Digital Signal Processing (DSP)

What is Digital Signal Processing?

Digital signal processing is the area of electronics which is on the rise for the past few years because of the inclusion and application of VLSI (very large scale integration) systems in DSP. It deals with the methods to extract information through various techniques from digital or analog signals through digital processors/hardware. Prior to getting the insight of Digital Signal Processing we need to have some fundamental ideas about function, signals, types of signals etc.

What are we going to learn in this Digital Signal Processing Tutorial:-

Ø Functions

Ø Signals

Ø Classification of Signals

Ø Analog and Digital Signal

Ø Need of Digital Signal Processing

Functions

To start with the learning of digital signal processing we first need to know about the concept of functions and signals. Functions are, in a clear mathematical way, dependent variable of one or more independent variable but the should be one to one or many to one correspondence between the independent and the dependent variable as shown in the picture below. There cannot be one to many correspondence, if there is then it should not be regarded as a Function.

Fig. 1: Diagram of a Function

Some mathematical functions are,

F(x) = x²+ 3x;

F(x) = x+5;

Signals

Signal is a function that carries some information with it which may or may not be potentially useful. For example, the waving of green or red flag by the station manager is a signal to the train driver about the clearance of the railway line. The indication of temperature of body by a thermometer is also a signal. The more mathematical example will be the alternation voltages delivered to our houses,

V= Asin(2?ft + Ø) or Asin(?t + Ø)

where f is the frequency(in sec^-1) , omega is the angular frequency(in rad/sec) and Ø is the phase of the signal. Now we will be having a brief idea about the classification of signals.

Classification of Signals

On the basis of number of independent variables and that of sources.

· Multi-channel: If the signal is generated from more than one source or sensor then it is known as Multi-channel signal. For example, the ground acceleration due to an earthquake consists of Primary waves and secondary waves propagate within the body of rocks. Primary waves are longitudinal and Secondary waves are transversal. The third wave is an elastic wave which is called surface wave as it travels near to the surface of earth. If I₁, I₂, I₃ represents the three waves then the earthquake signal can be represented as,

Digital Signal Processing

· Multi-dimensional: If the signal generated is the function of more than one independent variablethen the signal is called multi-dimensional signal. For example, the contrast of the television screen can be understood as a multi-dimensional signal as it is dependent on the relative position(x & y co-ordinates) and also on time.

On the basis of characteristics independent variable and the values they assume.

· Continuous Time: These type of signals are defined for every value of independent variable and also they take on values for every point in the continuous interval (a, b). For example,

y (x)= Sin(x) , for all -? < x < ?

· Discrete Time: These signals are only defined at certain specific values of the independent variable. These intervals need not to be eqi-distant from each other and also the value of the signal is not zero but undefined between these intervals. One should not assume the values of the dependent variable as zero between the intervals. For example,

Digital Signal Processing

On the basis of characteristics of the dependent variable and the values they assume.

· Continuous valued: If the Dependent variable of the signal assumes or takes all the possible values on an finite or an infinite set of values then the signal is said to be continuous valued signal. For example, the function y(x) = Sin(x) is a continuous valued signal as it takes all the values between the interval [-1, 1].

· Discrete-valued: If the signal takes some specific or certain values in a finite or infinite set of values then then signal is said to be discrete valued signal. For example, the greatest integer function,

y (x)= [x] ,

This signal takes only specific integral values whatever may be the input.

Analog Signal and Digital Signal

Analog Signal and Digital Signal

What is an analog Signal? The answer is the analog signal in a very lucid manner can be said to be consist of Continuous-time and Discrete-time signal. The general misconception about the analog signal is that it is only continuous signal and if the independent variable is discretized it is not an analog signal but this is not correct. This arise the question about the criterion for a signal to be a digital signal. The Digital Signal is a discrete-time signal having a set of discrete values of the dependent variable. That is if the o/p or the values attained by the dependent variable of the discrete-time signal is also discretized then the signal obtained is a digital signal. This discretization is done through Sampling or A/D conversion of the signal which is going to be discussed in the later chapters of this tutorial on Digital Signal Processing.

Fig. 2: Image showing classification of signals

Need of Digital Signal Processing

First of all we need to know what is processing then we can move to the need and advantages of DSP. Processing is an activity done to obtain a desirable form of signal either for transmission or after receiving. There are many advantages of digital signal processing which overshadows that of analog signal processing. The advantages of Digital Signal Processing are –

· Digital programming systems allow flexibility in re-configuring the DSP operations by just changing the program. We don’t need to change the whole hardware as in the case of Analog Signal Processing (ASP).

· Accuracy of processors of digital systems is very good unlike the heavy tolerances of Analog systems digital systems have minimal tolerance values.

· The storage of digital signals can be done in a very efficient way in the magnetic tapes and hard-disks without any loss of deformation of the signal over a considerable period of time.

· Also sometimes DSP is proved to be cheaper than ASP.

There are some disadvantages also in Digital signal processing being that the speed of A/D convertors are fixed sometimes there is a limitation on the speed of the processing. The digital signal processors for the large bandwidth of analog signals are beyond the state of art of digital hardware.

In the upcoming tutorial we are going to learn more about discrete time signals, some basic discrete-time signals, sampling process and sampling theorem.