is applied at the input to this filter the output will be x(t) .

Each sample in g(t) results a sinc pulse having amplitude equal to the strength of sample. If we add all these sinc pulses that gives the original signal x(t) .

$g(t) = x(kT_{s})\delta (t-kT_{s})$ .

$x(t) =\sum_{k} x(kT_{s})\ h (t-kT_{s})$ .

$x(t) =\sum_{k} x(kT_{s})\ sinc(2\pi f_{m} (t-kT_{s}))$ .

$x(t) =\sum_{k} x(kT_{s})\ sinc(2\pi f_{m}t-k\pi )$ .

This is known as interpolation formula

It is assumed that the signal x(t) is strictly band limited but in general an information signal may contain a wide range of frequencies and can not be strictly band limited this means that the maximum frequency in the signal can not be predictable.

then it is not possible to select suitable sampling frequency f_s .

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Month: September 2022

Relation between Laplace and Fourier transform

Basic block diagram of analog communication system

Introduction:-

Reconstruction filter(Low Pass Filter)