Discrete Communication Systems Group C

Questions: Q. Why is it important to work out signals and systems in discrete variables? Q. How does the periodicity retain its structure at a discrete level? Q. How does communication take place?

Major terms used : Signal: A signal is a function that conveys information about the behavior of some phenomena. Systems: Systems in this context refer to the mathematical representations between the input and the output signals. Discrete Variables: A variable that takes values from a finite or countable set.(i.e having a limited range of values)

Major terms used : Periodicity: We are familiar with periodicity of any signal or function i.e the tendency to recur at intervals. Sampling: Reduction of a continuous signal to a discrete signal. Communication: Purposeful exchange of information.

Relation of these terms: Signals and Systems: The field of Electrical Engineering that studies input and output signals, and the mathematical representations between them.

Relation of these terms: Periodicity at Discrete Level: The periodicity is preserved when we shift from continuous to discrete level.(will be elaborated in the coming slides) Discrete Signals: Discrete signals are defined at discrete values of an independent variable. Discrete signals are represented as sequences of numbers. Communication by Signals: The process through which wireless communication takes place is nothing else but the same conversion of analogue signal into a discrete signal(sampling).

DISCRETE DOMAIN

We take samples at regular intervals. Each sample is created by multiplying a unit impulse by the signal at the instant of each of those equally spaced intervals. x(t)  x[t]

DISCRETE DOMAIN

DISCRETE FOURIER TRANSFORM

IMPORTANCE OF CONVERTING TO DISCRETE DOMAIN

Discrete signals have many attractive features. They can be perceived with great flexibility with a variety of technologies, such as charge transport devices, surface acoustic wave devices, general purpose digital computers or high speed microprocessors. Discrete time systems can be used to simulate analog systems or, more importantly, to realize signal transformations that cannot be implemented with continuous time hardware. Thus, discrete time representations of signals are often desirable when sophisticated and flexible signal processing is required.

Advantages of sampling are that conversion between the time domain and the frequency domain using Fourier analysis is a very powerful technique that allows you to do a lot of different things, such as compression and filtering, without needing advanced electronics. You can also transmit the digital samples from one point to another, using digital electronics, rather than analog electronics.

ADVANTAGES OF DISCRETE SIGNALS

FLEXIBILTY Flexibility of processing given by the fact that the characteristics of discrete systems are determined only by algorithms and numerical parameters, which can both be easily changed. A change, for example, of frequency response can be made by changing constants in the systems memory or even by merely changing the sampling frequency. The discrete-system function is determined by its inner program so that arbitrary changes of behavior and consequently of system characteristics can be achieved by changing the algorithm as, for example, is the case with complicated types of adaptive filtering.

STABILITY OF PROPERTIES IN TIME Stability of properties in time, particularly in the case of discrete signal processing, is also given by the fact that system properties are determined only by programs and parameters saved in memory which cannot spontaneously change. Therefore, when the system is in working condition, its characteristics cannot change without intervention into the system information. There is no ageing or wear, so that any adjustment, tuning and balancing, needed in most analogue systems/ continuous signals is unnecessary; the maintenance is limited to diagnosing the mere functionality, digital processing is therefore perfectly reproducible.

TIME UNLIMITED MEMORY Time unlimited memory of discrete systems provides an easy way of processing very slow signals. This can be seen for instance, in the control of extensive production units where time constants can be from seconds unto weeks, or even in the process of historical, economic or astronomical data sampled over years. And discrete elements are far more reliable for long time periods and are incomparably easier to construct than cumbersome analogue memory elements acting as energy stores (e.g. inductances and capacitances).

COMPATIBILITY WITH INFORMATION Compatibility with information systems enabled by a similar type of data processing and possibility of using compatible data representations are important features used by integrating signal and measurement data processing into automatic control and management systems, such as in automatic production, traffic control, in hospital information systems for intensive care monitoring and computer assisted diagnostics.

POSSIBILITY OF MULTIPLEX OPERATIONS The digital processors (which process discrete signals) with a high computing capacity than necessary for a given signal-processing task can be used in time sharing for more tasks without introducing any interference among individual tasks. (For example, one signal processor can realize the complete filter bank, or even different processing phases such as the filtering of a signal, its frequency analysis and real time classification.)

ROBUSTNESS Robustness is the ability of a computer system to cope with errors during execution. Robustness can also be defined as the ability of an algorithm to continue operating despite abnormalities in input, calculations, etc.

Few other Advantages: Lower complexity More noise immunity Regeneration Storage Capability

How periodicity retain its structure?

In continuous domain, if a signal x(t) is periodic, then there exists a T > 0 such that x(t) = x(t + T) If no T > 0 can be found, then x(t) is non-periodic Period in discrete time of a signal is given by N=2π/Ω Therefore, a discrete-time sinusoid is periodic if its radian frequency Ω is a rational multiple of π.

How does Communication take place ?

After sampling of our voices they are converted into a binary equivalent, this equivalent even though in binary form is a wave for ones and zeros.

This wave is superposed with the frequency band being used for sending data and transmitted by radio transmitter to the nearest hub, which then transfers it to the person you are talking with.

When the person receives this transmission it is decoded inside and again converted back to simple binary wave, which we already know was sampled over a constant rate. Now this binary information is converted into audio at the same rate it was encoded and we receive the exact same voice on the other end[Well almost the same!].

How does communication take place?

Still the mystery remains, can we shoot people over the phone? :-p